Class 12 Physics (Part 1) Chapter 5 Electric Resistance and Ohm’s law

Class 12 Physics (Part 1) Chapter 5 Electric Resistance and Ohm's law

This quiz on Chapter 5: Electric Resistance and Ohm’s Law for ICSE Class 12 Physics is designed to assess students’ understanding of fundamental electrical concepts, including the nature of resistance, the factors affecting it, and the precise application of Ohm’s Law in various contexts. The quiz covers key topics such as resistivity, conductivity, temperature dependence of resistance, series and parallel combinations of resistors, and practical applications like the use of a rheostat and measurement with an ammeter and voltmeter. It aims to reinforce conceptual clarity and problem-solving skills through a variety of question types that test both theoretical knowledge and numerical proficiency. This formative assessment supports learners in building a solid foundation for advanced topics in current electricity and electrical circuits.

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Category: Mobility of Electrons

1. In a semiconductor with electron concentration $n = 10^{16} \, \text{cm}^{-3}$ and mobility $\mu_e = 1000 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1}$, what electric field strength is required to produce a current density of $1.6 \, \text{A/cm}^2$ due to electron flow only?

a) 0.1 V/m

b) 1 V/m

c) 10 V/m

d) 100 V/m

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Category: Relation between drift velocity, current, and resistance.

2. (A) In a conductor of non-uniform cross-section, if the current is kept constant, the drift velocity of electrons is higher where the cross-sectional area is smaller.
(R) The drift velocity $v_d$ is inversely proportional to the cross-sectional area $A$ of the conductor, as given by $v_d = \frac{I}{n e A}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Dynamic Resistance

3. A thermistor has a resistance-temperature relationship given by $R = R_0 e^{B/T}$, where $R_0$ and $B$ are constants. If the temperature changes slightly from $T_1$ to $T_2$, what is the dynamic resistance approximation?

a) $R \frac{B}{T^2}$

b) $-R \frac{B}{T^2}$

c) $R \frac{T^2}{B}$

d) $-R \frac{T^2}{B}$

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Category: Flow of charge (electrons) in a conductor.

4. A copper wire of cross-sectional area $2 \times 10^{-6} \, \text{m}^2$ carries a current of 3.2 A. If the number density of free electrons in copper is $8.5 \times 10^{28} \, \text{m}^{-3}$, what is the drift velocity of the electrons?

a) $0.0588 \, \text{mm/s}$

b) $0.1176 \, \text{mm/s}$

c) $0.2352 \, \text{mm/s}$

d) $0.4704 \, \text{mm/s}$

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Category: Ratio of potential difference to current.

5. (A) The resistance of a conductor remains constant if the temperature is unchanged.
(R) According to Ohm’s law, $R = \frac{V}{I}$ is valid only when the physical conditions like temperature remain unchanged.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Ohm’s Law in Vector Form

6. In an isotropic conductor, the current density $\vec{j}$ is related to the electric field $\vec{E}$ by which of the following equations?

a) $\vec{j} = \rho \vec{E}$

b) $\vec{j} = \frac{1}{\sigma} \vec{E}$

c) $\vec{j} = \sigma \vec{E}$

d) $\vec{j} = \tau \vec{E}$

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Category: V-I graph for metallic conductors.

7. What does a straight-line V-I graph passing through the origin indicate for a metallic conductor?

a) The conductor has variable resistance

b) The conductor obeys Ohm's law with constant resistance

c) The conductor is non-ohmic

d) The conductor shows negative resistance

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Category: Behavior of free electrons in conductors.

8. (A) In the absence of an electric field, free electrons in a conductor move randomly with no net direction.
(R) Random thermal motion of free electrons averages to zero net velocity when no external force is applied.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Electric current, measured as the rate of flow of charge.

9. (A) The current density in a conductor of non-uniform cross-sectional area varies inversely with the area at any point along the length of the conductor.

(R) The current density $j$ is given by $j = \frac{I}{A}$, where $I$ is the current and $A$ is the cross-sectional area.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Dependence of Resistance on Dimensions

10. A wire has resistance $R_1$. If its cross-sectional area is increased by 3 times while its length remains constant, what will be its new resistance $R_2$?

a) $R_1$

b) $3R_1$

c) $\frac{R_1}{9}$

d) $\frac{R_1}{3}$

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Category: Electric Current

11. (A) The direction of conventional current is opposite to the direction of electron flow in a conductor.
(R) The direction of current is defined as the direction in which positive charges would move, even though electrons are negatively charged.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Series and parallel combinations of resistors.

12. Five identical resistors each of resistance $R$ are connected in such a way that the maximum possible equivalent resistance is obtained. Later, they are reconnected to achieve the minimum possible equivalent resistance. What is the ratio of the maximum to the minimum equivalent resistances?

a) $25$

b) $5$

c) $10$

d) $15$

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Category: Derivation of Ohm’s Law

13. How does the relaxation time $\tau$ affect the resistance $R$ of a conductor?

a) Resistance increases with increasing relaxation time.

b) Resistance decreases with increasing relaxation time.

c) Resistance is independent of relaxation time.

d) Resistance becomes zero for infinite relaxation time.

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Category: Resistance depends on length and cross-sectional area.

14. (A) When a cylindrical wire is stretched to twice its original length, its resistance becomes four times the original resistance.
(R) The resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Dependence of Resistance on Dimensions

15. A wire of resistance $R$ is stretched such that its length increases by 20\%. Assuming uniform stretching and constant volume, what will be the percentage change in its resistance?

a) 10\% decrease

b) 20\% increase

c) 44\% increase

d) 50\% increase

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Category: Resistance depends on length and cross-sectional area.

16. (A) If a wire is stretched to twice its original length, its resistance becomes four times the original resistance.
(R) Resistance of a conductor is directly proportional to the square of its length when volume remains constant.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Relation between drift velocity, current, and resistance.

17. A copper wire of cross-sectional area $2.5 \times 10^{-6} m^2$ carries a current of 1.5 A. If the free-electron density in copper is $8.4 \times 10^{28} m^{-3}$, what is the drift velocity of the electrons?

a) $1.12 \times 10^{-5} m/s$

b) $4.46 \times 10^{-5} m/s$

c) $8.93 \times 10^{-5} m/s$

d) $2.23 \times 10^{-5} m/s$

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Category: Behavior of free electrons in conductors.

18. A conductor has a relaxation time $\tau = 10^{-14}$ s for its free electrons. If an electric field of $100$ V/m is applied, what is the drift velocity of the electrons? Assume the mass of an electron is $9.1 \times 10^{-31}$ kg and charge is $1.6 \times 10^{-19}$ C.

a) $1.758 \times 10^5$ m/s

b) $1.758 \times 10^{-5}$ m/s

c) $3.516 \times 10^{-3}$ m/s

d) $0.879 \times 10^2$ m/s

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Category: Average distance between collisions.

19. What happens to the average distance between collisions if the gas pressure increases?

a) It remains constant

b) It increases proportionally

c) It decreases

d) It becomes zero immediately

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Category: Resistance for non-ohmic components.

20. For a thermistor, the voltage changes from 2 V to 3 V causes the current to change from 0.5 A to 0.6 A. What is the dynamic resistance of the thermistor in this range?

a) 20 $\Omega$

b) 10 $\Omega$

c) 5 $\Omega$

d) 15 $\Omega$

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Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

21. A copper wire of length 2 m and cross-sectional area $1 \times 10^{-6}$ m$^2$ carries a current of 3 A. If the relaxation time of free electrons in copper is $2 \times 10^{-14}$ s and the number density of free electrons is $8.5 \times 10^{28}$ m$^{-3}$, what is the drift velocity of electrons?

a) $0.44 \times 10^{-3}$ m/s

b) $0.22 \times 10^{-3}$ m/s

c) $1.1 \times 10^{-3}$ m/s

d) $2.2 \times 10^{-3}$ m/s

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Category: Directional flow of charge.

22. (A) The direction of electric current is taken as the direction of flow of positive charges.
(R) By convention, the direction of current is opposite to the direction of flow of electrons.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

23. A metallic wire initially follows Ohm’s law but starts deviating from linearity when the current is increased beyond a certain limit. What is the most likely reason for this deviation?

a) Increase in electron mobility

b) Decrease in resistivity due to cooling

c) Change in material composition

d) Rise in temperature causing increased resistance

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Category: Resistance for non-ohmic components.

24. What does dynamic resistance represent in a non-ohmic circuit?

a) Constant resistance for all voltages

b) The slope of the $V-I$ curve at a point

c) The inverse of current

d) The product of voltage and current

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Category: Specific Resistance or Electrical Resistivity

25. A wire of length 5 m and cross-sectional area \$4 \times 10^{-6}\$ m\$^2\$ has a resistance of 8 \$\Omega\$. What is the resistivity of the material?

a) \$1.6 \times 10^{-6}\$ \$\Omega \text{-m}\$

b) \$3.2 \times 10^{-6}\$ \$\Omega \text{-m}\$

c) \$6.4 \times 10^{-6}\$ \$\Omega \text{-m}\$

d) \$12.8 \times 10^{-6}\$ \$\Omega \text{-m}\$

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Category: V-I graph for metallic conductors.

26. A metallic conductor has a V-I graph with a slope of 0.5. If the current passing through it is doubled while maintaining the same physical conditions, what will be the new voltage across the conductor?

a) 0.25 V

b) 0.5 V

c) 1.0 V

d) 2.0 V

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Category: Ratio of potential difference to current.

27. The resistance of a conductor depends on:

a) Only the potential difference applied

b) Only the current passing through it

c) Both potential difference and current

d) Material, dimensions, and temperature

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Category: Effect of Temperature on Resistivity

28. Why are alloys preferred over pure metals for making standard resistances?

a) Alloys have lower resistivity than pure metals

b) Alloys have high resistivity and weak temperature dependence

c) Alloys are cheaper than pure metals

d) Alloys have higher conductivity than pure metals

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Category: Series and parallel combinations of resistors.

29. Two resistors of 4Ω and 8Ω are connected in parallel. What is their equivalent resistance?

a) 2 $\Omega$

b) 2.67 $\Omega$

c) 4 $\Omega$

d) 6 $\Omega$

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Category: Dependence of Resistance on Dimensions

30. (A) The resistance of a wire becomes four times its original value when stretched to double its length.
(R) Resistance is directly proportional to the square of the length and inversely proportional to the area of cross-section when volume remains constant.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Current Density

31. If the current density $\vec{j}$ is not uniform over a cross-sectional area $\vec{A}$ of a conductor, how is the total current calculated?

a) $I = j \cdot A$

b) $I = \frac{\vec{j}}{A}$

c) $I = \int \vec{j} \cdot d\vec{A}$

d) $I = \vec{j} \times \vec{A}$

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Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

32. When verifying Ohm's law experimentally, a student observes that the V-I graph for a certain resistor is linear up to point A but starts deviating beyond it. The deviation is most likely due to:

a) The rheostat not being adjusted properly.

b) The ammeter and voltmeter having high internal resistance.

c) The increase in temperature of the resistor altering its resistance.

d) The resistor being made of a non-ohmic material like a diode.

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Category: Non-ohmic conductors.

33. (A) The $V-I$ graph for a vacuum diode is linear.
(R) Vacuum diodes are non-ohmic conductors.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Flow of charge (electrons) in a conductor.

34. In a conductor, the drift velocity of electrons is $1.2 \times 10^{-4}\, m/s$ under an electric field of $0.5 \, V/m$. Calculate the relaxation time of electrons if the electron's mass is $9.1 \times 10^{-31}\, kg$ and charge is $1.6 \times 10^{-19}\, C$.

a) $1.82 \times 10^{-15} s$

b) $1.37 \times 10^{-15} s$

c) $2.74 \times 10^{-16} s$

d) $9.1 \times 10^{-16} s$

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Category: Introduction

35. A wire has a charge of 8 C passing through it in 4 seconds. If the current increases to double its initial value for another 4 seconds, what is the total charge that flows through the wire in the entire duration?

a) 12 C

b) 24 C

c) 32 C

d) 48 C

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Category: Ohm’s Law in Vector Form

36. If the resistivity ($\rho$) of a material is known, how can the current density ($\vec{j}$) be expressed in terms of the electric field ($\vec{E}$)?

a) $\vec{j} = \rho \vec{E}$

b) $\vec{j} = \frac{\vec{E}}{\rho}$

c) $\vec{j} = \rho \frac{d\vec{E}}{dt}$

d) $\vec{j} = \vec{E} + \rho$

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Category: Behavior of free electrons in conductors.

37. What does the mean free path of electrons in a conductor represent?

a) The total distance traveled by an electron in one second

b) The shortest distance between two atoms in the conductor

c) The average distance between two successive collisions of an electron

d) The maximum velocity attained by an electron in the conductor

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Category: Dependence of Resistance on Dimensions

38. A wire has resistance $R_1$. If the length of the wire is doubled while keeping its cross-sectional area constant, what will be its new resistance $R_2$?

a) $R_1$

b) $2R_1$

c) $4R_1$

d) $\frac{R_1}{2}$

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Category: Electric current, measured as the rate of flow of charge.

39. Two wires carry currents $I_1 = 4$ A and $I_2 = 3$ A towards each other at an angle of 60\textdegree. What is the resultant current at the junction point?

a) 1 A

b) 5 A

c) 7 A

d) 12 A

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Category: Ohm’s Law in Vector Form

40. In Ohm’s law in vector form for isotropic materials, how are $\vec{j}$ and $\vec{E}$ related in terms of direction?

a) They are perpendicular to each other.

b) They have opposite directions.

c) They have the same direction.

d) They are independent of each other.

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Category: Average distance between collisions.

41. An electron in a metal has a mobility ($\mu_e$) of $2 \times 10^{-3} \, \text{m}^2/\text{V}\cdot\text{s}$. If an electric field of $10 \, \text{V/m}$ is applied, what is the drift velocity ($v_d$) of the electron?

a) $1 \times 10^{-2} \, \text{m/s}$

b) $2 \times 10^{-2} \, \text{m/s}$

c) $4 \times 10^{-2} \, \text{m/s}$

d) $5 \times 10^{-2} \, \text{m/s}$

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Category: Colour Code of Carbon Resistors

42. A carbon resistor has the colour bands in the order: Yellow, Violet, Orange, Gold. What is its resistance value and tolerance?

a) 4700 $\Omega$ with $5\%$ tolerance

b) 47000 $\Omega$ with $5\%$ tolerance

c) 47000 $\Omega$ with $10\%$ tolerance

d) 4700 $\Omega$ with $10\%$ tolerance

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Category: Current electricity in daily life

43. A conductor carries a current of 2.5 A. How much charge flows through it in 4 minutes?

a) 300 C

b) 450 C

c) 600 C

d) 750 C

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Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

44. A conductor has a varying cross-sectional area $A(x) = 2x + 1$ (where $x$ is in meters and $A(x)$ is in $\text{m}^2$) and carries a current density $\vec{j}$ of magnitude $3x^2 \, \text{N/m}^2$ perpendicular to the cross-section. What is the total current flowing through the conductor from $x = 0$ to $x = 2$ meters?

a) 10 A

b) 12 A

c) 16 A

d) 20 A

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Category: Commercial Units of Electricity Consumption

45. (A) A 1000 watt appliance running for 1 hour consumes 1 kilowatt-hour of electrical energy.
(R) The commercial unit for measuring electrical energy consumption is the joule.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Average distance between collisions.

46. An electron in a conductor experiences an electric field of $5 \times 10^{-4}$ V/m. If its relaxation time is $2 \times 10^{-14}$ s and mass is $9.1 \times 10^{-31}$ kg, what is its drift velocity? (Take electronic charge $e = 1.6 \times 10^{-19}$ C)

a) $1.76 \times 10^{-7}$ m/s

b) $1.76 \times 10^{-6}$ m/s

c) $1.76 \times 10^{-5}$ m/s

d) $1.76 \times 10^{-4}$ m/s

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Category: Ratio of potential difference to current.

47. A device follows the relationship $V = k I^2$, where $k$ is a constant. What can be concluded about this device?

a) It obeys Ohm’s law because $V$ is proportional to $I$.

b) It does not obey Ohm’s law because $V/I$ is not constant.

c) It behaves like a superconductor with zero resistance.

d) Its resistance decreases with increasing current.

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Category: V-I graph for metallic conductors.

48. (A) The V-I graph for a metallic conductor is a straight line passing through the origin.
(R) Metallic conductors obey Ohm's law, which states that $V = IR$ where resistance $R$ is constant.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Electric Resistance

49. What is the mathematical form of Ohm's Law?

a) $V = \frac{I}{R}$

b) $I = VR$

c) $V = IR$

d) $R = VI$

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Category: Current density at a point in a conductor.

50. The direction of current density $\vec{j}$ in a conductor is:

a) Opposite to the motion of electrons

b) Same as the electric field direction inside the conductor

c) Random due to thermal motion of electrons

d) Same as the motion of positive charges

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Category: Dynamic Resistance

51. A non-ohmic circuit has a voltage-current characteristic where a small change in voltage $\Delta V$ of 5\,V leads to a change in current $\Delta I$ of 1\,mA. What is the dynamic resistance of this circuit?

a) 50\,\Omega

b) 500\,\Omega

c) 1000\,\Omega

d) 5000\,\Omega

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Category: Electric conduction in metals.

52. What is the order of magnitude of drift velocity of electrons in a metallic conductor under an applied electric field?

a) $10^5 \, \text{m/s}$

b) $10^{-3} \, \text{m/s}$

c) $10^8 \, \text{m/s}$

d) $10^{-6} \, \text{m/s}$

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Category: Derivation of Ohm’s Law

53. (A) The resistance of a wire remains unchanged when it is bent at one or more points.
(R) Bending the wire does not alter the number of free electrons or their relaxation time.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Role of free electrons in conduction.

54. If the relaxation time of free electrons in a metal increases by 20\% while keeping the electric field constant, how does the drift velocity change?

a) Remains the same

b) Increases by 10\%

c) Increases by 20\%

d) Decreases by 20\%

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Category: Mobility of Electrons

55. If the relaxation time of electrons in a conductor decreases by 30\% when temperature increases from 300K to 400K, by what percentage does the electron mobility change between these temperatures? Assume effective mass remains constant.

a) Decreases by 70\%

b) Decreases by 30\%

c) Increases by 30\%

d) Increases by 70\%

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Category: Flow of charge (electrons) in a conductor.

56. (A) The direction of current is taken as the direction of flow of positive charge.
(R) By convention, the direction of current is opposite to the direction of electron flow.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Flow of charge (electrons) in a conductor.

57. A copper wire has a cross-sectional area of $2 \times 10^{-6} m^2$ and carries a current of 3 A. If the number density of free electrons in copper is $8.5 \times 10^{28} m^{-3}$, what is the drift velocity of the electrons?

a) $1.1 \times 10^{-4}\, m/s$

b) $5.5 \times 10^{-5}\, m/s$

c) $2.2 \times 10^{-4}\, m/s$

d) $8.8 \times 10^{-5}\, m/s$

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Category: Derivation of Ohm’s Law

58. What is the formula for specific resistance (\$\rho\$) in terms of resistance ($R\$), area ($A\$), and length ($l\$) of a conductor?

a) $\rho = \frac{l}{RA}$

b) $\rho = \frac{RA}{l}$

c) $\rho = \frac{Rl}{A}$

d) $\rho = \frac{A}{Rl}$

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Category: Vector quantity, SI unit: A/m².

59. (A) The current density ($\vec{j}$) is directly proportional to the applied electric field ($\vec{E}$).
(R) According to Ohm’s law in vector form, $\vec{j} = \sigma \vec{E}$, where $\sigma$ is the specific conductance.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Series and parallel combinations of resistors.

60. Three resistors of 3Ω, 6Ω, and 9Ω are connected in series. What is their equivalent resistance?

a) 9 $\Omega$

b) 12 $\Omega$

c) 15 $\Omega$

d) 18 $\Omega$

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Category: Mobility of Electrons

61. (A) The mobility of electrons in a semiconductor decreases with increasing temperature.
(R) At higher temperatures, electron-lattice collisions become more frequent, reducing the relaxation time $\tau$ of electrons.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Series and parallel combinations of resistors.

62. Three resistors of $3 \Omega$, $6 \Omega$, and $9 \Omega$ are connected in series. What is their equivalent resistance?

a) $12 \Omega$

b) $15 \Omega$

c) $18 \Omega$

d) $21 \Omega$

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Category: Vector quantity, SI unit: A/m².

