Class 12 Physics (Part 1) Chapter 8 Torque on a Current-Loop : Moving-Coil Galvanometer

This quiz on Chapter 8: Torque on a Current-Loop – Moving-Coil Galvanometer for ICSE Class 12 Physics is designed to assess students’ conceptual understanding and application of electromagnetic principles. The quiz covers key topics such as the torque experienced by a current-carrying loop in a magnetic field, the construction and working of a moving-coil galvanometer, sensitivity and damping, and its conversion into an ammeter or voltmeter. Students will encounter a mix of conceptual, numerical, and application-based questions that test their grasp of magnetic torque, magnetic moment, and the operational principles of galvanometers. This quiz aims to reinforce theoretical knowledge while encouraging analytical thinking and problem-solving skills relevant to both board examinations and competitive tests.

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Category: Moving-Coil Galvanometer

1. A galvanometer has a current sensitivity of $10 \, \text{deg/mA}$. If the number of turns is doubled and the magnetic field is halved while keeping other parameters constant, what will be the new current sensitivity?

a) $5 \, \text{deg/mA}$

b) $10 \, \text{deg/mA}$

c) $20 \, \text{deg/mA}$

d) $40 \, \text{deg/mA}$

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Category: Magnetic Moment and Torque

2. (A) The torque acting on a current-carrying coil in a uniform magnetic field is maximum when the plane of the coil is perpendicular to the magnetic field.
(R) The magnitude of torque depends on the angle between the magnetic moment and the magnetic field, given by $\tau = mB\sin\theta$.

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: Definition of magnetic moment.

3. A solenoid with 200 turns, length $0.2 \, \text{m}$, and carrying a current of $3 \, \text{A}$ is placed in a uniform magnetic field of $0.4 \, \text{T}$ such that its axis makes an angle of $60^\circ$ with the field. What is the torque experienced by the solenoid?

a) $1.2 \, \text{N} \cdot \text{m}$

b) $2.078 \, \text{N} \cdot \text{m}$

c) $3.6 \, \text{N} \cdot \text{m}$

d) $4.8 \, \text{N} \cdot \text{m}$

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Category: Sensitivity and factors affecting it.

4. What is the primary reason for using a soft-iron core in a galvanometer to enhance sensitivity?

a) To reduce the mass of the coil

b) To concentrate the magnetic field lines and increase $B$

c) To decrease the resistance of the coil

d) To minimize air friction

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Category: Conversion of Galvanometer in Ammeter

5. If a galvanometer with resistance 30 Ω and full-scale deflection current 3 mA is converted into an ammeter of range 0 to 9 A using a shunt but the shunt is incorrectly chosen as 0.015 Ω instead of the correct value, what will be the percentage error in the ammeter reading when measuring a current of 6 A?

a) 0.11\%

b) 0.22\%

c) 0.33\%

d) 0.44\%

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Category: Definition of magnetic moment.

6. (A) The magnetic moment $\vec{m}$ of a coil is defined as $N I \vec{A}$, where $N$ is the number of turns, $I$ is the current, and $\vec{A}$ is the area vector of the coil.

(R) The direction of the magnetic moment is always perpendicular to the plane of the coil and its magnitude gives the maximum torque experienced by the coil when placed in a uniform magnetic field of unit strength.

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: Torque on a Current-Loop in a Uniform Magnetic Field

7. (A) For a planar current-carrying loop placed in a uniform magnetic field, if the net torque acting on it is zero, the loop must be in stable equilibrium.
(R) The torque on a current-carrying loop in a uniform magnetic field is given by $\vec{\tau} = N I \vec{A} \times \vec{B}$, and zero torque occurs when $\theta = 0^\circ$ or $\theta = 180^\circ$, but only $\theta = 0^\circ$ corresponds to stable equilibrium.

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: Moving-Coil Galvanometer

8. In a moving-coil galvanometer with a radial magnetic field, if the number of turns in the coil is doubled while keeping all other parameters constant, how does the current sensitivity change?

a) It becomes half

b) It remains the same

c) It doubles

d) It quadruples

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Category: Definition of magnetic moment.

9. (A) The magnetic moment of a coil is given by $m = NIA$, where $N$ is the number of turns, $I$ is the current, and $A$ is the area of the coil.
(R) The magnetic moment represents the maximum torque experienced by the coil in a uniform magnetic field of unit strength when the plane of the coil is parallel to the 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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Category: Principle of operation.