63. In a conductor obeying Ohm's law in vector form, if the electric field $\vec{E}$ is doubled, what happens to the current density $\vec{j}$?

a) It remains the same

b) It doubles

c) It quadruples

d) It halves

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Category: Colour Code of Carbon Resistors

64. What would be the colour code for a resistor with a value of 470 $\Omega$ and a tolerance of 20\%?

a) Yellow, Violet, Black

b) Yellow, Violet, Brown

c) Yellow, Green, Brown

d) Red, Violet, Brown

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Category: Combinations of Resistances

65. In a circuit, three resistors $R_1 = 3\Omega$, $R_2 = 6\Omega$, and $R_3 = 9\Omega$ are connected such that $R_1$ is in series with the parallel combination of $R_2$ and $R_3$. If a potential difference of 12V is applied across the combination, what is the current through $R_2$?

a) $\frac{10}{11}A$

b) $\frac{12}{11}A$

c) $\frac{14}{11}A$

d) $\frac{16}{11}A$

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Category: V-I graph for metallic conductors.

66. If the slope of a V-I graph for a metallic conductor is 5 \$
Omega\$, what is its resistance?

a) 2.5 \$ Omega\$

b) 5 \$ Omega\$

c) 10 \$ Omega\$

d) 20 \$ Omega\$

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Category: Effect of Temperature on Resistivity

67. A copper wire has a resistance of $10 \Omega$ at $20^\circ \text{C}$. If its temperature coefficient of resistance is $0.004 \, ^\circ \text{C}^{-1}$, what will be its resistance at $80^\circ \text{C}$?

a) $10.8 \Omega$

b) $11.6 \Omega$

c) $12.4 \Omega$

d) $13.2 \Omega$

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Category: Series and parallel combinations of resistors.

68. A circuit has two resistors of $5 \Omega$ and $10 \Omega$ connected in series, which are then connected in parallel with a $30 \Omega$ resistor. What is the total equivalent resistance?

a) $8 \Omega$

b) $10 \Omega$

c) $45 \Omega$

d) $20 \Omega$

69 / 513

Category: Directional flow of charge.

69. (A) The direction of conventional current is opposite to the direction of electron flow because electrons are negatively charged.
(R) Current is a scalar quantity as it does not follow the vector laws of addition.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

70 / 513

Category: Resistance depends on length and cross-sectional area.

70. A wire of resistance $R$ is stretched such that both its length and cross-sectional area change. If the wire's length increases by a factor of 3, what is its new resistance?

a) 3R

b) 6R

c) 9R

d) R/9

71 / 513

Category: Resistivity as a material property.

71. Which of the following factors does NOT affect the resistivity of a material?

a) Free-electron density

b) Relaxation time

c) Length of the conductor

d) Electron charge

72 / 513

Category: Resistivity as a material property.

72. (A) The resistivity of a material depends on its dimensions.
(R) Resistivity is given by $\rho = \frac{m}{n e^2 \tau}$, where $m$ is electron mass, $n$ is free-electron density, and $\tau$ is relaxation time.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

73 / 513

Category: Derivation of Ohm’s Law

73. What happens to the resistance of a wire if its length is doubled and its cross-sectional area is halved? Assume all other conditions remain unchanged.

a) The resistance doubles.

b) The resistance halves.

c) The resistance quadruples.

d) The resistance remains the same.

74 / 513

Category: V-I graph for metallic conductors.

74. Which of the following materials will NOT show a linear V-I graph under normal conditions?

a) Copper wire

b) Silver wire

c) Semiconductor diode

d) Nichrome wire

75 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

75. What type of electrons are responsible for electrical conduction in metals?

a) Valence electrons

b) Core electrons

c) Protons

d) Neutrons

76 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

76. In a p-n junction diode, no measurable current flows until the applied voltage reaches 0.7 V. Beyond this voltage, the current starts increasing rapidly. What does this indicate about the diode?

a) The diode obeys Ohm's law for voltages above 0.7 V.

b) The diode's resistance is constant beyond 0.7 V.

c) The diode exhibits non-linear V-I characteristics.

d) The diode behaves like a thermistor.

77 / 513

Category: Dependence of Resistance on Dimensions

77. A wire of resistance $R$ is stretched to double its length while keeping the volume constant. What will be its new resistance?

a) $R$

b) $2R$

c) $4R$

d) $8R$

78 / 513

Category: Colour Code of Carbon Resistors

78. A resistor has the colour bands Brown, Black, Red, and no fourth band. What is its tolerance?

a) $5\%$

b) $10\%$

c) $15\%$

d) $20\%$

79 / 513

Category: Ratio of potential difference to current.

79. (A) The ratio of potential difference to current is called electric conductance.
(R) Electric resistance is the reciprocal of electric conductance.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

80 / 513

Category: Electric Current

80. Two currents $I_1 = 3$ A and $I_2 = 4$ A meet at an angle of 90°. What is the resultant current at the junction?

a) 5 A

b) 7 A

c) 12 A

d) 1 A

81 / 513

Category: Electric Energy and Power

81. A resistor of 10 Ω carries a current of 3 A. What is the power dissipated across the resistor?

a) 30 W

b) 60 W

c) 90 W

d) 120 W

82 / 513

Category: Resistance in terms of fundamental unit

82. (A) The dimensions of resistance are $[M L^2 T^{-3} A^{-2}]$.
(R) Resistance can be expressed as the ratio of voltage to current, where voltage has dimensions $[M L^2 T^{-3} A^{-1}]$ and current has dimensions $[A]$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

83 / 513

Category: V-I graph for metallic conductors.

83. A metallic conductor has a V-I graph with a slope of 4. What is the resistance of the conductor?

a) 1 $\Omega$

b) 2 $\Omega$

c) 4 $\Omega$

d) 8 $\Omega$

84 / 513

Category: Role of free electrons in conduction.

84. What is the relationship between drift velocity ($v_d$) and the applied electric field ($E$) in a conductor?

a) Drift velocity is inversely proportional to the electric field.

b) Drift velocity is directly proportional to the square of the electric field.

c) Drift velocity is independent of the electric field.

d) Drift velocity is directly proportional to the electric field.

85 / 513

Category: Relation between drift velocity, current, and resistance.

85. Two wires of different diameters carry the same current. If the diameter of the first wire is twice that of the second, how does their current density compare?

a) The current density is the same in both wires

b) The current density in the first wire is twice that of the second

c) The current density in the first wire is half that of the second

d) The current density in the first wire is one-fourth that of the second

86 / 513

Category: Resistance in terms of fundamental unit

86. What are the dimensions of electric conductance?

a) [M L$^2$ T$^{-3}$ A$^{-2}$]

b) [M$^{-1}$ L$^{-2}$ T$^3$ A$^2$]

c) [M L$^{-2}$ T$^2$ A$^{-1}$]

d) [M$^{2}$ L$^{-1}$ T$^{-3}$ A$^{-2}$]

87 / 513

Category: Current Density

87. What is the SI unit of current density?

a) $A \, s^{-1}$

b) $A \, m^{-2}$

c) $V \, m^{-1}$

d) $\Omega \, m^{-1}$

88 / 513

Category: Electric Energy and Power

88. An industrial motor runs at 5 hp with 80\% efficiency when connected to a 440 V supply. If it operates for 8 hours daily for 30 days, what will be the electricity bill at \$0.12 per kWh?

a) \$98.56

b) \$112.45

c) \$126.72

d) \$134.28

89 / 513

Category: Resistance in terms of fundamental unit

89. (A) The dimensional formula of resistance is $[\text{M L}^2 \text{T}^{-3} \text{A}^{-2}]$.
(R) Resistance can be expressed as $\frac{\text{newton-metre}}{\text{ampere}^2 \text{-second}}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

90 / 513

Category: Resistivity as a material property.

90. A wire has resistance \$R = 10\,\Omega\$, length \$l = 2\,\text{m}\$, and cross-sectional area \$A = 1\,\text{mm}^2\$. What is the resistivity (\$\rho\$) of its material?

a) \$5 \times 10^{-6}\,\Omega\text{-m}\$

b) \$10^{-5}\,\Omega\text{-m}\$

c) \$2 \times 10^{-6}\,\Omega\text{-m}\$

d) \$20\,\Omega\text{-m}\$

91 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

91. The drift velocity (\$v_d\$) of electrons in a conductor is related to the electric field (\$E\$) by:

a) Inversely proportional to \$E\$

b) Independent of \$E\$

c) Directly proportional to \$E\$

d) Proportional to the square of \$E\$

92 / 513

Category: Commercial Units of Electricity Consumption

92. Which of the following is the correct definition of a board of trade unit (BTU)?

a) The energy consumed by 1 watt in 1 second

b) The energy consumed by 1000 watts in 1 minute

c) The energy consumed by 1000 watts in 1 hour

d) The energy consumed by 1000 joules in 1 hour

93 / 513

Category: Behavior of free electrons in conductors.

93. Which of the following describes the relaxation time of electrons in a conductor?

a) The time taken for all electrons to stop moving

b) The time for which the electric field is applied

c) The average time between two successive collisions of an electron

d) The lifetime of an electron in the conductor

94 / 513

Category: Combinations of Resistances

94. Three resistors of resistance $4 \Omega$, $6 \Omega$, and $10 \Omega$ are connected in series. What is their equivalent resistance?

a) $12 \Omega$

b) $18 \Omega$

c) $20 \Omega$

d) $24 \Omega$

95 / 513

Category: Electric current, measured as the rate of flow of charge.

95. The charge passing through a conductor varies with time as $q(t) = 2t^2 + 3t + 1$ (where $q$ is in coulombs and $t$ is in seconds). What is the instantaneous current at $t = 2$ s?

a) 7 A

b) 9 A

c) 11 A

d) 15 A

96 / 513

Category: Resistance in terms of fundamental unit

96. (A) The electric conductance $G$ of a material increases when its resistance $R$ decreases.
(R) The dimensions of electric conductance are the inverse of the dimensions of resistance.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

97 / 513

Category: Resistivity as a material property.

97. The current density ($j$) in a conductor when an electric field ($E$) is applied is given by:

a) $j = \rho E$

b) $j = \frac{\rho}{E}$

c) $j = \frac{E}{\rho}$

d) $j = \sigma \rho$

98 / 513

Category: Electric conduction in metals.

98. Why does silver have higher electrical conductivity compared to copper?

a) Because silver has fewer free electrons than copper

b) Due to higher drift velocity in silver at lower temperatures

c) Because silver has a higher number of free electrons and lower resistance

d) Due to the larger size of silver atoms

99 / 513

Category: V-I graph for metallic conductors.

99. (A) The V-I graph for a metallic conductor at high temperatures deviates from linearity due to the increase in resistance caused by electron-phonon collisions.
(R) At high temperatures, the lattice vibrations in a metallic conductor increase, leading to more frequent electron-phonon collisions and higher resistance.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

100 / 513

Category: Ohm’s Law

100. In an experiment to verify Ohm’s law, a student plots a graph of current (I) versus potential difference (V) for a resistor. If the slope of the graph is found to be 0.02 A/V, what is the resistance of the resistor?

a) 0.02 $\Omega$

b) 5 $\Omega$

c) 20 $\Omega$

d) 50 $\Omega$

101 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

101. In a metallic conductor, electric current is due to the flow of:

a) Protons

b) Electrons

c) Neither protons nor electrons

d) Both protons and electrons

102 / 513

Category: Introduction

102. A conductor carries a current of 2 A. How many electrons pass through a cross-section of the conductor in 5 seconds?

a) $3.125 \times 10^{19}$ electrons

b) $6.25 \times 10^{19}$ electrons

c) $1.25 \times 10^{20}$ electrons

d) $3.125 \times 10^{20}$ electrons

103 / 513

Category: Resistance for non-ohmic components.

103. Which of the following devices exhibits non-ohmic behavior due to temperature dependence?

a) Copper wire

b) Carbon resistor

c) Filament of a bulb

d) Gold-plated terminal

104 / 513

Category: Flow of charge (electrons) in a conductor.

104. What is drift velocity in a conductor?

a) mm/s

b) Speed of light

c) Zero

d) Thermal velocity

105 / 513

Category: Derivation of Ohm’s Law

105. A metallic wire of length $l$ and cross-sectional area $A$ carries a current $I$. If the number density of free electrons is $n$, the charge on an electron is $e$, and the relaxation time is $\tau$, what is the drift velocity $v_d$ of the electrons?

a) $\frac{Il}{nAe}$

b) $\frac{I\tau}{ml}$

c) $\frac{InA}{\tau e}$

d) $\frac{I}{nAe}$

106 / 513

Category: Dependence of Resistance on Dimensions

106. A wire with initial resistance $R_1$ is stretched such that its length becomes twice its original length. What will be its new resistance $R_2$?

a) $R_1$

b) $2R_1$

c) $4R_1$

d) $8R_1$

107 / 513

Category: Average distance between collisions.

107. If the root mean square velocity ($v_{rms}$) of an electron is $1.5 \times 10^6$ m/s and the relaxation time ($\tau$) is $2 \times 10^{-14}$ s, what is the mean free path ($\lambda$) of the electron?

a) $15 \, \text{nm}$

b) $20 \, \text{nm}$

c) $30 \, \text{nm}$

d) $45 \, \text{nm}$

108 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

108. (A) The V-I graph for a p-n junction diode is non-linear because its resistance depends on the applied potential difference.
(R) Ohm's law does not hold for p-n junction diodes as they are non-ohmic components.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

109 / 513

Category: Role of free electrons in conduction.

109. (A) The drift velocity of electrons in a conductor increases when the applied potential difference across it is increased.
(R) The drift velocity $v_d$ is directly proportional to the electric field $E$ applied across the conductor, as given by $v_d = \frac{eE\tau}{m}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

110 / 513

Category: Mobility of Electrons

110. How does electron mobility ($\mu_e$) change with increasing temperature in a conductor?

a) Increases linearly with temperature

b) Decreases due to increased collisions

c) Remains constant regardless of temperature

d) First increases, then decreases

111 / 513

Category: Current density at a point in a conductor.

111. A copper wire of cross-sectional area $5 \times 10^{-6} \, m^2$ carries a current of 3 A. If the free-electron density in copper is $8.4 \times 10^{28} \, m^{-3}$, what is the drift velocity of the electrons?

a) $4.46 \times 10^{-4} \, m/s$

b) $4.46 \times 10^{-5} \, m/s$

c) $8.92 \times 10^{-5} \, m/s$

d) $2.23 \times 10^{-5} \, m/s$

112 / 513

Category: Current Density

112. A conductor has a varying cross-sectional area along its length. At a certain point, the current density vector $\vec{j}$ makes an angle of $60^\circ$ with the area vector $\vec{A}$. If the magnitude of $\vec{j}$ is $2.0 \times 10^6 \, \text{A m}^{-2}$ and the magnitude of $\vec{A}$ is $1.5 \times 10^{-6} \, \text{m}^2$, what is the current through this section?

a) $0.75 \, \text{A}$

b) $1.0 \, \text{A}$

c) $1.5 \, \text{A}$

d) $2.0 \, \text{A}$

113 / 513

Category: Electric Energy and Power

113. How much energy is consumed by a 100 W bulb in 5 hours in kilowatt-hour (kW-h)?

a) 50 kW-h

b) 5 kW-h

c) 0.5 kW-h

d) 0.05 kW-h

114 / 513

Category: Electric conduction in metals.

114. (A) Metals are good conductors of electricity because they have a large number of free electrons.
(R) The electrical conductivity of a substance depends on the number of free electrons it has.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

115 / 513

Category: Current electricity in daily life

115. Three bulbs with power ratings 40 W, 60 W, and 100 W are connected in series across a voltage source. Which bulb will glow the brightest?

a) 40 W bulb

b) 60 W bulb

c) 100 W bulb

d) All glow equally

116 / 513

Category: Commercial Units of Electricity Consumption

116. A factory uses ten 500 W machines for 8 hours and five 200 W lamps for 12 hours daily. If the electricity rate is \$0.10 per kW-h, what is the total energy cost for a week (7 days)?

a) \$25.20

b) \$30.80

c) \$36.40

d) \$42.00

117 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

117. (A) In the absence of an electric field, the net current in a metal is zero because the average thermal velocity of free electrons is zero.
(R) The random motion of free electrons cancels out in all directions, resulting in no net flow of charge.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

118 / 513

Category: Effect of Temperature on Resistivity

118. (A) The resistivity of pure metals increases linearly with temperature in the high-temperature region because electron-phonon scattering dominates.
(R) At high temperatures, the mean free path of electrons decreases due to increased lattice vibrations, leading to a proportional increase in resistivity.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

119 / 513

Category: Resistivity as a material property.

119. Which of the following statements about resistivity is correct?

a) Resistivity depends on the length of the conductor.

b) Resistivity is inversely proportional to the relaxation time (\$\tau\$).

c) Resistivity changes with the cross-sectional area of the conductor.

d) Resistivity is independent of the conductor's shape and size.

120 / 513

Category: Ohm’s Law

120. A device exhibits a V-I characteristic where no measurable current flows until a threshold voltage $V_0$ is applied, after which the current increases linearly with voltage. Which of the following best describes this behavior?

a) The device follows Ohm’s law throughout the entire range.

b) The device does not conduct electricity at any voltage.

c) The device shows ohmic behavior below $V_0$ and non-ohmic above $V_0$.

d) The device does not follow Ohm’s law initially but shows linear behavior beyond $V_0$.

121 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

121. Why does the filament of a bulb deviate from Ohm's law when the current increases?

a) Due to decrease in temperature

b) Because of constant resistance

c) Resistance decreases with more current

d) Temperature rise increases resistance

122 / 513

Category: Electric Energy and Power

122. A power station delivers 10 MW at 50 kV through transmission lines having total effective resistance of 5 Ω. What percentage of power is lost in transmission if the voltage is stepped up to 200 kV while keeping power delivered constant?

a) 2.0\%

b) 1.25\%

c) 0.50\%

d) 0.125\%

123 / 513

Category: Electric Current

123. Which of the following best explains why metals are good conductors of electricity?

a) Metals have tightly bound outer electrons

b) Metals lack any free electrons

c) Metals have a large number of free electrons

d) Metals have only positive ions

124 / 513

Category: Rate at which electrons move under an electric field.

124. An electron in a conductor has a relaxation time $\tau = 2.5 \times 10^{-14}\, \text{s}$ under an electric field of $50\, \text{V/m}$. If the mass of the electron is $9.1 \times 10^{-31}\, \text{kg}$, what is its drift velocity?

a) $1.5 \times 10^{-1}\, \text{m/s}$

b) $2.197 \times 10^{-1}\, \text{m/s}$

c) $3.2 \times 10^{-1}\, \text{m/s}$

d) $4.0 \times 10^{-1}\, \text{m/s}$

125 / 513

Category: Directional flow of charge.

125. If $6.25 \times 10^{18}$ electrons enter a conductor at one end per second, what is the current flowing through the conductor?

a) 0.5 A

b) 1 A

c) 2 A

d) 4 A

126 / 513

Category: Current density at a point in a conductor.

126. (A) The current density $\vec{j}$ at a point in a conductor is always in the direction of motion of positive charges.
(R) Current density is a vector quantity whose direction is defined as the direction of flow of positive charge carriers.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

127 / 513

Category: Dependence of Resistance on Dimensions

127. A wire of resistance $R$ is stretched to twice its original length without changing its volume. What is the new resistance of the wire?

a) $\frac{R}{2}$

b) $R$

c) $2 R$

d) $4 R$

128 / 513

Category: Resistivity as a material property.

128. A conductor of resistivity $\rho$ has a free-electron density $n$. If the relaxation time $\tau$ of electrons is doubled and the cross-sectional area $A$ of the conductor is halved while keeping its length constant, how does the resistance $R$ of the conductor change?

a) Resistance doubles

b) Resistance halves

c) Resistance remains unchanged

d) Resistance quadruples

129 / 513

Category: Power dissipation in resistive circuits.

129. (A) When two resistors of equal resistance are connected in parallel to a voltage source, the power dissipated in each resistor is four times the power dissipated when the same resistors are connected in series to the same voltage source.
(R) The equivalent resistance of two identical resistors in parallel is half their individual resistance, leading to higher current and thus higher power dissipation compared to their series combination.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

130 / 513

Category: Role of free electrons in conduction.

130. How is current density ($j$) defined for a conductor with uniform current distribution?

a) The total charge passing through the conductor per second.

b) The current divided by the length of the conductor.

c) The current flowing through unit cross-sectional area of the conductor.

d) The resistance per unit length of the conductor.

131 / 513

Category: Relation between drift velocity, current, and resistance.

131. A wire of length 2 m and cross-sectional area $4 \times 10^{-6} m^2$ has a resistance of 5 $\Omega$. What is its resistivity?

a) $8 \times 10^{-6} \Omega \cdot m$

b) $1 \times 10^{-5} \Omega \cdot m$

c) $1.5 \times 10^{-5} \Omega \cdot m$

d) $2 \times 10^{-5} \Omega \cdot m$

132 / 513

Category: Rate at which electrons move under an electric field.

132. An electric field of $E = 2 \, \text{V/m}$ is applied to a conductor. If the electron mobility $\mu_e$ is $5 \times 10^{-3} \, \text{m}^2 \text{V}^{-1} \text{s}^{-1}$, what is the drift velocity $v_d$ of the electrons?

a) $5 \times 10^{-3} \, \text{m/s}$

b) $1 \times 10^{-2} \, \text{m/s}$

c) $2 \times 10^{-3} \, \text{m/s}$

d) $2.5 \times 10^{-2} \, \text{m/s}$

133 / 513

Category: Average distance between collisions.

133. If molecules travel an average of 200 nm between collisions at standard conditions, what would be their average distance between collisions if the temperature doubles while keeping pressure constant?

a) 100 nm

b) 200 nm

c) 400 nm

d) 800 nm

134 / 513

Category: Ratio of potential difference to current.

134. (A) The resistance of a conductor is independent of the applied potential difference if the physical conditions remain constant.
(R) According to Ohm’s law, the ratio $\frac{V}{I}$ remains constant for a conductor as long as its temperature and other physical states do not change.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

135 / 513

Category: Electric conduction in metals.

135. A non-uniform conductor has varying cross-sectional area $A(x)$ along its length $x$. The current density $\vec{J}$ at any point is related to the electric field $\vec{E}$ and conductivity $\sigma$ by:

a) $\vec{J} = \frac{\sigma}{\vec{E}}$

b) $\vec{J} = \sigma + \vec{E}$

c) $\vec{J} = \sigma \vec{E}$

d) $\vec{J} = \sigma - \vec{E}$

136 / 513

Category: Introduction

136. (A) The unit of electric current, ampere, is defined based on the force between two parallel current-carrying conductors.
(R) This definition ensures a reproducible standard for measuring electric current.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

137 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

137. A cylindrical conductor of radius 2 mm carries a current of 5 A uniformly distributed across its cross-section. What is the magnitude of the current density?

a) $1.99 \times 10^5 \, \text{A/m}^2$

b) $3.98 \times 10^5 \, \text{A/m}^2$

c) $7.96 \times 10^5 \, \text{A/m}^2$

d) $9.95 \times 10^4 \, \text{A/m}^2$

138 / 513

Category: Current density at a point in a conductor.

138. A material has a conductivity $\sigma = 5.8 \times 10^7 \, S/m$. If the electric field inside it is $0.1 \, V/m$, what is the current density?

a) $5.8 \times 10^5 \, A/m^2$

b) $5.8 \times 10^6 \, A/m^2$

c) $5.8 \times 10^7 \, A/m^2$

d) $5.8 \times 10^8 \, A/m^2$

139 / 513

Category: Colour Code of Carbon Resistors

139. What will be the colour sequence for a resistor with a value of $5600 \, \Omega \pm 10\%$?

a) Green, Blue, Red, Gold

b) Green, Blue, Black, Silver

c) Green, Blue, Red, Silver

d) Blue, Green, Red, Silver

140 / 513

Category: Directional flow of charge.

140. (A) In an electric circuit, the direction of current is taken as the direction opposite to the flow of electrons.
(R) By convention, the direction of current is considered as the direction in which positive charges would move.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

141 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

141. (A) The drift velocity of electrons in a conductor increases with an increase in temperature.
(R) As temperature increases, the relaxation time of electrons decreases due to increased collisions.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

142 / 513

Category: Current electricity in daily life

142. (A) A 100 W bulb connected in series with a 40 W bulb will glow brighter than the 40 W bulb because it dissipates more power.
(R) The resistance of a 100 W bulb is lower than that of a 40 W bulb when operating at the same voltage.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

143 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

143. (A) The V-I graph for a semiconductor diode is nonlinear, indicating it does not obey Ohm’s law.
(R) Semiconductor diodes have a resistance that depends on the applied voltage, making them non-ohmic conductors.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

144 / 513

Category: Current density at a point in a conductor.

144. (A) Current density at a point in a conductor is a vector quantity.
(R) Current density has both magnitude and direction, as it represents the flow of charge per unit area perpendicular to the direction of current flow.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

145 / 513

Category: Power dissipation in resistive circuits.

145. (A) The power dissipated in a resistor increases if the current passing through it increases.
(R) Power dissipation in a resistor is given by $P = I^2 R$, which shows that power is directly proportional to the square of the current.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

146 / 513

Category: Electric Current

146. (A) The current in a conductor remains constant when the cross-sectional area of the conductor is changed.
(R) Current is a scalar quantity and does not depend on the geometry of the conductor.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

147 / 513

Category: Role of free electrons in conduction.

147. What role do free electrons play in the conduction of electricity in metals?

a) They provide structural stability to the metal lattice.

b) They carry electrical energy by moving through the metal.

c) They neutralize positive ions in the metal.

d) They absorb thermal energy from the surroundings.

148 / 513

Category: Directional flow of charge.

148. Two currents, $I_1 = 7$ A and $I_2 = 3$ A, meet at a junction at an angle of $60^\circ$. What is the resultant current leaving the junction?

a) 4 A

b) 8.66 A

c) 10 A

d) 12 A

149 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

149. (A) The V-I characteristic curve of a p-n junction diode is linear for small applied voltages.
(R) For non-ohmic conductors, the resistance depends on the applied voltage and current.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

150 / 513

Category: Flow of charge (electrons) in a conductor.

150. (A) The drift velocity of electrons in a conductor decreases when its cross-sectional area is increased while keeping the current constant.
(R) Drift velocity $v_d$ is inversely proportional to the cross-sectional area $A$ as given by $v_d = \frac{I}{neA}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

151 / 513

Category: Electric Current

151. What is the SI unit of electric current?

a) Coulomb

b) Volt

c) Ampere

d) Ohm

152 / 513

Category: Electric conduction in metals.

152. What is the relationship between drift velocity ($v_d$), electric field ($E$), and relaxation time ($\tau$) of electrons in a conductor?

a) $v_d = \frac{m}{e E \tau}$

b) $v_d = \frac{e E}{m \tau}$

c) $v_d = \frac{e E \tau}{m}$

d) $v_d = \frac{E \tau}{m e}$

153 / 513

Category: Resistance in terms of fundamental unit

153. Convert 5 mega-ohms to ohms.

a) $5 \times 10^3$ ohm

b) $5 \times 10^4$ ohm

c) $5 \times 10^5$ ohm

d) $5 \times 10^6$ ohm

154 / 513

Category: Mobility of Electrons

154. (A) The mobility of electrons in a conductor decreases with an increase in temperature.
(R) As temperature increases, the relaxation time $\tau$ of electrons decreases due to more frequent collisions with the lattice.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

155 / 513

Category: Ohm’s Law

155. A metallic conductor follows Ohm's law under certain conditions. If the temperature of the conductor increases due to current flow, how does its resistance change and what happens to the V-I curve?

a) Resistance decreases, and the V-I curve becomes steeper.

b) Resistance remains constant, and the V-I curve remains linear.

c) Resistance increases, and the V-I curve becomes non-linear.

d) Resistance decreases, and the V-I curve becomes non-linear.

156 / 513

Category: Ohm’s Law in Vector Form

156. For a non-ohmic conductor, the relationship between current density $\vec{j}$ and electric field $\vec{E}$ is given by $\vec{j} = k |\vec{E}|^2 \hat{E}$, where $k$ is a constant. If $|\vec{E}| = 2 \, V/m$, what is the angle between $\vec{j}$ and $\vec{E}$?

a) $0^\circ$

b) $45^\circ$

c) $90^\circ$

d) $180^\circ$

157 / 513

Category: Ohm’s Law

157. In an experiment to verify Ohm's law, the potential difference across a resistor is measured as 12 V when the current through it is 3 A. What is the resistance of the resistor?

a) 0.25 $\Omega$

b) 1 $\Omega$

c) 4 $\Omega$

d) 36 $\Omega$

158 / 513

Category: Introduction

158. If a charge of 4 coulombs flows through a conductor in 2 seconds, what is the electric current?

a) 1 A

b) 2 A

c) 4 A

d) 8 A

159 / 513

Category: Role of free electrons in conduction.

159. (A) Metals are good conductors of electricity because they have a large number of free electrons.
(R) Free electrons in metals are responsible for carrying electrical energy from one place to another.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

160 / 513

Category: Electric conduction in metals.

160. What does the relaxation time of an electron represent in the context of electric conduction in metals?

a) Time taken for an electron to travel from one end of the conductor to the other

b) Average time-interval between two successive collisions of an electron

c) Time required for an electron to reach thermal equilibrium

d) Time taken for an electron to gain maximum velocity

161 / 513

Category: Commercial Units of Electricity Consumption

161. What is the commercial unit of electrical energy?

a) Joule

b) Volt-ampere

c) Kilowatt-hour

d) Watt-second

162 / 513

Category: Ohm’s Law in Vector Form

162. How is the microscopic form of Ohm’s law expressed?

a) $E = \sigma j$

b) $E = \rho j$

c) $j = \sigma E$

d) $j = \rho E$

163 / 513

Category: Combinations of Resistances

163. (A) If three resistors of resistances $1\Omega$, $2\Omega$, and $3\Omega$ are connected in series, the equivalent resistance is $6\Omega$.
(R) In a series combination, the equivalent resistance is the sum of individual resistances.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

164 / 513

Category: Current Density

164. A wire carries a current of 5 A and has a cross-sectional area of $2 \times 10^{-6} \, m^2$. What is the current density in the wire?

a) $1.0 \times 10^6 \, A \, m^{-2}$

b) $2.5 \times 10^6 \, A \, m^{-2}$

c) $5.0 \times 10^6 \, A \, m^{-2}$

d) $10.0 \times 10^6 \, A \, m^{-2}$

165 / 513

Category: Ohm’s Law in Vector Form

165. What is the mathematical expression of Ohm’s law in vector form?

a) $\vec{E} = \rho \vec{j}$

b) $\vec{j} = \rho \vec{E}$

c) $\vec{j} = \sigma \vec{E}$

d) $\vec{E} = \sigma \vec{j}$

166 / 513

Category: Current electricity in daily life

166. An electric bulb rated 100 W is used for 6 hours daily. If the cost of electricity is \$0.10 per unit, what is the total cost of electricity consumed by the bulb in 30 days?

a) \$1.2

b) \$1.5

c) \$1.8

d) \$2.1

167 / 513

Category: Dependence of Resistance on Dimensions

167. A wire of radius $r$ and resistance $R$ is melted and recast into a wire of half its original radius. What will be the new resistance? Assume volume remains constant.

a) $2R$

b) $4R$

c) $8R$

d) $16R$

168 / 513

Category: Dynamic Resistance

168. On a $V-I$ curve, which line segment represents the change in current ($\Delta I$) when calculating dynamic resistance using points $P$ and $Q$?

a) Line segment $PS$

b) Line segment $SQ$

c) Line segment $QS$

d) Line segment $PQ$

169 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

169. Which of the following devices does NOT obey Ohm’s law even for small currents?

a) Copper wire at room temperature

b) P-N junction diode

c) Constantan wire

d) Nichrome wire

170 / 513

Category: Series and parallel combinations of resistors.

170. A circuit contains two resistors $R_1 = 5 \Omega$ and $R_2 = 10 \Omega$ in series, and this combination is connected in parallel with another resistor $R_3 = 15 \Omega$. If the total current supplied to the circuit is $3 A$, what is the potential difference across $R_3$?

a) $22.5 V$

b) $15 V$

c) $30 V$

d) $7.5 V$

171 / 513

Category: Non-ohmic conductors.

171. For a liquid electrolyte, the current starts flowing only when the applied voltage exceeds the threshold voltage $V_0$. If the current-voltage relationship beyond $V_0$ is $I = k(V - V_0)^2$, what is the dynamic resistance at $V = 2V_0$?

a) $\frac{1}{kV_0}$

b) $\frac{1}{2kV_0}$

c) $\frac{1}{4kV_0}$

d) $\frac{1}{8kV_0}$

172 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

172. The dimensions of current density can be expressed in terms of fundamental quantities as [$A L^{-2}$]. If a new system defines charge in "coulombs" (C), length in "meters" (m), and time in "seconds" (s), what is the dimensional formula for current density in this system?

a) [C m$^{-2}$ s$^{-1}$]

b) [C$^{-1}$ m$^{2}$ s]

c) [C m$^{2}$ s$^{-1}$]

d) [C$^{-1}$ m$^{-2}$ s]

173 / 513

Category: Ohm’s Law in Vector Form

173. (A) The current density $\vec{j}$ is always parallel to the electric field $\vec{E}$ in an isotropic medium.
(R) Ohm’s law in vector form states $\vec{j} = \sigma \vec{E}$, where $\sigma$ is the conductivity of the material.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

174 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

174. (A) The drift velocity of electrons in a conductor decreases with an increase in temperature.
(R) As temperature increases, the relaxation time of electrons decreases due to more frequent collisions.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

175 / 513

Category: Dynamic Resistance

175. For a non-ohmic conductor, which statement correctly describes dynamic resistance?

a) It is constant for all values of current and voltage.

b) It represents the slope of the tangent to the V-I curve at a particular point.

c) It is inversely proportional to the current flowing through the conductor.

d) It exists only when the conductor follows Ohm’s law.

176 / 513

Category: Ohm’s Law

176. According to Ohm's law, the ratio of potential difference ($V$) and current ($I$) is equal to what?

a) Power

b) Conductance

c) Resistance

d) Capacitance

177 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

177. A current of 2 A flows through a copper wire of cross-sectional area $1.0 \times 10^{-6}$ m$^2$. If the electron density in copper is $8.5 \times 10^{28}$ m$^{-3}$, what is the drift velocity of the electrons?

a) $1.47 \times 10^{-4}$ m/s

b) $2.94 \times 10^{-4}$ m/s

c) $3.68 \times 10^{-4}$ m/s

d) $5.88 \times 10^{-4}$ m/s

178 / 513

Category: Ohm’s Law in Vector Form

178. (A) The current density $\vec{j}$ is directly proportional to the electric field $\vec{E}$.
(R) According to Ohm’s law in vector form, $\vec{j} = \sigma \vec{E}$, where $\sigma$ is the conductivity.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

179 / 513

Category: Effect of Temperature on Resistivity

179. A metallic wire has a resistance of 10 ohms at $20^\circ$C and 12 ohms at $80^\circ$C. What is the temperature coefficient of resistance of the material?

a) $\frac{1}{200}$ per $^\circ$C

b) $\frac{1}{250}$ per $^\circ$C

c) $\frac{1}{300}$ per $^\circ$C

d) $\frac{1}{350}$ per $^\circ$C

180 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

180. What is the purpose of the rheostat ($R_h$) in the circuit for verifying Ohm's law?

a) To measure the potential difference

b) To act as the test resistor

c) To control the current in the circuit

d) To calibrate the voltmeter

181 / 513

Category: Introduction

181. In a circuit, the number of electrons flowing per second is $1.25 \times 10^{18}$. What is the current in the circuit?

a) 0.1 A

b) 0.2 A

c) 0.5 A

d) 1.0 A

182 / 513

Category: Current Density

182. An aluminum wire with a cross-sectional area of $2.0 \times 10^{-6} \, \text{m}^2$ carries a current of $3.0 \, \text{A}$. If the free-electron density is $6.0 \times 10^{28} \, \text{m}^{-3}$ and the length of the wire is $10 \, \text{m}$, how long does it take for an electron to travel the full length of the wire?

a) $6.41 \times 10^3 \, \text{s}$

b) $6.41 \times 10^4 \, \text{s}$

c) $6.41 \times 10^5 \, \text{s}$

d) $6.41 \times 10^6 \, \text{s}$

183 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

183. A current density $\vec{j} = (3\hat{i} + 4\hat{j}) \, \text{A/m}^2$ flows through a surface with area vector $\vec{A} = (2\hat{i} + 1\hat{j}) \, \text{m}^2$. What is the current passing through this surface?

a) 6 A

b) 8 A

c) 10 A

d) 12 A

184 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

184. (A) If the current in a conductor is 1 A, then the number of electrons flowing through its cross-section per second is $6.25 \times 10^{18}$.
(R) The charge carried by one electron is $1.6 \times 10^{-19} \text{ C}$, and $1 \text{ A} = 1 \text{ C s}^{-1}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

185 / 513

Category: Introduction

185. What is the SI unit of electric current?

a) Volt

b) Ohm

c) Ampere

d) Coulomb

186 / 513

Category: Electric Current

186. If a charge of 20 C flows through a conductor in 5 seconds, what is the current?

a) 0.25 A

b) 4 A

c) 5 A

d) 100 A

187 / 513

Category: Electric Resistance

187. (A) The resistance of a metallic conductor decreases when its temperature is increased from 20°C to 40°C.
(R) The temperature coefficient of resistance for metals is negative.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

188 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

188. A copper wire of length 2 m and cross-sectional area $1 \times 10^{-6} \, \text{m}^2$ carries a current of 1 A. If the number density of free electrons in copper is $8.5 \times 10^{28} \, \text{m}^{-3}$, what is the drift velocity of electrons? ($e = 1.6 \times 10^{-19} \, \text{C}$)

a) $0.735 \, \text{mm/s}$

b) $0.00735 \, \text{mm/s}$

c) $0.0735 \, \text{mm/s}$

d) $0.000735 \, \text{mm/s}$

189 / 513

Category: Rate at which electrons move under an electric field.

189. How does the mobility of electrons in a conductor change when the temperature increases?

a) It remains constant

b) It decreases

c) It increases

d) It becomes zero

190 / 513

Category: Resistance for non-ohmic components.

190. Which of the following is an example of a non-ohmic component?

a) Copper wire

b) Carbon resistor

c) P-n junction diode

d) Aluminum rod

191 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

191. For a p-n junction diode, the dynamic resistance at a particular operating point is calculated by taking two points P and Q on its V-I curve. If PS = 0.5 V and QS = 10 mA, what is the dynamic resistance?

a) 5 ohms

b) 50 ohms

c) 500 ohms

d) 0.05 ohms

192 / 513

Category: Non-ohmic conductors.

192. (A) The V-I characteristic curve of a semiconductor diode is non-linear.
(R) The resistance of a semiconductor diode depends on the applied voltage.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

193 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

193. Which of the following devices does NOT obey Ohm's law even for small currents?

a) Manganin wire

b) Copper wire

c) p-n junction diode

d) Constantan resistor

194 / 513

Category: Current Density

194. A current density of $4.8 \times 10^6 \, A \, m^{-2}$ flows through a conductor with a free-electron density of $8.5 \times 10^{28} \, m^{-3}$. Calculate the drift velocity of electrons. (Charge of electron, $e = 1.6 \times 10^{-19} \, C$)

a) $2.5 \times 10^{-4} \, m \, s^{-1}$

b) $3.5 \times 10^{-4} \, m \, s^{-1}$

c) $4.5 \times 10^{-4} \, m \, s^{-1}$

d) $5.5 \times 10^{-4} \, m \, s^{-1}$

195 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

195. If the drift velocity of electrons in a conductor is $0.1 \, \text{mm/s}$ when an electric field of $0.5 \, \text{V/m}$ is applied, what is the average relaxation time of electrons? (Given: electron charge $e = 1.6 \times 10^{-19} \, \text{C}$, electron mass $m = 9.1 \times 10^{-31} \, \text{kg}$)

a) $2.28 \times 10^{-15} \, \text{s}$

b) $1.14 \times 10^{-15} \, \text{s}$

c) $4.56 \times 10^{-15} \, \text{s}$

d) $0.57 \times 10^{-15} \, \text{s}$

196 / 513

Category: Electric current, measured as the rate of flow of charge.

196. How many electrons pass through a point in a conductor in 2 seconds if the current flowing is 2 amperes? (Given: Charge on one electron $= 1.6 \times 10^{-19}$ C)

a) $1.25 \times 10^{19}$

b) $2.5 \times 10^{19}$

c) $3.75 \times 10^{19}$

d) $5 \times 10^{19}$

197 / 513

Category: Electric current, measured as the rate of flow of charge.