10. A moving-coil galvanometer has a coil with 50 turns and area $2 \times 10^{-4}$ m$^2$. When placed in a radial magnetic field of 0.2 T with torsional constant $5 \times 10^{-8}$ Nm/rad, it shows a deflection of 30$^\circ$. What current flows through the coil?

a) 52.36 mA

b) 130.9 μA

c) 261.8 μA

d) 65.45 μA

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Category: Torque on Current-Loop

11. An equilateral triangular coil of side length 0.05 m, having 20 turns and carrying a current of 1 A, is placed perpendicular to a magnetic field of 0.1 T. What is the maximum torque acting on the coil?

a) 1.083 $\times$ 10$^{-3}$ Nm

b) 2.166 $\times$ 10$^{-3}$ Nm

c) 3.249 $\times$ 10$^{-3}$ Nm

d) 4.332 $\times$ 10$^{-3}$ Nm

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Category: Moving-Coil Galvanometer Principle

12. A moving-coil galvanometer connected to a lamp and scale arrangement shows a deflection of 15 cm when a current of 30 $\mu$A is passed through it. If the distance from the mirror to the scale is increased from 1.5 m to 3 m, what should be the current to produce the same displacement of 15 cm on the new scale?

a) $15 \mu\text{A}$

b) $30 \mu\text{A}$

c) $45 \mu\text{A}$

d) $60 \mu\text{A}$

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Category: Current and Voltage Sensitivity

13. (A) Increasing the number of turns ($N$) in a galvanometer coil increases its current sensitivity.
(R) The current sensitivity is given by $\frac{N A B}{c}$.

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 sensitivity.

14. A galvanometer has a current sensitivity of $3 \times 10^6$ rad/A and a coil resistance of 50 ohms. What is its voltage sensitivity?

a) $6 \times 10^4$ rad/V

b) $1.5 \times 10^5$ rad/V

c) $6 \times 10^3$ rad/V

d) $1.5 \times 10^4$ rad/V

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Category: Formulae for both sensitivities.

15. (A) Increasing the number of turns ($N$) in a galvanometer always increases its voltage sensitivity.
(R) Voltage sensitivity is given by $\frac{\phi}{V} = \frac{NAB}{cR}$, where $R$ is the resistance of the coil.

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: Moving-Coil Galvanometer

16. (A) A moving-coil galvanometer measures electric current based on the torque experienced by a current-carrying coil in a magnetic field.
(R) The deflection of the coil is proportional to 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.

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Category: Conversion of Galvanometer in Voltmeter

17. (A) To convert a galvanometer into a voltmeter, a high resistance is connected in series with it.
(R) The resistance of an ideal voltmeter should be infinite to avoid drawing current from 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.

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Category: Sensitivity and factors affecting it.

18. A galvanometer has a current sensitivity of $\frac{\phi}{I} = \frac{N A B}{c}$. Which of the following changes will increase its current sensitivity?

a) Increasing the resistance of the coil

b) Decreasing the area of the coil

c) Increasing the number of turns in the coil

d) Increasing the torsional constant of the suspension

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Category: Current and Voltage Sensitivity

19. If the galvanometer coil in the previous question has a resistance $R = 20 \, \Omega$, what is its voltage sensitivity?

a) 0.5 rad/V

b) 1.0 rad/V

c) 2.25 rad/V

d) 4.5 rad/V

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Category: Definition of Magnetic Moment of a Coil

20. A circular coil has 50 turns, a current of 2 A, and an area of 0.02 m$^2$. What is its magnetic moment?

a) 1 A$\cdot$m$^2$

b) 2 A$\cdot$m$^2$

c) 4 A$\cdot$m$^2$

d) 0.5 A$\cdot$m$^2$

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Category: Torque on Current-Loop

21. (A) The torque on a current-carrying loop in a uniform magnetic field is maximum when the plane of the loop is parallel to the magnetic field.
(R) The torque depends on $\sin \theta$, where $\theta$ is the angle between the normal to the plane of the loop and the magnetic field, and $\sin \theta$ is maximum when $\theta = 90^\circ$.

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 sensitivity.

22. For a moving-coil galvanometer, if the number of turns is doubled while keeping other parameters constant, how does the current sensitivity change?

a) It becomes half

b) It remains the same

c) It doubles

d) It quadruples

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Category: Torque on Current-Loop

23. A circular loop of radius 0.1 m has 100 turns and carries a current of 2 A. If it is placed in a magnetic field of 0.5 T at an angle of $45^\circ$, what is the torque experienced by the loop?

a) 1.11 Nm

b) 2.22 Nm

c) 3.14 Nm

d) 4.44 Nm

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Category: Moving-Coil Galvanometer

24. (A) In a pivoted-coil galvanometer, the deflecting torque remains constant for any angular displacement of the coil.

(R) The magnetic field in a pivoted-coil galvanometer is radial, ensuring $\sin \theta = 1$ at all positions of the coil.

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: Construction and working of a moving-coil galvanometer.