197. (A) Electric current is a scalar quantity because it does not obey the vector laws of addition.
(R) The algebraic sum of currents meeting at a junction is always zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

198 / 513

Category: Specific Resistance or Electrical Resistivity

198. The resistivity of a conductor is given by $\rho = \frac{m}{n e^2 \tau}$, where $m$ is the electron mass, $n$ is the free electron density, $e$ is the electron charge, and $\tau$ is the relaxation time. If the number of free electrons per unit volume in a conductor is doubled while keeping all other parameters constant, how does the resistivity change?

a) It remains the same

b) It doubles

c) It halves

d) It quadruples

199 / 513

Category: Resistance for non-ohmic components.

199. (A) The resistance of a filament bulb increases as the current through it increases.
(R) The temperature of the filament rises with increasing current, causing its resistance to change.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

200 / 513

Category: Commercial Units of Electricity Consumption

200. (A) The kilowatt-hour (\textbf{kW-h}) is a unit of electrical energy commonly used for billing purposes in households and industries.
(R) The kilowatt-hour represents the amount of energy consumed when a 1 kW appliance operates continuously for one hour.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

201 / 513

Category: Current Density

201. A copper wire has a current density of $5.0 \times 10^6 \, \text{A m}^{-2}$. If the free-electron density is $8.4 \times 10^{28} \, \text{m}^{-3}$, what is the drift velocity of the electrons?

a) $3.72 \times 10^{-5} \, \text{m s}^{-1}$

b) $3.72 \times 10^{-4} \, \text{m s}^{-1}$

c) $3.72 \times 10^{-3} \, \text{m s}^{-1}$

d) $3.72 \times 10^{-2} \, \text{m s}^{-1}$

202 / 513

Category: Current density at a point in a conductor.

202. A conductor carries a current of 3.2 A. If the cross-sectional area of the conductor is $8 \times 10^{-6} \, m^2$, what is the current density at any point on this cross-section?

a) $4 \times 10^5 \, A \, m^{-2}$

b) $2.56 \times 10^6 \, A \, m^{-2}$

c) $1.6 \times 10^6 \, A \, m^{-2}$

d) $8 \times 10^5 \, A \, m^{-2}$

203 / 513

Category: Role of free electrons in conduction.

203. As the temperature of a semiconductor increases, its resistivity decreases because:

a) Free electrons collide more frequently with ions

b) The mean free path of electrons decreases

c) More electrons become available for conduction

d) The electron mobility decreases

204 / 513

Category: Vector quantity, SI unit: A/m².

204. A conductor has a non-uniform cross-sectional area. If the current density $\vec{j}$ is not uniform, which expression correctly gives the total current through the conductor?

a) $I = j \cdot A$

b) $I = \int \vec{j} \cdot d\vec{A}$

c) $I = \sigma E$

d) $I = \frac{V}{R}$

205 / 513

Category: Colour Code of Carbon Resistors

205. What does the colour "Red" represent in the first band of a carbon resistor?

a) Black

b) Red

c) Orange

d) Yellow

206 / 513

Category: Ohm’s Law

206. Which of the following is an example where Ohm's law is not strictly valid?

a) A copper wire at constant temperature.

b) A manganin resistor at room temperature.

c) A semiconductor diode.

d) The filament of a torch bulb.

207 / 513

Category: Rate at which electrons move under an electric field.

207. (A) The drift velocity of electrons in a conductor is inversely proportional to the relaxation time when the electric field is kept constant.
(R) As per the relation $v_d = \frac{e \tau}{m} E$, drift velocity ($v_d$) is directly proportional to the relaxation time ($\tau$).

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

208 / 513

Category: Power dissipation in resistive circuits.

208. Two resistors, $R_1 = 50 \Omega$ and $R_2 = 200 \Omega$, are connected in parallel to a 100 V source. If the power dissipated in $R_1$ is $P_1$, what is the power dissipated in $R_2$?

a) 12.5 W

b) 25 W

c) 50 W

d) 100 W

209 / 513

Category: Vector quantity, SI unit: A/m².

209. What is the SI unit of current density?

a) $A \cdot m$

b) $A / m^2$

c) $A^2 / m$

d) $m^2 / A$

210 / 513

Category: Electric current, measured as the rate of flow of charge.

210. If a current of 10 A flows uniformly through a conductor with a cross-sectional area of 5 $\text{m}^2$, what is the current density at any point on the conductor?

a) 0.5 A/m$^2$

b) 1 A/m$^2$

c) 2 A/m$^2$

d) 5 A/m$^2$

211 / 513

Category: Current electricity in daily life

211. Why are household appliances like bulbs and fans connected in parallel rather than in series?

a) To reduce power consumption

b) To ensure each device works independently at full voltage

c) To increase resistance in the circuit

d) To minimize heating effects

212 / 513

Category: Derivation of Ohm’s Law

212. In a conductor with cross-sectional area $A$, the drift velocity of electrons is $v_d$ when a potential difference $V$ is applied across its ends. If the potential difference is doubled while keeping all other parameters constant, how does the drift velocity change?

a) It halves

b) It remains the same

c) It doubles

d) It quadruples

213 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

213. What is the drift velocity of electrons in a conductor when an electric field $E$ is applied? (Given: $e$ is charge of electron, $m$ is mass of electron, $\tau$ is relaxation time)

a) $v_d = \frac{mE}{e\tau}$

b) $v_d = \frac{E\tau}{em}$

c) $v_d = \frac{eE}{m} \tau$

d) $v_d = \frac{e\tau}{mE}$

214 / 513

Category: Flow of charge (electrons) in a conductor.

214. What is the SI unit of electric current?

a) Coulomb

b) Volt

c) Ampere

d) Ohm

215 / 513

Category: Resistance for non-ohmic components.

215. A silicon diode has a characteristic curve where at point P, the voltage is 0.7 V and current is 1 mA, while at point Q, the voltage is 0.8 V and current is 10 mA. What is the dynamic resistance of the diode between these two points?

a) 100 $\Omega$

b) 50 $\Omega$

c) 11.11 $\Omega$

d) 5 $\Omega$

216 / 513

Category: Introduction

216. (A) Electric current is defined as the rate of flow of charge.
(R) The SI unit of electric current is ampere, which is equivalent to 1 coulomb per second.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

217 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

217. A thermistor has a resistance of 2000 $\Omega$ at 25°C and its resistance decreases to 500 $\Omega$ when the temperature rises to 50°C. Which statement best describes its behavior?

a) It follows Ohm's law as resistance remains constant.

b) It shows non-linear V-I characteristics due to temperature dependence.

c) Its resistance increases with temperature.

d) It behaves like an ohmic conductor for small currents.

218 / 513

Category: Mobility of Electrons

218. A semiconductor has electron mobility of $1500 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1}$ and hole mobility of $500 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1}$. When both electrons and holes contribute equally to current under an electric field of $10^4 \, \text{V/m}$, what is the average drift velocity of charge carriers?

a) 750 m/s

b) 1000 m/s

c) 1250 m/s

d) 2000 m/s

219 / 513

Category: Resistance for non-ohmic components.

219. (A) The dynamic resistance of a diode is negative when the current through it increases with a decrease in voltage.
(R) The V-I characteristic curve of a diode shows non-linear behavior where the current may not increase proportionally with the voltage.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

220 / 513

Category: Dependence of Resistance on Dimensions

220. (A) If a wire is stretched to three times its original length, its resistance increases to nine times the original value.
(R) The resistance of a conductor is directly proportional to the square of the length when the volume remains constant.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

221 / 513

Category: Derivation of Ohm’s Law

221. Which of the following equations represents Ohm's Law?

a) $V = \frac{I}{R}$

b) $V = IR$

c) $I = \frac{V}{R^2}$

d) $R = \frac{V^2}{I}$

222 / 513

Category: Vector quantity, SI unit: A/m².

222. (A) The current density $\vec{j}$ is directly proportional to the electric field $\vec{E}$ for an isotropic substance.
(R) Ohm's law in vector form states that $\vec{j} = \sigma \vec{E}$, where $\sigma$ is the conductivity of the material.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

223 / 513

Category: Electric Resistance

223. The specific resistance ($\rho$) of a material is given by:

a) $\rho = \frac{l}{RA}$

b) $\rho = \frac{Rl}{A}$

c) $\rho = R \cdot \frac{A}{l}$

d) $\rho = \frac{V}{I}$

224 / 513

Category: Relation between drift velocity, current, and resistance.

224. A uniform wire of length 10 m and resistance 5 $\Omega$ has an electric field of 2 V/m established along it. What is the potential difference across the wire?

a) 5 V

b) 10 V

c) 15 V

d) 20 V

225 / 513

Category: Behavior of free electrons in conductors.

225. (A) The drift velocity of electrons in a conductor is directly proportional to the applied electric field.
(R) The mean free path of electrons decreases with an increase in temperature.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

226 / 513

Category: Electric current, measured as the rate of flow of charge.

226. A wire carries a current of 5 A. If the charge of an electron is $1.6 \times 10^{-19}$ C, how many electrons pass through a cross-section of the wire in 2 minutes?

a) $3.75 \times 10^{20}$

b) $3.75 \times 10^{21}$

c) $7.50 \times 10^{20}$

d) $7.50 \times 10^{21}$

227 / 513

Category: Electric conduction in metals.

227. (A) The drift velocity of electrons in a metal decreases with an increase in temperature.
(R) At higher temperatures, the thermal vibrations of the lattice ions increase, leading to more frequent collisions and reduced relaxation time.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

228 / 513

Category: Rate at which electrons move under an electric field.

228. (A) The drift velocity of electrons in a conductor is directly proportional to the applied electric field.
(R) The mobility of electrons ($\mu_e$) is defined as $\mu_e = \frac{v_d}{E}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

229 / 513

Category: Ratio of potential difference to current.

229. What is the ratio of potential difference to current called?

a) Electric conductance

b) Dynamic resistance

c) Specific resistance

d) Electric resistance

230 / 513

Category: Non-ohmic conductors.

230. (A) The dynamic resistance of a semiconductor diode decreases as the applied forward bias voltage increases beyond the threshold voltage.
(R) In a forward-biased semiconductor diode, the current increases exponentially with the applied voltage, causing the slope of the $V-I$ curve to steepen.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

231 / 513

Category: Electric Resistance

231. A 220 V, 100 W bulb is connected to a 110 V supply. What is the power consumed by the bulb under this condition?

a) 50 W

b) 100 W

c) 25 W

d) 200 W

232 / 513

Category: Ratio of potential difference to current.

232. A conductor has a resistance of 10 ohms at room temperature. If the potential difference across it is increased such that the current flowing through it becomes 3 times the initial current, what will be the new resistance of the conductor if the temperature remains constant?

a) 30 ohms

b) 10 ohms

c) 3.33 ohms

d) 0.1 ohms

233 / 513

Category: Ohm’s Law in Vector Form

233. For an isotropic material, if the current density $\vec{j}$ is doubled, what happens to the electric field $\vec{E}$, assuming all other conditions remain unchanged?

a) The electric field $\vec{E}$ becomes zero.

b) The electric field $\vec{E}$ doubles.

c) The electric field $\vec{E}$ halves.

d) The electric field $\vec{E}$ quadruples.

234 / 513

Category: Current density in vector form.

234. The current density $\vec{j}$ in a cylindrical conductor varies radially as $\vec{j}(r) = 5r^2 \hat{z}$ A/m$^2$, where $r$ is the radial distance from the axis. The conductor has a radius of 2 m. What is the total current through the conductor if the cross-section is perpendicular to $\hat{z}$?

a) 10$\pi$ A

b) 20$\pi$ A

c) 30$\pi$ A

d) 40$\pi$ A

235 / 513

Category: Role of free electrons in conduction.

235. A copper wire carries a current of 2 A. If the cross-sectional area of the wire is $1 \times 10^{-6}$ m$^2$ and the number density of free electrons is $8.5 \times 10^{28}$ per m$^3$, what is the drift velocity of the electrons?

a) $1.47 \times 10^{-4}$ m/s

b) $2.94 \times 10^{-4}$ m/s

c) $7.35 \times 10^{-5}$ m/s

d) $3.68 \times 10^{-5}$ m/s

236 / 513

Category: Flow of charge (electrons) in a conductor.

236. A steady current of 2 A flows through a conductor for 5 minutes. How much charge passes through the conductor in this time?

a) 1200 C

b) 600 C

c) 300 C

d) 150 C

237 / 513

Category: Mobility of Electrons

237. (A) The drift velocity of electrons in a conductor is directly proportional to the applied electric field.
(R) According to the relation $v_d = \mu_e E$, mobility $\mu_e$ is constant for a given material at a fixed temperature.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

238 / 513

Category: Ohm’s Law

238. (A) The $V-I$ graph for a conductor is linear only if the physical state of the conductor remains unchanged.
(R) For metallic conductors, resistance $R$ increases with temperature due to increased collisions between electrons and lattice ions.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

239 / 513

Category: Electric Current

239. A conductor carries a current of 2 amperes. How many electrons pass through its cross-section in 5 seconds?

a) $31.25 \times 10^{18}$ electrons

b) $62.5 \times 10^{18}$ electrons

c) $125 \times 10^{18}$ electrons

d) $7.81 \times 10^{18}$ electrons

240 / 513

Category: Relation between drift velocity, current, and resistance.

240. A copper wire of cross-sectional area $1.5 \times 10^{-6} m^2$ carries a current of 2 A. If the free-electron density in copper is $8.4 \times 10^{28} m^{-3}$, calculate the drift velocity of electrons. ($e = 1.6 \times 10^{-19} C$)

a) $9.92 \times 10^{-5} m/s$

b) $1.24 \times 10^{-4} m/s$

c) $7.45 \times 10^{-5} m/s$

d) $5.68 \times 10^{-4} m/s$

241 / 513

Category: Resistance for non-ohmic components.

241. A diode has the following $V-I$ characteristic curve. If the current increases rapidly with a small change in voltage but then saturates at higher voltages, which statement is true about its resistance?

a) The resistance remains constant throughout the entire range of applied voltage.

b) The resistance decreases initially and then increases at higher voltages.

c) The resistance increases initially and then decreases at higher voltages.

d) The resistance is always zero.

242 / 513

Category: Mobility of Electrons

242. How does the mobility of electrons change if the temperature of a semiconductor increases, keeping all other factors constant?

a) It increases because thermal energy enhances electron motion.

b) It decreases due to increased scattering from lattice vibrations.

c) It remains unchanged as temperature does not affect mobility.

d) It first increases then decreases beyond a critical temperature.

243 / 513

Category: Relation between drift velocity, current, and resistance.

243. (A) If the potential difference across a conductor is doubled, the drift velocity of electrons will also double.
(R) The drift velocity $v_d$ is directly proportional to the electric field $E$, and $E$ is directly proportional to the potential difference $V$ for a given conductor.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

244 / 513

Category: Resistance for non-ohmic components.

244. For a non-ohmic component, if the potential difference increases from 2V to 4V and the current changes from 1A to 3A, what is the dynamic resistance?

a) 0.5 Ω

b) 1 Ω

c) 1.5 Ω

d) 2 Ω

245 / 513

Category: Power dissipation in resistive circuits.

245. Two resistors of powers $P_1 = 30 W$ and $P_2 = 60 W$ are connected in parallel. What is the total power dissipated in the combination?

a) 20 W

b) 45 W

c) 90 W

d) 180 W

246 / 513

Category: Series and parallel combinations of resistors.

246. (A) The equivalent resistance of two resistors in parallel is always less than the smallest individual resistance.
(R) In a parallel combination, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

247 / 513

Category: Resistivity as a material property.

247. (A) The resistivity of a material depends on the charge carrier density and relaxation time of the electrons.
(R) According to the relation $\rho = \frac{m}{ne^2 \tau}$, resistivity is inversely proportional to both electron density $n$ and relaxation time $\tau$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

248 / 513

Category: Commercial Units of Electricity Consumption

248. An electric heater rated at 220 V and 1100 W is used for 4 hours daily. If the resistance of the heater is halved and the voltage remains the same, how much more will it cost in 15 days at \$0.12 per kW-h compared to the original setup?

a) \$3.96

b) \$7.92

c) \$15.84

d) \$23.76

249 / 513

Category: Derivation of Ohm’s Law

249. (A) The resistance of a wire depends on its length and cross-sectional area.
(R) Resistance is given by $R = \rho \frac{l}{A}$, where $\rho$ is resistivity, $l$ is length, and $A$ is cross-sectional area.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

250 / 513

Category: Current Density

250. A copper wire with a cross-sectional area of $3.0 \times 10^{-6} \, m^2$ carries a current of 15 A. What is the current density in the wire?

a) $1.5 \times 10^6 \, A \, m^{-2}$

b) $3.0 \times 10^6 \, A \, m^{-2}$

c) $5.0 \times 10^6 \, A \, m^{-2}$

d) $7.5 \times 10^6 \, A \, m^{-2}$

251 / 513

Category: Directional flow of charge.

251. The charge flowing through a conductor varies with time as $q(t) = 3t^2 + 2t + 1$ (where $q$ is in coulombs and $t$ is in seconds). What is the instantaneous current at $t = 2$ s?

a) 10 A

b) 12 A

c) 14 A

d) 16 A

252 / 513

Category: Mobility of Electrons

252. A copper wire has a current density of $2.5 \times 10^6 \, \text{A/m}^2$ when an electric field of $0.05 \, \text{V/m}$ is applied. If the number density of conduction electrons is $8.5 \times 10^{28} \, \text{m}^{-3}$, what is the mobility of electrons in this wire?

a) $18.4 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1}$

b) $36.8 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1}$

c) $73.6 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1}$

d) $9.2 \, \text{cm}^2 \, \text{V}^{-1} \, \text{s}^{-1}$

253 / 513

Category: Combinations of Resistances

253. A $2\Omega$ resistor is connected in series with a parallel combination of $3\Omega$ and $6\Omega$ resistors. What is the total equivalent resistance?

a) $3\Omega$

b) $4\Omega$

c) $5\Omega$

d) $6\Omega$

254 / 513

Category: V-I graph for metallic conductors.

254. (A) The V-I graph of a metallic conductor is always linear.
(R) The resistance of a metallic conductor remains constant regardless of the current passing through it.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

255 / 513

Category: Resistance depends on length and cross-sectional area.

255. Two wires of the same material have lengths in the ratio 3:2 and diameters in the ratio 4:5. What is the ratio of their resistances?

a) $4:5$

b) $12:25$

c) $75:32$

d) $16:25$

256 / 513

Category: Rate at which electrons move under an electric field.

256. What is the relationship between current density ($j$), number density of electrons ($n$), electron charge ($e$), and drift velocity ($v_d$)?

a) $j = \frac{n}{ev_d}$

b) $j = ne^2v_d$

c) $j = nev_d$

d) $j = \frac{nev_d}{2}$

257 / 513

Category: Flow of charge (electrons) in a conductor.

257. An electric field of $0.5 \, \text{V/m}$ is applied to a conductor, causing electrons to drift. If the electron mobility is $4 \times 10^{-3} \, \text{m}^2/\text{V}\cdot\text{s}$, what is the relaxation time of the electrons? (Mass of electron $= 9.1 \times 10^{-31} \, \text{kg}$, charge of electron $= 1.6 \times 10^{-19} \, \text{C}$)

a) $1.1375 \times 10^{-14} \, \text{s}$

b) $2.275 \times 10^{-14} \, \text{s}$

c) $4.55 \times 10^{-14} \, \text{s}$

d) $9.1 \times 10^{-14} \, \text{s}$

258 / 513

Category: V-I graph for metallic conductors.

258. If a current of 2 A flows through a metallic conductor with resistance 5 $\Omega$, what is the potential difference across it?

a) 5 V

b) 7.5 V

c) 10 V

d) 12.5 V

259 / 513

Category: Colour Code of Carbon Resistors

259. A carbon resistor has the colour code Green, Blue, Red, Gold. What is the range of possible resistance values considering the tolerance?

a) 5000 $\Omega$ to 6000 $\Omega$

b) 5320 $\Omega$ to 5880 $\Omega$

c) 5400 $\Omega$ to 5800 $\Omega$

d) 5200 $\Omega$ to 6000 $\Omega$

260 / 513

Category: Ohm’s Law

260. If a graph is plotted between $V$ (potential difference) and $I$ (current) for an ohmic resistor, what shape should it have?

a) Parabola

b) Hyperbola

c) Straight line passing through origin

d) Circle

261 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

261. In the experimental verification of Ohm's law, what does the slope of the $I$ vs. $V$ graph represent?

a) Reciprocal of resistance

b) Current flowing through the resistor

c) Potential difference across the resistor

d) Resistance of the resistor

262 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

262. A p-n junction diode has the following data points for its $V-I$ curve: At $V_1 = 0.5\,V$, $I_1 = 5\,mA$ and at $V_2 = 0.7\,V$, $I_2 = 20\,mA$. What is its dynamic resistance in this region?

a) $40\,\Omega$

b) $25\,\Omega$

c) $13.33\,\Omega$

d) $10\,\Omega$

263 / 513

Category: Series and parallel combinations of resistors.

263. (A) The equivalent resistance of three identical resistors connected in parallel is always less than the smallest individual resistance.
(R) In a parallel combination, the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

264 / 513

Category: Current density at a point in a conductor.

264. (A) The current density $\vec{j}$ at a point in a conductor is independent of the cross-sectional area of the conductor when the current $I$ is constant.
(R) For a given material with free-electron density $n$ and charge $e$, the drift velocity $v_d$ depends only on the current density $\vec{j}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

265 / 513

Category: Specific Resistance or Electrical Resistivity

265. What is the SI unit of specific resistance (\$\rho\$)?

a) Ohm-second (\$\Omega \text{-s}\$)

b) Ohm-metre (\$\Omega \text{-m}\$)

c) Siemens per metre (S/m)

d) Volt-ampere (\$V \cdot A\$)

266 / 513

Category: Mobility of Electrons

266. What is the definition of electron mobility?

a) The speed at which electrons move in a conductor without any electric field

b) The drift velocity of electrons per unit magnetic field

c) The drift velocity of electrons per unit electric field

d) The number density of free electrons in a conductor

267 / 513

Category: Directional flow of charge.

267. Why is electric current considered a scalar quantity?

a) Because it has both magnitude and direction

b) Because it follows the parallelogram law of addition

c) Because it does not follow vector laws of addition

d) Because it is measured in amperes

268 / 513

Category: Resistance in terms of fundamental unit

268. A cylindrical conductor has its length doubled and cross-sectional area halved while keeping all other parameters like electron density and relaxation time constant. How does its resistance change?

a) Resistance becomes half

b) Resistance doubles

c) Resistance becomes four times

d) Resistance remains unchanged

269 / 513

Category: Power dissipation in resistive circuits.

269. A resistor of $10 \Omega$ is connected to a voltage source of $20 V$. What is the power dissipated in the resistor?

a) 2 W

b) 20 W

c) 40 W

d) 200 W

270 / 513

Category: Electric current, measured as the rate of flow of charge.

270. What is the SI unit of electric current?

a) Volt

b) Ohm

c) Ampere

d) Coulomb

271 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

271. In an experiment to verify Ohm’s law, a graph of current (\textit{I}) versus potential difference (\textit{V}) is plotted for a resistor. If the graph is a straight line passing through the origin, what does its slope represent?

a) Resistance of the resistor

b) Reciprocal of resistance

c) Current flowing through the resistor

d) Power dissipated in the resistor

272 / 513

Category: Electric Resistance

272. An iron block has dimensions $2 \, \text{cm} \times 2 \, \text{cm} \times 10 \, \text{cm}$ and resistivity $9.68 \times 10^{-8} \, \Omega \cdot m$. What is its resistance along the longest side?

a) $2.42 \times 10^{-5} \, \Omega$

b) $9.68 \times 10^{-8} \, \Omega$

c) $4.84 \times 10^{-6} \, \Omega$

d) $1.21 \times 10^{-5} \, \Omega$

273 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

273. What is the SI unit of electric current?

a) Coulomb

b) Ampere

c) Volt

d) Ohm

274 / 513

Category: Commercial Units of Electricity Consumption

274. A device operates at 200 volts and draws a current of 5 amperes for 4 hours. How many units (kW-h) of electricity does it consume?

a) 4 kW-h

b) 40 kW-h

c) 0.4 kW-h

d) 400 kW-h

275 / 513

Category: Non-ohmic conductors.

275. What is the formula for dynamic resistance in a non-ohmic conductor?

a) $R = \frac{V}{I}$

b) $R = \frac{I}{V}$

c) $R = \frac{\Delta I}{\Delta V}$

d) $R = \frac{\Delta V}{\Delta I}$

276 / 513

Category: Role of free electrons in conduction.

276. A metal wire has a current density of $4 \times 10^6$ A/m$^2$ and a free electron density of $8 \times 10^{28}$ m$^{-3}$. What is the drift velocity of the electrons?

a) $3.125 \times 10^{-3}$ m/s

b) $3.125 \times 10^{-4}$ m/s

c) $6.25 \times 10^{-4}$ m/s

d) $1.5625 \times 10^{-4}$ m/s

277 / 513

Category: Resistance in terms of fundamental unit

277. What are the dimensions of electrical resistance?

a) $[M L T^{-1} A^{-1}]$

b) $[M^2 L T^{-3} A^{-2}]$

c) $[M L^2 T^{-3} A^{-2}]$

d) $[M^{-1} L^{-2} T^3 A^2]$

278 / 513

Category: Resistivity as a material property.

278. A wire with a length of 10 m and a cross-sectional area of $4 \times 10^{-6} \, \text{m}^2$ has a resistance of 2 $\Omega$. What is the resistivity of the material?

a) $5 \times 10^{-7} \, \Omega \cdot \text{m}$

b) $8 \times 10^{-7} \, \Omega \cdot \text{m}$

c) $1 \times 10^{-6} \, \Omega \cdot \text{m}$

d) $2 \times 10^{-6} \, \Omega \cdot \text{m}$

279 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

279. (A) 1 ampere is equal to the flow of $6.25 \times 10^{18}$ electrons per second through a conductor.
(R) 1 coulomb of charge is carried by $6.25 \times 10^{18}$ electrons, and 1 ampere is defined as 1 coulomb per second.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

280 / 513

Category: Series and parallel combinations of resistors.

280. A potential difference of 24 V is applied across a resistor of 12Ω. What is the current flowing through it?

a) 0.5 A

b) 1 A

c) 2 A

d) 4 A

281 / 513

Category: Current density at a point in a conductor.

281. A conductor has a varying cross-sectional area described by $A(x) = A_0(1 + kx)$, where $A_0 = 2 \times 10^{-6} \, m^2$ and $k = 0.1 \, m^{-1}$. If the current density at $x = 0$ is $10^6 \, A/m^2$, what is the total current through the conductor at $x = 0$?

a) 1 A

b) 2 A

c) 3 A

d) 4 A

282 / 513

Category: Ratio of potential difference to current.

282. A conductor has a potential difference of 12 V across its ends and carries a current of 3 A. What is its resistance?

a) 1 \$\Omega\$

b) 2 \$\Omega\$

c) 4 \$\Omega\$

d) 6 \$\Omega\$

283 / 513

Category: Resistance depends on length and cross-sectional area.

283. A cylindrical wire has a resistance of $R$. If its radius is reduced to half of its original value while keeping the length unchanged, what will be its new resistance?

a) 2R

b) 4R

c) R/2

d) R/4

284 / 513

Category: Colour Code of Carbon Resistors

284. (A) A carbon resistor with colour bands Red, Black, Brown, Gold has a resistance value of 200 $\Omega$ with 5\% tolerance.
(R) The colour 'Red' in the first band corresponds to the digit '2', 'Black' in the second band corresponds to '0', and 'Brown' in the third band corresponds to the multiplier $10^1$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

285 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

285. Which of the following devices does NOT obey Ohm's law under normal conditions?

a) Metal wire at low current

b) P-N junction diode

c) Vacuum tube

d) Thermistor

286 / 513

Category: Current density in vector form.

286. (A) The current density $\vec{j}$ in a conductor is always parallel to the applied electric field $\vec{E}$.
(R) For isotropic materials, the relationship between $\vec{j}$ and $\vec{E}$ is given by $\vec{j} = \sigma \vec{E}$, where $\sigma$ is the conductivity.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

287 / 513

Category: Ratio of potential difference to current.

287. Which of the following represents the dimensional formula for electric conductance?

a) $[\text{M L}^2 \text{T}^{-3} \text{A}^{-2}]$

b) $[\text{M}^{-1} \text{L}^{-2} \text{T}^3 \text{A}^{2}]$

c) $[\text{M L}^{-2} \text{T}^{3} \text{A}^{-2}]$

d) $[\text{M}^{-1} \text{L}^{2} \text{T}^{-3} \text{A}^{2}]$

288 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

288. (A) In the absence of an electric field, the average velocity of free electrons in a metal is zero.
(R) The random motion of free electrons due to thermal agitation results in no net displacement over time.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

289 / 513

Category: Power dissipation in resistive circuits.

289. A resistor with a maximum power rating of 25 W has a resistance of $4 \Omega$. What is the maximum voltage that can be applied across it without exceeding the power rating?

a) 5 V

b) 7.5 V

c) 10 V

d) 12.5 V

290 / 513

Category: Electric Resistance

290. A wire of resistance $R$ at $0^\circ C$ is heated to $t^\circ C$. If the temperature coefficient of resistance is $\alpha$, what is the new resistance of the wire?

a) $R (1 + \alpha t)$

b) $R (1 - \alpha t)$

c) $R \alpha t$

d) $R / (1 + \alpha t)$

291 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

291. In a metallic conductor, the mean free path of electrons is $1.5 \times 10^{-7}$ m and the r.m.s. velocity of electrons is $1.2 \times 10^6$ m/s at room temperature. If the temperature is increased by 100\%, what will be the new relaxation time of electrons assuming the mean free path remains unchanged?

a) $1.25 \times 10^{-13}$ s

b) $8.84 \times 10^{-14}$ s

c) $2.50 \times 10^{-13}$ s

d) $6.25 \times 10^{-14}$ s

292 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

292. For a non-ohmic conductor, if the \textit{V-I} curve is nonlinear, how is dynamic resistance calculated at a specific point on the curve?

a) By taking the tangent to the curve at that point and finding its slope

b) By calculating the average resistance over the entire curve

c) By measuring the area under the curve up to that point

d) By dividing total voltage by total current at that point

293 / 513

Category: Electric Current

293. A conductor has a non-uniform cross-sectional area. The current density at a point P is $j$ and the area vector at P makes an angle of 60° with the direction of current. If the total current through the conductor is I, what is the correct expression for the current density $j$?

a) $\frac{I}{A}$

b) $\frac{2I}{A}$

c) $\frac{I}{2A}$

d) $\frac{4I}{A}$

294 / 513

Category: Electric Energy and Power

294. (A) The power dissipated in a resistor is higher when the resistance is lower for a given voltage.
(R) Power $P$ is given by $P = \frac{V^2}{R}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

295 / 513

Category: Flow of charge (electrons) in a conductor.

295. According to free electron theory, what enables metals to conduct electricity efficiently?

a) Strong nuclear forces

b) Presence of positive ions

c) Large number of free electrons

d) High thermal conductivity

296 / 513

Category: Current electricity in daily life

296. How much energy is consumed by a 1500 W heater running for 2 hours? (Given: 1 kW-h = 3.6 \times 10^6 J)

a) 3000 J

b) 10,800,000 J

c) 5400 J

d) 7,200,000 J

297 / 513

Category: Resistance in terms of fundamental unit

297. What are the dimensions of electric conductance?

a) $[M L^2 T^{-3} A^{-2}]$

b) $[M^{-1} L^{-2} T^3 A^2]$

c) $[M L^{-2} T^2 A^{-1}]$

d) $[M^{0} L^{0} T^{0} A^{0}]$

298 / 513

Category: Dynamic Resistance

298. (A) The dynamic resistance of a non-ohmic conductor is always positive because it represents the slope of the $V-I$ curve at any point.

(R) For a non-ohmic conductor, the $V-I$ curve can have regions where the current decreases with increasing voltage.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

299 / 513

Category: V-I graph for metallic conductors.

299. A filament bulb shows a non-linear V-I graph. If the applied voltage is increased, why does the graph deviate from linearity?

a) The resistance decreases with voltage

b) The current becomes zero at high voltage

c) The resistance increases with temperature

d) The conductor turns superconducting

300 / 513

Category: Electric Current

300. (A) The SI unit of electric current is ampere.
(R) Ampere is defined based on the force acting between two current-carrying, parallel conductors.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

301 / 513

Category: Effect of Temperature on Resistivity

301. (A) The resistivity of a pure metal wire increases when its temperature is raised.
(R) The increase in temperature reduces the mean free path of electrons and increases their rms speed.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

302 / 513

Category: Electric Energy and Power

302. An electric heater operates at $220 \text{ V}$ and draws a current of $5 \text{ A}$. How much energy (in kWh) does it consume if left on for 3 hours?

a) 1.65 kWh

b) 3.3 kWh

c) 6.6 kWh

d) 5.5 kWh

303 / 513

Category: Vector quantity, SI unit: A/m².

303. A conductor has a non-uniform circular cross-section with radius varying as $r = r_0(1 + \alpha x)$, where $x$ is the distance along the conductor and $\alpha$ is a constant. If a constant current $I$ flows through it, what is the expression for current density $j(x)$ at any point $x$?

a) $\frac{I}{\pi r_0^2(1 + \alpha x)}$

b) $\frac{I}{\pi r_0^2(1 + \alpha x)^2}$

c) $\frac{I}{2\pi r_0(1 + \alpha x)^2}$

d) $\frac{I}{\pi r_0^2(1 + 2\alpha x)}$

304 / 513

Category: Resistance depends on length and cross-sectional area.

304. A wire has a resistance of $10\,\Omega$. If its radius is reduced to half of its original value without changing its length, what will be its new resistance?

a) $5\,\Omega$

b) $20\,\Omega$

c) $40\,\Omega$

d) $80\,\Omega$

305 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

305. A wire carries a current of 5 A. How much charge flows through the wire in 2 seconds?

a) 2.5 C

b) 5 C

c) 10 C

d) 20 C

306 / 513

Category: Specific Resistance or Electrical Resistivity

306. Two wires, one made of copper ($\rho_{Cu} = 1.72 \times 10^{-8} \Omega m$) and another of aluminium ($\rho_{Al} = 2.63 \times 10^{-8} \Omega m$), have the same resistance. The copper wire has a mass of 5 g. What is the approximate mass of the aluminium wire, given their densities are $8.9 \text{ g/cm}^3$ and $2.7 \text{ g/cm}^3$ respectively?

a) 1.8 g

b) 2.3 g

c) 3.7 g

d) 4.5 g

307 / 513

Category: Relation between drift velocity, current, and resistance.

307. If the applied voltage across a conductor is doubled, what happens to the drift velocity ($v_d$) of the electrons?

a) It becomes half

b) It doubles

c) It becomes four times

d) It remains the same

308 / 513

Category: Electric conduction in metals.

308. A copper wire of radius $r$ carries a current $I$. If the same current flows through an iron wire of the same radius, how does the drift velocity of electrons compare between the two wires? Given: Free electron density of copper ($n_{Cu}$) is higher than that of iron ($n_{Fe}$).

a) Drift velocity is higher in the copper wire.

b) Drift velocity is higher in the iron wire.

c) Drift velocity remains the same in both wires.

d) Cannot be determined without knowing the exact values of $n_{Cu}$ and $n_{Fe}$.

309 / 513

Category: Combinations of Resistances

309. Five resistors, each of resistance $10\Omega$, are available. What is the ratio of the maximum possible resistance to the minimum possible resistance that can be obtained using these resistors?

a) 5

b) 10

c) 15

d) 25

310 / 513

Category: Effect of Temperature on Resistivity

310. What is the temperature coefficient of resistance ($\alpha$) for a metal if its resistance at $0^\circ C$ is $R_0$ and at $t^\circ C$ is $R_t$?

a) $\frac{R_t + R_0}{R_0 \cdot t}$

b) $\frac{R_t - R_0}{R_0}$

c) $\frac{R_t - R_0}{R_0 \cdot t}$

d) $\frac{R_0 - R_t}{R_0 \cdot t}$

311 / 513

Category: Average distance between collisions.

311. (A) The mean free path $\lambda$ of electrons in a conductor decreases with increasing temperature.
(R) At higher temperatures, the r.m.s. velocity $v_{\text{rms}}$ of electrons increases, leading to more frequent collisions.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

312 / 513

Category: Dependence of Resistance on Dimensions

312. Three resistors of resistances $R$, $2R$, and $3R$ are connected in parallel. What is the equivalent resistance of this combination?

a) $\frac{6R}{11}$

b) $\frac{11R}{6}$

c) $\frac{5R}{12}$

d) $\frac{12R}{5}$

313 / 513

Category: Electric Energy and Power

313. (A) A 100 W bulb connected in series with a 60 W bulb will cause the 60 W bulb to glow brighter than when they are connected in parallel.
(R) In a series connection, the power dissipated is proportional to the resistance ($P = I^2 R$), and higher resistance (lower wattage rating) leads to more power dissipation.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

314 / 513

Category: Electric Energy and Power

314. A resistor of $20 \Omega$ is connected to a battery with a potential difference of $10 \text{ V}$. What is the power dissipated in the resistor?

a) 2 W

b) 5 W

c) 10 W

d) 20 W

315 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

315. Which statement about relaxation time (\$\tau\$) is correct?

a) It decreases with increase in temperature

b) It is independent of temperature

c) It increases with increase in temperature

d) It is inversely proportional to the charge of the electron

316 / 513

Category: Average distance between collisions.

316. (A) The average distance between collisions of gas molecules decreases with increasing pressure.
(R) Higher pressure reduces the mean free path of molecules.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

317 / 513

Category: Introduction

317. (A) If a conductor carries a current of 1 ampere, it means $6.25 \times 10^{18}$ electrons are passing through any cross-section of the conductor per second.
(R) An electric current is defined as the flow of charge per unit time, and 1 ampere corresponds to the flow of 1 coulomb of charge per second, where 1 coulomb equals the charge of $6.25 \times 10^{18}$ electrons.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

318 / 513

Category: Series and parallel combinations of resistors.

318. Three resistors of $4 \Omega$, $8 \Omega$, and $16 \Omega$ are connected in parallel. What is their equivalent resistance?

a) $\frac{7}{16} \Omega$

b) $\frac{16}{7} \Omega$

c) $28 \Omega$

d) $2.5 \Omega$

319 / 513

Category: Resistance for non-ohmic components.

319. (A) The dynamic resistance of a diode decreases as the forward bias voltage increases beyond the knee voltage.
(R) For a diode operating in the forward bias region, the rate of increase in current with respect to voltage becomes steeper at higher voltages.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

320 / 513

Category: Electric Current

320. In conventional terms, what defines the direction of electric current?

a) Direction of electron flow

b) Direction of proton flow

c) Opposite to the direction of electron flow

d) Random direction

321 / 513

Category: Colour Code of Carbon Resistors

321. (A) A carbon resistor with colour bands in the sequence Violet, Green, Black, Gold has a resistance value of $75 \Omega \pm 5\%$.
(R) The third band (Black) corresponds to a multiplier of $10^0$, and the fourth band (Gold) indicates a tolerance of $5\%$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

322 / 513

Category: Ohm’s Law in Vector Form

322. (A) The current density $\vec{j}$ is always parallel to the electric field $\vec{E}$ in an isotropic conductor.
(R) According to Ohm’s law in vector form, $\vec{j} = \sigma \vec{E}$, where $\sigma$ is the conductivity of the material.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

323 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

323. A diode has a V-I curve where the change in voltage $\Delta V$ is 1.5 V and the corresponding change in current $\Delta I$ is 0.3 mA. What is the dynamic resistance of the diode at this operating point?

a) 2500 $\Omega$

b) 5000 $\Omega$

c) 7500 $\Omega$

d) 10000 $\Omega$

324 / 513

Category: Combinations of Resistances

324. (A) The equivalent resistance of two resistors $R_1$ and $R_2$ in parallel is always less than the smaller of the two resistances.
(R) In a parallel combination, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

325 / 513

Category: Electric Resistance

325. A wire has a length of 10 m and a cross-sectional area of $2 \times 10^{-6} \, \text{m}^2$. If the resistivity of the material is $5 \times 10^{-7} \, \Omega \text{-m}$, what is the resistance of the wire?

a) 1 \$\Omega\$

b) 2.5 \$\Omega\$

c) 5 \$\Omega\$

d) 10 \$\Omega\$

326 / 513

Category: Relation between drift velocity, current, and resistance.

326. The relation between electric current ($I$), drift velocity ($v_d$), and number density of free electrons ($n$) in a conductor is given by:

a) $I = n v_d / A$

b) $I = n e v_d / A$

c) $I = n e A v_d$

d) $I = n A v_d / e$

327 / 513

Category: Combinations of Resistances

327. Two resistors of $4\Omega$ and $6\Omega$ are connected in parallel. What is their equivalent resistance?

a) $1.5\Omega$

b) $2.4\Omega$

c) $3.0\Omega$

d) $4.0\Omega$

328 / 513

Category: Commercial Units of Electricity Consumption

328. A household has two appliances: a 2000 W air conditioner running for 5 hours and a 100 W bulb running for 10 hours daily. If electricity costs \$0.15 per kW-h, what is the total cost for 30 days?

a) \$45.00

b) \$49.50

c) \$55.50

d) \$60.00

329 / 513

Category: Introduction

329. A wire carries a current of 2 A for 5 seconds. How much charge flows through the wire?

a) 5 C

b) 10 C

c) 15 C

d) 20 C

330 / 513

Category: Effect of Temperature on Resistivity

330. (A) The resistance of a metallic wire increases with temperature.
(R) With rise in temperature, the mean free path of electrons decreases and their root-mean-square speed increases.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

331 / 513

Category: Specific Resistance or Electrical Resistivity

331. (A) The resistivity of a material depends on its dimensions.
(R) Resistivity is defined as $\rho = \frac{R A}{l}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

332 / 513

Category: Derivation of Ohm’s Law

332. If the drift velocity ($v_d\$) of electrons in a conductor is related to the current ($I\$) as $v_d = \frac{I}{Ane}$, where $A\$ is the cross-sectional area,$n\$ is the number density of electrons, and $e\$ is the charge of an electron, what is the correct expression relating acceleration ($a\$) and relaxation time ($\tau\$)?

a) $a\tau = \frac{I}{Ane}$

b) $a\tau = \frac{Ane}{I}$

c) $a\tau = \frac{eV}{ml}$

d) $a\tau = \frac{ml}{eV}$

333 / 513

Category: Effect of Temperature on Resistivity

333. If the mean free path ($\lambda$) of electrons in a metal decreases by half and the root-mean-square speed ($v_{rms}$) doubles, how does the resistivity ($\rho$) change?

a) Remains the same

b) Doubles

c) Quadruples

d) Halves

334 / 513

Category: Mobility of Electrons

334. A uniform electric field of $10 \, \text{V/m}$ is applied across a conductor. If the electron mobility is $5 \times 10^{-3} \, \text{m}^2 \, \text{V}^{-1} \, \text{s}^{-1}$, what is the drift velocity of electrons?

a) $0.005 \, \text{m/s}$

b) $0.05 \, \text{m/s}$

c) $0.5 \, \text{m/s}$

d) $5 \, \text{m/s}$

335 / 513

Category: Behavior of free electrons in conductors.

335. What is the drift velocity of electrons in a conductor when an electric field $E$ is applied?

a) Zero, as electrons move randomly

b) Proportional to the square of the electric field

c) Given by $v_d = \frac{e E \tau}{m}$

d) Equal to the speed of light

336 / 513

Category: Specific Resistance or Electrical Resistivity

336. The dimensions of electrical resistivity are:

a) $[M L^{-1} T^{-3} A^{-2}]$

b) $[M L^3 T^{-3} A^{-2}]$

c) $[M L^2 T^{-2} A^{-1}]$

d) $[M^2 L T^{-3} A^{-2}]$

337 / 513

Category: Introduction

337. If a current of 1 A flows through a conductor, how many electrons pass through it per second?

a) $1.6 \times 10^{-19}$

b) $3.2 \times 10^{19}$

c) $6.25 \times 10^{18}$

d) $1.25 \times 10^{19}$

338 / 513

Category: Current electricity in daily life

338. A 100 W electric bulb is used for 5 hours daily. What is the energy consumed by the bulb in 30 days, in kilowatt-hours?

a) 10 kW-h

b) 12.5 kW-h

c) 15 kW-h

d) 17.5 kW-h

339 / 513

Category: Electric Energy and Power

339. What is the electric power consumed by a device if a current of 2 A flows through it at a potential difference of 220 V?

a) 110 W

b) 220 W

c) 440 W

d) 880 W

340 / 513

Category: Power dissipation in resistive circuits.

340. A circuit consists of three resistors connected in series: $R_1 = 10 \Omega$, $R_2 = 20 \Omega$, and $R_3 = 30 \Omega$. The total voltage across the combination is 120 V. What is the power dissipated by $R_2$?

a) 40 W

b) 60 W

c) 80 W

d) 100 W

341 / 513

Category: Current density in vector form.

341. A conductor has a non-uniform cross-sectional area given by $\vec{A} = 5\hat{i} + 2\hat{j}$ m$^2$. The current density in the conductor is $\vec{j} = 3\hat{i} + 4\hat{j}$ A/m$^2$. What is the total current flowing through the conductor?

a) 10 A

b) 15 A

c) 20 A

d) 23 A

342 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

342. In an experiment to verify Ohm's law, the I-V graph is plotted with I on the X-axis and V on the Y-axis. The slope of the graph is measured between two points (I$_1$, V$_1$) = (2 A, 4 V) and (I$_2$, V$_2$) = (4 A, 8 V). What is the resistance of the resistor?

a) 1 ohm

b) 2 ohms

c) 4 ohms

d) 0.5 ohms

343 / 513

Category: Introduction

343. How many electrons constitute a charge of 1 coulomb?

a) $6.25 \times 10^{17}$ electrons

b) $6.25 \times 10^{18}$ electrons

c) $1.6 \times 10^{19}$ electrons

d) $1.6 \times 10^{-19}$ electrons

344 / 513

Category: Dependence of Resistance on Dimensions

344. (A) The resistance of a wire increases when its length is doubled while keeping the cross-sectional area constant.
(R) Resistance is directly proportional to the length and inversely proportional to the cross-sectional area of the conductor.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

345 / 513

Category: Commercial Units of Electricity Consumption

345. An electric heater rated at 2000 W is used for 3 hours daily. What is the energy consumed in kW-h over 30 days?

a) 60 kW-h

b) 120 kW-h

c) 180 kW-h

d) 240 kW-h

346 / 513

Category: Vector quantity, SI unit: A/m².

346. A wire carries a current of 4 A and has a cross-sectional area of $2 \times 10^{-6}$ m$^2$. If the current density is uniform, what is its magnitude in A/m$^2$?

a) $1 \times 10^6$ A/m$^2$

b) $2 \times 10^6$ A/m$^2$

c) $4 \times 10^6$ A/m$^2$

d) $8 \times 10^6$ A/m$^2$

347 / 513

Category: Specific Resistance or Electrical Resistivity

347. A wire of length 10 m and cross-sectional area $4.0 \times 10^{-7}$ m$^2$ has a resistance of 2.5 $\Omega$. What is the resistivity of the material?

a) $8.0 \times 10^{-8} \Omega \text{m}$

b) $6.25 \times 10^{-7} \Omega \text{m}$

c) $1.0 \times 10^{-7} \Omega \text{m}$

d) $2.5 \times 10^{-6} \Omega \text{m}$

348 / 513

Category: Current density at a point in a conductor.

348. Which of the following correctly describes the direction of current density $\vec{j}$ at a point in a conductor?

a) Opposite to the electric field direction

b) Same as the direction of electron motion

c) Same as the direction of positive charge motion

d) Perpendicular to the cross-sectional area

349 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

349. If a current of 2 A flows through a conductor with a cross-sectional area of 4 m$^2$, what is the current density?

a) 0.25 A/m$^2$

b) 0.5 A/m$^2$

c) 8 A/m$^2$

d) 2 A/m$^2$

350 / 513

Category: Colour Code of Carbon Resistors

350. What does a silver-coloured fourth band indicate on a carbon resistor?

a) 5\% tolerance

b) 10\% tolerance

c) 20\% tolerance

d) No tolerance specified

351 / 513

Category: Vector quantity, SI unit: A/m².

351. According to microscopic Ohm's law in vector form, how is current density $\vec{j}$ related to the electric field $\vec{E}$?

a) $\vec{j} = \rho \vec{E}$

b) $\vec{j} = \frac{\vec{E}}{\rho}$

c) $\vec{j} = \sigma \vec{E}$

d) $\vec{j} = \frac{1}{\sigma} \vec{E}$

352 / 513

Category: Colour Code of Carbon Resistors

352. If a carbon resistor has colour bands: Brown, Black, Red, Gold, what is its resistance value?

a) 100 $\Omega$

b) 10 $\Omega$

c) 1000 $\Omega$

d) 10000 $\Omega$

353 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

353. The mean free path (\$\lambda\$) of electrons in a conductor depends on:

a) Temperature and density of the conductor

b) Only the applied electric field

c) Only the mass of the electron

d) Only the charge of the electron

354 / 513

Category: Electric Energy and Power

354. If a current of $2 \text{ A}$ flows through a $50 \Omega$ resistor for 10 minutes, how much heat is produced?

a) 60 kJ

b) 120 kJ

c) 240 kJ

d) 30 kJ

355 / 513

Category: Electric current, measured as the rate of flow of charge.

355. A wire carries a current of 3 amperes. What is the total charge passing through the cross-section of the wire in 5 seconds?

a) 12 C

b) 15 C

c) 18 C

d) 20 C

356 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

356. What does the mean free path of an electron in a metal represent?

a) Total length of the conductor

b) Distance between two nuclei

c) Average distance between two successive collisions of an electron

d) Time between two collisions

357 / 513

Category: Effect of Temperature on Resistivity

357. Why is nichrome preferred over pure metals for making heating elements?

a) It has lower resistivity than pure metals.

b) Its resistivity decreases significantly with temperature.

c) Its resistivity is high and nearly independent of temperature.

d) Its resistivity becomes negligible at high temperatures.

358 / 513

Category: Dynamic Resistance

358. What is the formula for dynamic resistance?

a) $R = \frac{I}{V}$

b) $R = \frac{\Delta V}{\Delta I}$

c) $R = \frac{V}{I}$

d) $R = \frac{\Delta I}{\Delta V}$

359 / 513

Category: Electric current, measured as the rate of flow of charge.

359. How many electrons flow per second to constitute a current of 1 ampere?

a) $1.6 \times 10^{-19}$

b) $6.25 \times 10^{18}$

c) $3.14 \times 10^{22}$

d) $9.81 \times 10^{15}$

360 / 513

Category: Ratio of potential difference to current.

360. According to Ohm’s law, if the temperature remains constant, what remains unchanged for a conductor?

a) Current

b) Potential difference

c) Resistance

d) Conductance

361 / 513

Category: Resistance depends on length and cross-sectional area.

361. (A) The resistance of a wire increases when its length is doubled while keeping the cross-sectional area constant.
(R) Resistance is directly proportional to the length of the conductor.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

362 / 513

Category: Derivation of Ohm’s Law

362. (A) The drift velocity of electrons in a conductor is directly proportional to the applied electric field.
(R) According to Ohm’s law, the current density in a conductor is directly proportional to the applied electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

363 / 513

Category: Ohm’s Law

363. (A) The resistance $R$ of a conductor remains constant if the temperature does not change.
(R) According to Ohm’s law, $V/I = R$, where $V$ is potential difference and $I$ is current.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

364 / 513

Category: Resistance for non-ohmic components.

364. A p-n junction diode shows no measurable current until the applied voltage reaches 0.6 V. Beyond this, the current increases rapidly with voltage. Which of the following best describes the behavior of the diode's dynamic resistance?

a) Dynamic resistance is constant regardless of voltage.

b) Dynamic resistance decreases as voltage increases beyond 0.6 V.

c) Dynamic resistance increases as voltage increases beyond 0.6 V.

d) Dynamic resistance is zero above 0.6 V.

365 / 513

Category: Current Density

365. What is the formula for current density when current $I$ flows uniformly through a cross-sectional area $A$ of a conductor?

a) $j = I \times A$

b) $j = \frac{A}{I}$

c) $j = \frac{I}{A}$

d) $j = I + A$

366 / 513

Category: Flow of charge (electrons) in a conductor.

366. A steady current of 2 A flows through a conductor for 30 minutes. How many electrons pass through a given cross-section of the conductor during this time? (Charge of electron $= 1.6 \times 10^{-19} \, \text{C}$)

a) $1.125 \times 10^{22}$

b) $2.25 \times 10^{22}$

c) $4.5 \times 10^{22}$

d) $9 \times 10^{22}$

367 / 513

Category: Average distance between collisions.

367. A conductor has electron mean free path $\lambda_1$ at temperature T$_1$. If the temperature is doubled to T$_2$ = 2T$_1$ and the r.m.s. velocity becomes $\sqrt{2}$ times its original value, what happens to the mean free path $\lambda_2$ at T$_2$ if relaxation time becomes half of its original value?

a) Becomes double

b) Becomes half

c) Becomes $1/\sqrt{2}$ times

d) Remains same

368 / 513

Category: Resistance in terms of fundamental unit

368. What is the SI unit of electric conductance?

a) Ohm (\$\Omega\$)

b) Mho (\$\mho\$)

c) Siemens (S)

d) Both b) and c)

369 / 513

Category: Commercial Units of Electricity Consumption

369. Two devices are marked 220 V-40 W and 220 V-100 W respectively. Which device has higher resistance?

a) 220 V-40 W device

b) 220 V-100 W device

c) Both have equal resistance

d) Cannot be determined

370 / 513

Category: Combinations of Resistances

370. (A) The equivalent resistance of two resistors $R_1$ and $R_2$ in parallel is always less than either $R_1$ or $R_2$.
(R) In a parallel combination, the reciprocal of the equivalent resistance is the sum of the reciprocals of individual resistances.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

371 / 513

Category: Electric current, measured as the rate of flow of charge.

371. (A) The SI unit of electric current is ampere (A).
(R) 1 ampere is defined as the flow of 1 coulomb of charge per second.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

372 / 513

Category: V-I graph for metallic conductors.

372. For a metallic wire, when $V = 6 \, \text{V}$, $I = 2 \, \text{A}$. If the wire is stretched to double its original length, what is the new resistance? (Assume uniform cross-section and constant density.)

a) 3 $\Omega$

b) 6 $\Omega$

c) 9 $\Omega$

d) 12 $\Omega$

373 / 513

Category: Commercial Units of Electricity Consumption

373. What is the equivalent of 1 kilowatt-hour in joules?

a) 3600 J

b) 3000000 J

c) $3.6 \times 10^6$ J

d) $3.6 \times 10^5$ J

374 / 513

Category: Directional flow of charge.

374. A conductor carries a current of 5 A. If the charge on an electron is $1.6 \times 10^{-19}$ C, how many electrons pass through a cross-section of the conductor in 8 seconds?

a) $1.25 \times 10^{19}$

b) $2.5 \times 10^{20}$

c) $3.2 \times 10^{18}$

d) $4.0 \times 10^{21}$

375 / 513

Category: Non-ohmic conductors.

375. A p-n junction diode has a voltage-current relationship given by $I = I_0(e^{V/V_T} - 1)$, where $I_0$ is the reverse saturation current and $V_T$ is the thermal voltage. What is the dynamic resistance of the diode at a point where the applied voltage is $V = 2V_T$?

a) $\frac{V_T}{I_0 e}$

b) $\frac{V_T}{I_0 e^2}$

c) $\frac{V_T}{I_0 e^3}$

d) $\frac{V_T}{I_0 e^4}$

376 / 513

Category: Combinations of Resistances

376. A circuit has three resistors: $R_1 = 2\Omega$, $R_2 = 4\Omega$, and $R_3 = 6\Omega$. If $R_1$ is in series with the parallel combination of $R_2$ and $R_3$, what is the equivalent resistance of the entire circuit?

a) $\frac{10}{3}\Omega$

b) $\frac{22}{5}\Omega$

c) $\frac{24}{5}\Omega$

d) $\frac{26}{5}\Omega$

377 / 513

Category: Role of free electrons in conduction.

377. How does the mean free path of free electrons in a metal change if the temperature is increased significantly, assuming all other conditions remain the same?

a) It increases proportionally to the temperature

b) It remains unchanged

c) It decreases

d) It first increases then decreases

378 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

378. In a metallic conductor at room temperature, the mean free path of free electrons is $4 \times 10^{-8}$ m and their thermal velocity is $1 \times 10^5$ m/s. If an electric field of 5 V/m is applied, what is the drift velocity? (Given: $e = 1.6 \times 10^{-19}$ C, $m_e = 9.1 \times 10^{-31}$ kg)

a) $0.17$ m/s

b) $0.35$ m/s

c) $0.70$ m/s

d) $1.40$ m/s

379 / 513

Category: Rate at which electrons move under an electric field.

379. A copper wire of length $10\, \text{m}$ and cross-sectional area $1 \times 10^{-6}\, \text{m}^2$ carries a current of $5\, \text{A}$. If the electron density in copper is $8.4 \times 10^{28}\, \text{m}^{-3}$ and the mobility of electrons is $4.5 \times 10^{-3}\, \text{m}^2 \, \text{V}^{-1} \, \text{s}^{-1}$, what is the electric field applied across the wire?

a) $0.010\, \text{V/m}$

b) $0.083\, \text{V/m}$

c) $0.15\, \text{V/m}$

d) $0.25\, \text{V/m}$

380 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

380. (A) The direction of conventional current is opposite to the direction of electron flow in a conductor.
(R) Conventional current assumes the flow of positive charge carriers, whereas electrons are negatively charged.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

381 / 513

Category: Rate at which electrons move under an electric field.

381. The mobility of electrons in a metal decreases by $20\%$ when the temperature is increased from $300\, \text{K}$ to $350\, \text{K}$. If the initial relaxation time was $3 \times 10^{-14}\, \text{s}$, what is the new relaxation time at the higher temperature?

a) $1.8 \times 10^{-14}\, \text{s}$

b) $2.4 \times 10^{-14}\, \text{s}$

c) $3.0 \times 10^{-14}\, \text{s}$

d) $3.6 \times 10^{-14}\, \text{s}$

382 / 513

Category: Relation between drift velocity, current, and resistance.

382. The current density ($J$) in a conductor is related to the drift velocity ($v_d$) of electrons by:

a) $J = n v_d$

b) $J = n e v_d$

c) $J = e v_d / n$

d) $J = v_d / n e$

383 / 513

Category: Ohm’s Law

383. (A) If two bulbs of power ratings $P_1$ and $P_2$ ($P_1 > P_2$) are connected in series across the same voltage supply, the bulb with rating $P_2$ will glow brighter.
(R) In a series connection, the bulb with higher resistance dissipates more power.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

384 / 513

Category: Relation between drift velocity, current, and resistance.

384. For a conductor with current density $j = 4 \times 10^6 A/m^2$, and free-electron density $n = 5 \times 10^{28} m^{-3}$, what is the drift velocity of electrons? ($e = 1.6 \times 10^{-19} C$)

a) $3.2 \times 10^{-4} m/s$

b) $5 \times 10^{-4} m/s$

c) $6.4 \times 10^{-4} m/s$

d) $8 \times 10^{-4} m/s$

385 / 513

Category: Current Density

385. (A) Current density is a vector quantity.
(R) Current density has both magnitude and direction.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

386 / 513

Category: Non-ohmic conductors.

386. The filament of an incandescent bulb follows the relation $R = R_0[1 + \alpha(T - T_0)]$, where $\alpha$ is the temperature coefficient of resistance. If the power dissipated in the bulb is $P = V^2/R$, and the temperature increases by $100^\circ\text{C}$, how does the dynamic resistance change when the voltage is doubled?

a) It remains unchanged

b) It decreases proportionally

c) It becomes half

d) It increases non-linearly

387 / 513

Category: Average distance between collisions.

387. (A) The mean free path $\lambda$ of electrons in a conductor decreases with increasing temperature.
(R) As temperature increases, the thermal velocity of electrons increases, leading to more frequent collisions and a shorter average distance between collisions.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

388 / 513

Category: Derivation of Ohm’s Law

388. If the drift velocity of electrons in a conductor is $v_d$ and the current through it is $I$, what would happen to the current if the drift velocity doubles while keeping all other parameters constant?

a) The current remains the same.

b) The current becomes half.

c) The current doubles.

d) The current quadruples.

389 / 513

Category: Non-ohmic conductors.

389. Which of the following is an example of a non-ohmic conductor?

a) Copper wire

b) Semiconductor diode

c) Silver wire

d) Aluminum wire

390 / 513

Category: Current density in vector form.

390. If the electric field $\vec{E}$ in a conductor is doubled, what happens to the current density $\vec{j}$ assuming the conductivity $\sigma$ remains constant?

a) The current density halves.

b) The current density doubles.

c) The current density becomes zero.

d) The current density remains unchanged.

391 / 513

Category: Resistivity as a material property.

391. The resistivity $\rho$ of a material is expressed as $\rho = \frac{m}{n e^2 \tau}$, where $m$ is the electron mass, $n$ is the free-electron density, $e$ is the electron charge, and $\tau$ is the relaxation time. If the temperature of the material increases, which of the following best describes the change in conductance $\sigma$ of the material? Assume the free-electron density $n$ remains approximately constant.

a) Conductance increases because $n$ increases

b) Conductance decreases because $\tau$ decreases

c) Conductance remains unchanged as $n$ and $\tau$ compensate

d) Conductance increases because $e$ changes

392 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

392. For a filament bulb, the resistance increases with temperature. If the voltage across the bulb is gradually increased from 0V to 10V, what happens to its dynamic resistance?

a) Dynamic resistance decreases linearly with voltage

b) Dynamic resistance remains constant regardless of voltage

c) Dynamic resistance increases as voltage increases

d) Dynamic resistance first decreases and then increases

393 / 513

Category: Combinations of Resistances

393. A $3 \Omega$ resistor is connected in series with a parallel combination of $6 \Omega$ and $12 \Omega$ resistors. What is the total equivalent resistance of the circuit?

a) $5 \Omega$

b) $7 \Omega$

c) $9 \Omega$

d) $21 \Omega$

394 / 513

Category: Current electricity in daily life

394. (A) A 60 W bulb consumes more power than a 100 W bulb when connected to the same voltage source.
(R) Power dissipated in a resistor is given by $P = \frac{V^2}{R}$, so higher wattage means lower resistance.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

395 / 513

Category: Resistivity as a material property.

395. A cylindrical conductor of length $L$ and radius $r$ carries a current $I$. If the electric field inside the conductor is $E$, what is the resistivity $\rho$ of the material in terms of $E$, $I$, $L$, and $r$?

a) $\frac{E I L}{\pi r^2}$

b) $\frac{E \pi r^2}{I}$

c) $\frac{E I}{\pi r^2 L}$

d) $\frac{E L}{I \pi r^2}$

396 / 513

Category: Current Density

396. (A) The current density at a point in a conductor depends on the direction of flow of positive charges at that point.
(R) Current density is a vector quantity whose direction is the same as the motion of positive charges.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

397 / 513

Category: Directional flow of charge.

397. The rate of charge flow in a circuit varies as $Q(t) = 3t^2 + 2t$ (where $Q$ is in coulombs and $t$ in seconds). What is the instantaneous current at $t = 2 \,s$?

a) 8 A

b) 12 A

c) 14 A

d) 16 A

398 / 513

Category: Electric Resistance

398. The resistance of a conductor at temperature $t$ is given by:

a) $R_t = R_0 (1 - \alpha t)$

b) $R_t = R_0 (1 + \alpha t)$

c) $R_t = R_0 \alpha t$

d) $R_t = \frac{R_0}{1 + \alpha t}$

399 / 513

Category: Resistivity as a material property.

399. (A) The resistivity of copper is lower than that of rubber because copper has a higher free-electron density.
(R) Resistivity depends on the nature of the material and is given by $\rho = \frac{m}{n e^2 \tau}$, where $n$ is the free-electron density.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

400 / 513

Category: Ohm’s Law

400. Under what condition does a conductor not obey Ohm's law?

a) When temperature increases

b) When voltage is doubled

c) When current is halved

d) When material is metallic

401 / 513

Category: Average distance between collisions.

401. If the relaxation time of electrons in a conductor decreases by 25\% when the temperature is increased, while keeping the mean free path constant, what is the percentage change in the r.m.s. velocity of electrons?

a) Decreases by 25\%

b) Increases by 25\%

c) Decreases by 33.3\%

d) Increases by 33.3\%

402 / 513

Category: Resistance depends on length and cross-sectional area.

402. A wire of resistance $R$ is stretched to double its original length while maintaining the same volume. What is the new resistance?

a) $2R$

b) $4R$

c) $R/2$

d) $R/4$

403 / 513

Category: Directional flow of charge.

403. What is the conventional direction of electric current in a conductor?

a) Same as the direction of electron flow

b) Opposite to the direction of electron flow

c) Perpendicular to the direction of electron flow

d) Random and changes with time

404 / 513

Category: Current density in vector form.

404. If the current density $\vec{j}$ is perpendicular to the cross-sectional area $\vec{A}$, how is the total current $I$ calculated?

a) $I = \frac{j}{A}$

b) $I = j + A$

c) $I = j A$

d) $I = j - A$

405 / 513

Category: Dynamic Resistance

405. In a V-I curve for a non-ohmic device, two points P and Q are selected such that PS (change in voltage) is 8\,V and QS (change in current) is 2\,mA. What is the dynamic resistance between these points?

a) 2000\,\Omega

b) 3000\,\Omega

c) 4000\,\Omega

d) 5000\,\Omega

406 / 513

Category: EXPERIMENTAL VERIFICATION OF OHM’S LAW

406. (A) In the experimental verification of Ohm’s law, the graph of current $I$ versus potential difference $V$ is a straight line passing through the origin for an Ohmic resistor.
(R) The slope of the $I-V$ graph gives the value of resistance $R$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

407 / 513

Category: Vector quantity, SI unit: A/m².

407. A material obeys Ohm's law in vector form with conductivity $\sigma$. If an electric field $\vec{E} = E_0\hat{i} + E_0\hat{j}$ is applied, what is the magnitude of the current density $\vec{j}$ produced?

a) $\sigma E_0$

b) $2\sigma E_0$

c) $\sigma E_0\sqrt{2}$

d) $\frac{\sigma E_0}{\sqrt{2}}$

408 / 513

Category: Behavior of free electrons in conductors.

408. Why do electrons in a conductor attain a steady drift velocity under an electric field instead of accelerating indefinitely?

a) Because electrons lose energy due to resistance.

b) Because collisions with ions limit their acceleration.

c) Because the battery provides only a limited voltage.

d) Because electrons have negligible mass.

409 / 513

Category: Resistance for non-ohmic components.

409. Which condition violates Ohm’s law due to changing physical conditions?

a) Current flowing through a copper wire at constant temperature

b) Voltage applied across a resistor at low temperatures

c) Filament of a torch bulb heating up with current

d) A superconductor below its critical temperature

410 / 513

Category: Non-ohmic conductors.

410. Why does the filament of an incandescent bulb not obey Ohm's law when it heats up?

a) Because the filament breaks down at high temperatures.

b) Because the resistance decreases as the temperature increases.

c) Because the resistance increases as the temperature increases.

d) Because the filament becomes superconducting at high temperatures.

411 / 513

Category: Vector quantity, SI unit: A/m².

411. (A) The current density $\vec{j}$ is always parallel to the electric field $\vec{E}$ in any material.
(R) According to Ohm's law in vector form, $\vec{j} = \sigma \vec{E}$, where $\sigma$ is a constant for isotropic materials.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

412 / 513

Category: Electric Resistance

412. (A) The resistance of a wire increases if its length is increased.
(R) Resistance $R$ is directly proportional to the length $l$ of the conductor, given by $R = \rho \frac{l}{A}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

413 / 513

Category: Electric Energy and Power

413. (A) A 60 W bulb glows brighter than a 100 W bulb when connected in series.
(R) In a series connection, the bulb with higher resistance dissipates more power ($P = I^2 R$) and hence glows brighter.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

414 / 513

Category: Electric Resistance

414. A conductor has a resistance of 10 \$\Omega\$ when its length is 2 m and cross-sectional area is $4 \times 10^{-6} \, \text{m}^2$. What is the specific resistance of the material?

a) $1 \times 10^{-5} \, \Omega\text{-m}$

b) $2 \times 10^{-5} \, \Omega\text{-m}$

c) $4 \times 10^{-5} \, \Omega\text{-m}$

d) $8 \times 10^{-5} \, \Omega\text{-m}$

415 / 513

Category: Ohm’s Law in Vector Form

415. An isotropic material with conductivity $\sigma = 4 \times 10^7 \, S/m$ carries an electric field $\vec{E} = 3 \times 10^{-3} \, V/m$. Calculate the magnitude of the current density $\vec{j}$.

a) $1.2 \times 10^2 \, A/m^2$

b) $1.2 \times 10^5 \, A/m^2$

c) $3.0 \times 10^4 \, A/m^2$

d) $4.0 \times 10^7 \, A/m^2$

416 / 513

Category: Current density in vector form.

416. What is the SI unit of current density?

a) $A \, m^{-1}$

b) $A \, m^{2}$

c) $A \, m^{-2}$

d) $A^{-1} \, m^{2}$

417 / 513

Category: Rate at which electrons move under an electric field.

417. How is electron mobility ($\mu_e$) related to drift velocity ($v_d$) and electric field ($E$)?

a) $\mu_e = v_d E$

b) $\mu_e = \frac{E}{v_d}$

c) $\mu_e = \frac{v_d}{E}$

d) $\mu_e = v_d + E$

418 / 513

Category: Current density in vector form.

418. (A) In an isotropic conductor, if the current density $\vec{j}$ is non-uniform and the cross-sectional area $\vec{A}$ is not constant, then the total current $I$ can be determined by integrating the dot product of $\vec{j}$ and $d\vec{A}$ over the surface.
(R) The relationship $\vec{j} = \sigma \vec{E}$ implies that the current density depends only on the electric field $\vec{E}$ and conductivity $\sigma$, regardless of the geometry of the conductor.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

419 / 513

Category: Colour Code of Carbon Resistors

419. (A) A carbon resistor with the colour bands Yellow, Violet, Orange, Gold has a resistance value of 47 k\Omega with a tolerance of 5\%.
(R) The third band (Orange) represents the multiplier $10^3$ for the significant figures 4 and 7.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

420 / 513

Category: Colour Code of Carbon Resistors

420. A resistor with the colour code Brown, Black, Orange, Silver is connected across a 10 V battery. What is the current flowing through the resistor, considering the maximum tolerance?

a) 0.909 mA

b) 1.0 mA

c) 0.833 mA

d) 0.667 mA

421 / 513

Category: Current electricity in daily life

421. A bulb has a power rating of 60 W when connected to a 220 V supply. What is the current flowing through it?

a) 0.27 A

b) 0.50 A

c) 1.20 A

d) 3.67 A

422 / 513

Category: Resistivity as a material property.

422. What is the SI unit of electrical resistivity (\$\rho\$)?

a) Ohm (\$\Omega\$

b) Siemens per metre (S/m)

c) Ohm-metre (\$\Omega\text{-m}\$)

d) Volt per ampere (V/A)

423 / 513

Category: Effect of Temperature on Resistivity

423. For most metals, how does resistance vary with absolute temperature ($T$)?

a) Inversely proportional to $T$

b) Directly proportional to $T$

c) Independent of $T$

d) Proportional to $\sqrt{T}$

424 / 513

Category: Rate at which electrons move under an electric field.

424. What is the formula for drift velocity ($v_d$) of electrons in terms of electric field ($E$), electron charge ($e$), mass ($m$), and relaxation time ($\tau$)?

a) $v_d = \frac{mE}{e\tau}$

b) $v_d = \frac{eE\tau}{m}$

c) $v_d = \frac{E\tau}{me}$

d) $v_d = \frac{me}{E\tau}$

425 / 513

Category: Series and parallel combinations of resistors.

425. (A) When three resistors are connected in series, the equivalent resistance is the sum of individual resistances.
(R) In a series combination, the same current flows through all resistors.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

426 / 513

Category: Electric conduction in metals.

426. Which of the following factors affects the mean free path of electrons in a metal?

a) Only the applied voltage across the conductor

b) Temperature and number of free electrons per unit volume

c) Density of defects and temperature

d) Mass of the electron only

427 / 513

Category: Flow of charge (electrons) in a conductor.

427. (A) In a conductor, the drift velocity of electrons is very small compared to their thermal velocity.
(R) The net current in a conductor is due to the drift of free electrons under an applied electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

428 / 513

Category: Dynamic Resistance

428. On a $V-I$ curve for a diode, two points are taken: $P$ at $(0.5\,V, 2\,mA)$ and $Q$ at $(0.6\,V, 20\,mA)$. What is the dynamic resistance between these points?

a) 4.44 $\Omega$

b) 5.56 $\Omega$

c) 6.67 $\Omega$

d) 7.78 $\Omega$

429 / 513

Category: V-I graph for metallic conductors.

429. Which of the following materials typically shows a linear V-I graph under normal conditions?

a) Copper wire

b) Silicon diode

c) Thermistor \paramagnetic material

430 / 513

Category: Specific Resistance or Electrical Resistivity

430. A cylindrical conductor of length $L$ and cross-sectional area $A$ carries a current $I$. The electric field inside the conductor is uniform and given by $E = \frac{V}{L}$, where $V$ is the potential difference across the conductor. If the resistivity of the material is $\rho$, which of the following expressions correctly represents the dimensions of $\rho$?

a) $[M L^2 T^{-2} A^{-1}]$

b) $[M L^3 T^{-3} A^{-2}]$

c) $[M^{-1} L^{-3} T^3 A^2]$

d) $[M L T^{-3} A^{-1}]$

431 / 513

Category: Ohm’s Law in Vector Form

431. A conductor has resistivity $\rho = 2 \times 10^{-8} \Omega\cdot m$ and carries a current density $\vec{j} = 5 \times 10^6 \, A/m^2$. What is the magnitude of the applied electric field $\vec{E}$ inside the conductor?

a) $50 \, V/m$

b) $100 \, V/m$

c) $200 \, V/m$

d) $250 \, V/m$

432 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

432. An electron in a metal has a relaxation time of $2 \times 10^{-14}$ s at 300 K. If the applied electric field is 1 V/m, what is the drift velocity acquired by the electron? (Given: mass of electron $m_e = 9.1 \times 10^{-31}$ kg, charge $e = 1.6 \times 10^{-19}$ C)

a) $3.52 \times 10^{-5}$ m/s

b) $3.52 \times 10^{-3}$ m/s

c) $1.76 \times 10^{-3}$ m/s

d) $7.04 \times 10^{-3}$ m/s

433 / 513

Category: Ratio of potential difference to current.

433. Which of the following is equivalent to 1 ohm in fundamental SI units?

a) kg$\cdot$m$\cdot$s$^{-2}$$\cdot$A$^{-1}$

b) kg$\cdot$m$^2$$\cdot$s$^{-3}$$\cdot$A$^{-2}$

c) m$^2$$\cdot$kg$\cdot$s$^{-3}$$\cdot$A$^{-1}$

d) s$^{-1}$$\cdot$A$^{-1}$$\cdot$kg$\cdot$m$^2$

434 / 513

Category: Current electricity in daily life

434. A steady current of 2 A flows through a conductor for 5 minutes. How many electrons pass through any cross-section of the conductor during this time?

a) $3.75 \times 10^{20}$

b) $7.50 \times 10^{20}$

c) $3.75 \times 10^{21}$

d) $7.50 \times 10^{21}$

435 / 513

Category: Dynamic Resistance

435. (A) The dynamic resistance of a diode decreases as the current through it increases.
(R) The slope of the V-I curve for a diode becomes steeper as the current increases, indicating a decrease in $\frac{\Delta V}{\Delta I}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

436 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

436. If a charge of 12 Coulombs flows through a point in a circuit in 3 seconds, what is the current?

a) 1 A

b) 2 A

c) 3 A

d) 4 A

437 / 513

Category: Specific Resistance or Electrical Resistivity

437. (A) The resistivity of a material depends on the free-electron density $n$ and relaxation time $\tau$ of the material.
(R) From the relation $\rho = \frac{m}{n e^2 \tau}$, it is clear that resistivity varies inversely with both $n$ and $\tau$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

438 / 513

Category: Introduction

438. If a total charge of 12 C flows through a conductor in 3 seconds, what is the current in the conductor?

a) 2 A

b) 3 A

c) 4 A

d) 5 A

439 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

439. (A) The dynamic resistance of a diode is determined by the slope of the V-I curve at a specific operating point.
(R) Dynamic resistance is given by the ratio $\frac{\Delta V}{\Delta I}$ where $\Delta V$ and $\Delta I$ are small changes around the operating point.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

440 / 513

Category: Measured in amperes (1 Ampere = 1 Coulomb/second).

440. How many electrons flow per second to constitute a current of 1 ampere?

a) $6.25 \times 10^{18}$

b) $3.12 \times 10^{18}$

c) $1.6 \times 10^{19}$

d) $3.2 \times 10^{18}$

441 / 513

Category: Dynamic Resistance

441. If the change in potential difference $\Delta V$ is 5 volts and the change in current $\Delta I$ is 1 ampere, what is the dynamic resistance?

a) $10 \, \Omega$

b) $5 \, \Omega$

c) $0.2 \, \Omega$

d) $1 \, \Omega$

442 / 513

Category: Vector quantity, SI unit: A/m².

442. In a conductor with electron density $n$, if the current density is $j$ and the drift velocity is $v_d$, what happens to $v_d$ when the conductor is stretched to double its length keeping volume constant?

a) Becomes $v_d/2$

b) Becomes $2v_d$

c) Remains same

d) Becomes $4v_d$

443 / 513

Category: Resistance in terms of fundamental unit

443. What are the dimensions of specific conductance $\sigma$ in terms of mass ($M$), length ($L$), time ($T$), and current ($A$)?

a) $[M L^3 T^{-3} A^{-2}]$

b) $[M^{-1} L^{-3} T^{3} A^{2}]$

c) $[M^2 L^4 T^{-4} A^{-2}]$

d) $[M^{-2} L^{-4} T^4 A^2]$

444 / 513

Category: Behavior of free electrons in conductors.

444. If the relaxation time of electrons in a conductor doubles while the electric field remains constant, how does the drift velocity change?

a) It halves

b) It doubles

c) It quadruples

d) It remains unchanged

445 / 513

Category: Power dissipation in resistive circuits.

445. Two resistors of resistances $5 \Omega$ and $10 \Omega$ are connected in parallel to a 20 V battery. Find the total power dissipated in the circuit.

a) 40 W

b) 80 W

c) 100 W

d) 120 W

446 / 513

Category: Ratio of potential difference to current.

446. What is the SI unit of electric resistance?

a) Volt

b) Ampere

c) Ohm

d) Siemens

447 / 513

Category: Ohm’s Law

447. A conductor obeys Ohm's law only if:

a) Its resistance changes with applied voltage.

b) Its $V-I$ graph is a straight line passing through the origin.

c) It is made of a non-metallic material.

d) The current decreases with increasing voltage.

448 / 513

Category: Electric Resistance

448. A bulb rated $100 \, \text{W}$ at $220 \, \text{V}$ is connected to a $110 \, \text{V}$ supply. What is the power consumed by the bulb?

a) $25 \, \text{W}$

b) $50 \, \text{W}$

c) $100 \, \text{W}$

d) $200 \, \text{W}$

449 / 513

Category: Current density at a point in a conductor.

449. A conductor has a non-uniform cross-section with varying current density $\vec{j} = 3x \, \hat{i} \, A \, m^{-2}$, where $x$ is measured in meters. What is the total current through a cross-sectional area from $x = 0$ to $x = 2 \, m$ if the width of the conductor is constant at $1 \, m$ along the y-axis?

a) $4 \, A$

b) $6 \, A$

c) $9 \, A$

d) $12 \, A$

450 / 513

Category: Rate at which electrons move under an electric field.

450. If an electron has a relaxation time $\tau = 1 \times 10^{-14} \, \text{s}$ and the mass of the electron is $9.1 \times 10^{-31} \, \text{kg}$, what is its mobility $\mu_e$?

a) $1.6 \times 10^{-3} \, \text{m}^2 \text{V}^{-1} \text{s}^{-1}$

b) $1.76 \times 10^{-3} \, \text{m}^2 \text{V}^{-1} \text{s}^{-1}$

c) $9.1 \times 10^{-3} \, \text{m}^2 \text{V}^{-1} \text{s}^{-1}$

d) $1 \times 10^{-3} \, \text{m}^2 \text{V}^{-1} \text{s}^{-1}$

451 / 513

Category: Relation between drift velocity, current, and resistance.

451. (A) The drift velocity of electrons in a conductor increases when the current through it increases.
(R) Drift velocity $v_d$ is directly proportional to the current $I$ as per the relation $I = n e A v_d$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

452 / 513

Category: Role of free electrons in conduction.

452. (A) The drift velocity of electrons in a conductor increases with an increase in temperature.

(R) At higher temperatures, the relaxation time of electrons decreases due to increased collisions with positive ions.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

453 / 513

Category: Vector quantity, SI unit: A/m².

453. If the current \$I\$ flows perpendicularly through a cross-sectional area \$A\$, what is the relation between \$I\$, current density \$j\$, and \$A\$?

a) $I = j + A$

b) $I = \frac{j}{A}$

c) $I = j \cdot A$

d) $I = j - A$

454 / 513

Category: Current electricity in daily life

454. An appliance running at 220 V draws a current of 4 A for 3 hours. If electricity costs Rs.0.50 per kW-h, what is the cost of running the appliance?

a) Rs.1.20

b) Rs.1.32

c) Rs.1.44

d) Rs.1.56

455 / 513

Category: Non-ohmic conductors.

455. What type of graph represents the V-I characteristics of a non-ohmic conductor?

a) Straight line passing through origin

b) Parabola

c) Hyperbola

d) Non-linear curve

456 / 513

Category: Electric Resistance

456. (A) The resistance of a wire remains unchanged when it is bent into any shape.
(R) Bending a wire does not alter its length, cross-sectional area, or the material properties affecting resistance.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

457 / 513

Category: Effect of Temperature on Resistivity

457. Which of the following statements is true regarding the resistivity of pure metals and alloys as temperature increases?

a) Resistivity of pure metals decreases with temperature, while alloys show no change.

b) Both pure metals and alloys show a decrease in resistivity with increasing temperature.

c) Pure metals show an increase in resistivity with temperature, while alloys show a much smaller increase.

d) Alloys have zero resistivity at absolute zero, unlike pure metals.

458 / 513

Category: Rate at which electrons move under an electric field.

458. (A) The drift velocity of electrons in a conductor decreases with increasing temperature.
(R) The relaxation time $\tau$ decreases with temperature, reducing the mobility of electrons.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

459 / 513

Category: Average distance between collisions.

459. How does the relaxation time ($\tau$) of electrons in a metal change as the temperature increases?

a) It increases linearly with temperature

b) It decreases with temperature

c) It remains constant

d) It first increases then decreases

460 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

460. A copper wire has electron mobility $\mu_e = 4.5 \times 10^{-3}$ m$^2$ V$^{-1}$ s$^{-1}$. What is the drift velocity of electrons when an electric field of 2 Vm$^{-1}$ is applied across the wire?

a) $4.5 \times 10^{-3}$ m/s

b) $6.0 \times 10^{-3}$ m/s

c) $9.0 \times 10^{-3}$ m/s

d) $12.0 \times 10^{-3}$ m/s

461 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

461. (A) The mean free path of electrons in a metal decreases with an increase in temperature.
(R) As temperature increases, the root mean square velocity ($v_{rms}$) of electrons increases, leading to more frequent collisions.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

462 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

462. What is dynamic resistance defined as?

a) $\frac{V}{I}$

b) $\frac{I}{V}$

c) $\frac{\Delta I}{\Delta V}$

d) $\frac{\Delta V}{\Delta I}$

463 / 513

Category: Commercial Units of Electricity Consumption

463. (A) The commercial unit of electrical energy is kilowatt-hour (kW-h).
(R) Kilowatt-hour represents the energy consumed when a device with a power rating of 1 kilowatt operates for 1 hour.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

464 / 513

Category: Combinations of Resistances

464. Three resistors of $2\Omega$, $3\Omega$, and $5\Omega$ are connected in series. What is the equivalent resistance?

a) $5\Omega$

b) $7\Omega$

c) $10\Omega$

d) $15\Omega$

465 / 513

Category: Role of free electrons in conduction.

465. The mean free path of electrons in a metal is $4 \times 10^{-8}$ m, and their thermal velocity is $1 \times 10^5$ m/s. What is the relaxation time of these electrons?

a) $4 \times 10^{-14}$ s

b) $2 \times 10^{-13}$ s

c) $4 \times 10^{-13}$ s

d) $8 \times 10^{-13}$ s

466 / 513

Category: Electric conduction in metals.

466. What is the charge-carrier responsible for electric conduction in metals?

a) Protons

b) Neutrons

c) Electrons

d) Both positive and negative ions

467 / 513

Category: Derivation of Ohm’s Law

467. A conductor has a resistance $R$ when its length is $l$ and cross-sectional area is $A$. If the conductor is stretched to twice its original length while maintaining the same volume, what will be its new resistance?

a) $R$

b) $2R$

c) $4R$

d) $8R$

468 / 513

Category: Electric Current

468. A cylindrical conductor has a current density of $4 \times 10^6 \, \text{A/m}^2$. If the cross-sectional area of the conductor is $2 \times 10^{-6} \, \text{m}^2$, what is the current flowing through it?

a) 2 A

b) 4 A

c) 6 A

d) 8 A

469 / 513

Category: Non-ohmic conductors.

469. A vacuum diode has a non-linear V-I characteristic curve. If the dynamic resistance at a certain point on the curve is 200 $\Omega$, what does this imply?

a) The resistance remains constant regardless of the applied voltage.

b) For every 200 V increase in voltage, the current decreases by 1 A.

c) For every 200 V increase in voltage, the current increases by 1 A.

d) The diode behaves like an ohmic conductor at this point.

470 / 513

Category: Electric Current

470. A wire carries a current of 2 A. How much charge passes through a cross-section of the wire in 5 minutes?

a) 10 C

b) 100 C

c) 600 C

d) 1200 C

471 / 513

Category: Current Density

471. (A) The current density $\vec{j}$ is always directed opposite to the drift velocity of electrons in a conductor.
(R) The direction of current density is conventionally taken as the direction of motion of positive charges, while electrons carry negative charge.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

472 / 513

Category: Specific Resistance or Electrical Resistivity

472. Which of the following statements about resistivity is correct?

a) Resistivity decreases with an increase in length of the conductor.

b) Resistivity increases with an increase in cross-sectional area of the conductor.

c) Resistivity is independent of the dimensions of the conductor.

d) Resistivity changes if the shape of the conductor is altered.

473 / 513

Category: Non-ohmic conductors.

473. In the V-I characteristic curve of a p-n junction diode, why does the current not increase linearly beyond a certain voltage?

a) Because the diode explodes after reaching the threshold voltage.

b) Because the diode starts emitting light instead of conducting.

c) Due to saturation effects and semiconductor junction properties.

d) Because the diode follows Ohm's law beyond the threshold voltage.

474 / 513

Category: Current density in vector form.

474. For a non-uniform current density $\vec{j}(x, y, z)$, which of the following correctly represents the total current $I$ passing through a surface $S$?

a) $I = \int_S |\vec{j}| \, dA$

b) $I = \int_S \vec{j} \cdot d\vec{A}$

c) $I = \int_S \sigma \vec{E} \cdot d\vec{A}$

d) $I = \int_V \vec{j} \cdot dV$

475 / 513

Category: Power dissipation in resistive circuits.

475. A $10 \Omega$ resistor and a $20 \Omega$ resistor are connected in series to a 60 V supply. What is the total power dissipated by the combination?

a) 80 W

b) 120 W

c) 160 W

d) 200 W

476 / 513

Category: Directional flow of charge.

476. How much charge flows through a conductor in one second when the current is 1 ampere?

a) 1 coulomb

b) 6.25 $\times$ 10$^{18}$ coulombs

c) 1.6 $\times$ 10$^{-19}$ coulombs

d) 0.5 coulombs

477 / 513

Category: Current density in vector form.

477. What is the relationship between current density $\vec{j}$ and electric field $\vec{E}$ for an isotropic substance?

a) $\vec{j} = \rho \vec{E}$

b) $\vec{j} = \frac{\vec{E}}{\sigma}$

c) $\vec{j} = \sigma \vec{E}$

d) $\vec{j} = \frac{\sigma}{\vec{E}}$

478 / 513

Category: Mobility of Electrons

478. The relationship between drift velocity $v_d$, electron mobility $\mu_e$, and electric field $E$ is:

a) $v_d = \mu_e / E$

b) $v_d = \mu_e + E$

c) $v_d = \mu_e E$

d) $v_d = \mu_e - E$

479 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

479. If the root mean square velocity of electrons in a conductor increases by a factor of 2, how does the relaxation time change?

a) Increases by a factor of 2

b) Decreases by a factor of 2

c) Remains unchanged

d) Increases by a factor of 4

480 / 513

Category: Current density at a point in a conductor.

480. What is the current density $j$ in a conductor of cross-sectional area $A = 4 \times 10^{-6} \, m^2$ carrying a current $I = 2 \, A$ uniformly distributed across its cross-section?

a) $1 \times 10^5 \, A \, m^{-2}$

b) $5 \times 10^5 \, A \, m^{-2}$

c) $2 \times 10^6 \, A \, m^{-2}$

d) $8 \times 10^5 \, A \, m^{-2}$

481 / 513

Category: Resistance in terms of fundamental unit

481. What are the fundamental SI units of resistance?

a) kg·m·s$^{-2}$

b) kg·m$^2$·A$^{-2}$·s$^{-3}$

c) A·s$^{-1}$

d) m$^2$·kg·s$^{-3}$

482 / 513

Category: Electric conduction in metals.

482. A metallic wire of resistance $R$ at temperature $T$ is heated such that its resistivity increases by 20\%. If the length and cross-sectional area remain unchanged, what is the new resistance?

a) $0.8R$

b) $1.2R$

c) $1.44R$

d) $R$ remains unchanged.

483 / 513

Category: Effect of Temperature on Resistivity

483. A metal’s resistivity increases when the temperature rises because:

a) Mean free path increases while electron speed remains constant.

b) Electron speed decreases while mean free path increases.

c) Both mean free path and electron speed increase.

d) Mean free path decreases while electron speed increases.

484 / 513

Category: Directional flow of charge.

484. Two currents $I_1 = 4\,A$ and $I_2 = 3\,A$ meet at an angle of $90^\circ$. What is the resultant current after they combine?

a) 5 A

b) 7 A

c) 9 A

d) 10 A

485 / 513

Category: Power dissipation in resistive circuits.

485. What is the power dissipated in a resistor of resistance $5 \Omega$ when a current of $2 A$ flows through it?

a) 10 W

b) 20 W

c) 40 W

d) 100 W

486 / 513

Category: Current density at a point in a conductor.

486. A copper wire has a current density of $2.5 \times 10^6 \, A \, m^{-2}$. If the free-electron density is $8.4 \times 10^{28} \, m^{-3}$, calculate the drift velocity of electrons.

a) $1.86 \times 10^{-4} \, m \, s^{-1}$

b) $3.72 \times 10^{-4} \, m \, s^{-1}$

c) $9.3 \times 10^{-5} \, m \, s^{-1}$

d) $4.65 \times 10^{-4} \, m \, s^{-1}$

487 / 513

Category: Electric conduction in metals.

487. (A) When a copper wire of length $l$ and cross-sectional area $A$ is stretched to double its original length, its drift velocity decreases by a factor of 4.
(R) The drift velocity $v_d$ is inversely proportional to the length of the conductor, as given by $v_d = \frac{eV\tau}{ml}$ where $V$ is the potential difference applied across the conductor.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

488 / 513

Category: Dependence of Resistance on Dimensions

488. A cylindrical conductor of resistivity $\rho$ has a resistance $R$. If both its length and radius are doubled, what will be its new resistance?

a) $\frac{R}{2}$

b) $R$

c) $2 R$

d) $4 R$

489 / 513

Category: Specific Resistance or Electrical Resistivity

489. Two wires of equal length and resistance, one made of copper ($\rho_{Cu} = 1.72 \times 10^{-8} \Omega \text{m}, d_{Cu} = 8.9$) and the other of aluminium ($\rho_{Al} = 2.63 \times 10^{-8} \Omega \text{m}, d_{Al} = 2.7$), are compared. Which statement is true?

a) The aluminium wire has lower resistivity but higher density

b) The copper wire is heavier due to lower resistivity

c) The aluminium wire is lighter despite higher resistivity

d) Both wires have the same mass since their resistances are equal

490 / 513

Category: Behavior of free electrons in conductors.

490. In the absence of an electric field, what characterizes the motion of free electrons in a conductor?

a) Electrons remain stationary.

b) Electrons move in a straight line continuously.

c) Electrons move randomly with no net direction.

d) Electrons align uniformly along the length of the conductor.

491 / 513

Category: Average distance between collisions.

491. What is meant by the term "average distance between collisions" in physics?

a) The total distance traveled by all particles in a system

b) The minimum distance between two colliding particles

c) The average distance a particle travels before it collides with another particle

d) The time taken for one complete collision cycle

492 / 513

Category: Behavior of free electrons in conductors.

492. What is the relationship between the drift velocity ($v_d$) of electrons in a conductor and the electric field ($E$) applied across it, if the relaxation time is $\tau$ and electron charge is $e$?

a) $v_d = e E / m$

b) $v_d = E \tau / m$

c) $v_d = e E \tau / m$

d) $v_d = e E m / \tau$

493 / 513

Category: Mean Free Path, Relaxation Time, and Drift Velocity

493. A copper wire has a current density of $4 \times 10^6$ A/m$^2$. If the number density of free electrons is $8.5 \times 10^{28}$ m$^{-3}$, what is the drift velocity of electrons when an electric field of 0.5 V/m is applied? (Given: electron mobility in copper is $4.5 \times 10^{-3}$ m$^2$ V$^{-1}$ s$^{-1}$)

a) $2.25 \times 10^{-3}$ m/s

b) $2.94 \times 10^{-4}$ m/s

c) $4.5 \times 10^{-3}$ m/s

d) $1.125 \times 10^{-3}$ m/s

494 / 513

Category: Power dissipation in resistive circuits.

494. A transmission line with a resistance of $0.5 \Omega$ carries a current of 100 A. If the power loss in the line must be reduced to half its original value while keeping the transmitted power constant, what should be the new current?

a) 35.36 A

b) 50 A

c) 70.71 A

d) 86.60 A

495 / 513

Category: Dynamic Resistance

495. A non-ohmic circuit has a voltage-current relationship given by $V = 2I^3 + I$. What is the dynamic resistance when the current is 1 A?

a) 5 $\Omega$

b) 6 $\Omega$

c) 7 $\Omega$

d) 8 $\Omega$

496 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

496. A current of 5 A flows through a wire of cross-sectional area $2 \times 10^{-6}$ m$^2$. If the drift velocity of electrons is $2 \times 10^{-4}$ m/s, what is the number density of free electrons? (Given: $e = 1.6 \times 10^{-19}$ C)

a) $3.9 \times 10^{28}$ m$^{-3}$

b) $7.8 \times 10^{28}$ m$^{-3}$

c) $1.56 \times 10^{29}$ m$^{-3}$

d) $3.12 \times 10^{29}$ m$^{-3}$

497 / 513

Category: Series and parallel combinations of resistors.

497. Three resistors $R_1 = 2 \Omega$, $R_2 = 4 \Omega$, and $R_3 = 6 \Omega$ are connected in parallel. The combination is then connected in series with a $3 \Omega$ resistor. What is the equivalent resistance of the entire circuit?

a) $\frac{45}{11} \Omega$

b) $\frac{12}{11} \Omega$

c) $\frac{33}{11} \Omega$

d) $\frac{21}{11} \Omega$

498 / 513

Category: Exceptions to Ohm’s Law (Non-Linear V-I Characteristics)

498. (A) The dynamic resistance of a diode decreases as the forward bias voltage increases beyond the threshold voltage.
(R) For non-ohmic conductors, the ratio $\Delta V / \Delta I$ is not constant and depends on the operating point on the V-I curve.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

499 / 513

Category: Behavior of free electrons in conductors.

499. For a material with conductivity $\sigma = 5.8 \times 10^7$ S/m, if the current density is $1.16 \times 10^6$ A/m², what is the magnitude of the applied electric field?

a) $0.02$ V/m

b) $2.0$ V/m

c) $20$ V/m

d) $200$ V/m

500 / 513

Category: Specific Resistance or Electrical Resistivity

500. (A) The specific resistance of a material is independent of the dimensions of the conductor.

(R) Specific resistance is a characteristic property of the material and depends only on the nature of the material.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

501 / 513

Category: Dynamic Resistance

501. (A) The dynamic resistance of a non-ohmic circuit is given by the ratio $\frac{\Delta V}{\Delta I}$.
(R) Dynamic resistance measures the change in current for a small change in potential difference across the circuit.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

502 / 513

Category: Resistance depends on length and cross-sectional area.

502. A wire of resistance $R$ is stretched to twice its original length while keeping the volume constant. What will be its new resistance?

a) 2R

b) 4R

c) R/2

d) R/4

503 / 513

Category: Electric current, measured as the rate of flow of charge.

503. What is the formula to calculate electric current when charge $Q$ flows in time $t$?

a) $\frac{t}{Q}$

b) $Q + t$

c) $Q - t$

d) $\frac{Q}{t}$

504 / 513

Category: Current density in vector form.

504. (A) The current density $\vec{j}$ is a vector quantity whose direction coincides with the electric field $\vec{E}$ for isotropic materials.
(R) According to Ohm's law in vector form, $\vec{j} = \sigma \vec{E}$, where $\sigma$ is the conductivity and is independent of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

505 / 513

Category: Current electricity in daily life

505. (A) Electric current is the flow of electric charge through a conductor.
(R) The SI unit of electric current is ampere, which is defined as the flow of 1 coulomb of charge per second.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

506 / 513

Category: Power dissipation in resistive circuits.

506. (A) When two resistors $R_1$ and $R_2$ are connected in parallel, the power dissipated in $R_1$ is greater than that in $R_2$ if $R_1 < R_2$. (R) In a parallel combination of resistors, the potential difference across each resistor is the same, and power dissipation follows $P = \frac{V^2}{R}$, meaning lower resistance leads to higher power dissipation.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

507 / 513

Category: Resistance in terms of fundamental unit

507. A conductor has a resistance of $5 \Omega$. If the potential difference across it is increased by 50\% while keeping the temperature constant, what happens to the current through the conductor according to Ohm's Law?

a) Current decreases by 50\%

b) Current increases by 50\%

c) Current remains unchanged

d) Current doubles

508 / 513

Category: Current density in vector form.

508. A current of 5 A flows through a conductor with a cross-sectional area of $2 \times 10^{-6} \, \text{m}^2$. What is the magnitude of the current density if the current flows perpendicular to the cross-section?

a) $1.25 \times 10^6 \, \text{A/m}^2$

b) $2.5 \times 10^6 \, \text{A/m}^2$

c) $5 \times 10^5 \, \text{A/m}^2$

d) $1 \times 10^7 \, \text{A/m}^2$

509 / 513

Category: Combinations of Resistances

509. Two resistors of resistances $5 \Omega$ and $10 \Omega$ are connected in parallel. What is their equivalent resistance?

a) $2.5 \Omega$

b) $3.33 \Omega$

c) $7.5 \Omega$

d) $15 \Omega$

510 / 513

Category: Electric Energy and Power

510. A 100 W bulb and a 60 W bulb are connected in series across a 220 V supply. Which bulb will glow brighter and by what percentage compared to the other? Assume both bulbs are designed for 220 V operation.

a) 100W bulb, 40\% brighter

b) 60W bulb, 67\% brighter

c) Both glow equally

d) 100W bulb, 67\% dimmer

511 / 513

Category: Current density in vector form.

511. An electric field $\vec{E} = 10\hat{i} + 5\hat{j}$ N/C is applied to a material with conductivity $\sigma = 2$ S/m. What is the magnitude of the current density vector $\vec{j}$ produced in the material?

a) 10 A/m$^2$

b) 15 A/m$^2$

c) 20 A/m$^2$

d) 22.36 A/m$^2$

512 / 513

Category: Behavior of free electrons in conductors.

512. (A) The drift velocity of electrons in a conductor increases when the potential difference across it is doubled.
(R) Doubling the potential difference doubles the electric field, which directly increases the acceleration of electrons, thereby increasing their drift velocity.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

513 / 513

Category: Mechanism of Flow of Charge in Metals (Free Electron Theory)

513. (A) If the potential difference across a metallic wire is doubled, the drift velocity of electrons also doubles.
(R) The drift velocity of electrons is directly proportional to the applied electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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