25. What is the purpose of the soft-iron core in a moving-coil galvanometer?

a) To increase the current-carrying capacity of the coil

b) To concentrate the magnetic field and enhance sensitivity

c) To reduce the resistance of the coil

d) To provide mechanical support to the suspension strip

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Category: Conversion of Galvanometer to Ammeter and Voltmeter

26. (A) A galvanometer can be converted into an ammeter by connecting a high resistance in series with it.
(R) The shunt resistance reduces the overall resistance of the ammeter, allowing it to measure higher currents.

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: Sensitivity of Galvanometer

27. What is the current sensitivity of a galvanometer defined as?

a) Deflection per unit voltage applied

b) Current required to produce full-scale deflection

c) Deflection per unit current passed through it

d) Voltage drop across the galvanometer per unit current

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Category: Conversion to Ammeter and Voltmeter

28. (A) A galvanometer can be converted into an ammeter by connecting a shunt resistance in parallel with it.
(R) The shunt resistance allows the majority of the current to bypass the galvanometer, enabling it to measure higher currents.

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: Sensitivity and factors affecting it.

29. Which factor affects the voltage sensitivity of a galvanometer directly?

a) Number of turns ($N$) only

b) Resistance of the coil ($R$) only

c) Area of the coil ($A$) and magnetic field ($B$)

d) Torsional constant ($c$) only

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Category: Definition of Magnetic Moment of a Coil

30. A rectangular coil with 100 turns, carrying a current of 1.5 A, is placed in a uniform magnetic field of 0.5 T. The area of the coil is 0.01 m$^2$ and the angle between the normal to the plane of the coil and the magnetic field is 30$^\circ$. Calculate the torque acting on the coil.

a) 0.1875 N$\cdot$m

b) 0.375 N$\cdot$m

c) 0.75 N$\cdot$m

d) 1.5 N$\cdot$m

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Category: Formulae for both sensitivities.

31. What is the formula for voltage sensitivity of a galvanometer?

a) $\frac{\phi}{I} = \frac{N A B}{c}$

b) $\frac{\phi}{V} = \frac{N A B}{c R}$

c) $\frac{V}{\phi} = \frac{c R}{N A B}$

d) $\frac{I}{\phi} = \frac{R c}{N A B}$

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Category: Conversion of Galvanometer in Ammeter

32. If a galvanometer with resistance 50 $\Omega$ is converted into an ammeter of range 0 to 2 A using a shunt, what fraction of the total current passes through the galvanometer when the ammeter shows full-scale deflection?

a) 0.01

b) 0.02

c) 0.05

d) 0.10

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Category: Torque on a Current-Loop in a Uniform Magnetic Field

33. Under what condition will the torque on a current-carrying loop placed in a uniform magnetic field be zero?

a) When the loop is parallel to the magnetic field.

b) When the loop is perpendicular to the magnetic field.

c) When the loop is at $45^\circ$ to the magnetic field.

d) When the loop is rotating in the field.

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Category: Current sensitivity.

34. What is the definition of current sensitivity in a galvanometer?

a) The resistance of the coil per unit current

b) The deflection produced per unit current

c) The magnetic field strength per unit current

d) The voltage drop per unit current

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Category: Radial Magnetic Field

35. (A) The torque acting on a current-carrying coil in a radial magnetic field is independent of the angle between the plane of the coil and the direction of the magnetic field.
(R) In a radial magnetic field, the field lines always lie in the plane of the coil regardless of its orientation.

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: Definition of Magnetic Moment of a Coil

36. (A) The magnetic moment of a coil is equal to the torque acting on it when placed in a uniform magnetic field of unit strength and oriented perpendicular to the field.
(R) For $\theta = 90^\circ$, the torque acting on the coil is given by $\tau = m B \sin \theta = m$ (when $B = 1 \, \text{T}$).

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: Definition of magnetic moment.

37. What is the SI unit of magnetic moment?

a) Newton-meter (N-m)

b) Tesla (T)

c) Ampere per meter (A/m)

d) Ampere-square meter (A-m$^2$)

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Category: Definition of Magnetic Moment of a Coil

38. What is the formula for the magnetic moment $\vec{m}$ of a coil with $N$ turns, area $A$, and current $I$?

a) $\vec{m} = N I \vec{B}$

b) $\vec{m} = N A \vec{I}$

c) $\vec{m} = N I \vec{A}$

d) $\vec{m} = I A \vec{N}$

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Category: Torque on a Current-Loop in a Uniform Magnetic Field

39. A rectangular coil of area $0.05\,m^2$, carrying a current of $3\,A$ with 20 turns, is placed in a uniform magnetic field of $0.02\,T$ such that the angle between the normal to the plane of the coil and the magnetic field is $90^\circ$. What is the torque acting on the coil?

a) $0.03\,Nm$

b) $0.06\,Nm$

c) $0.09\,Nm$

d) $0.12\,Nm$

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Category: Derivation of the expression for torque on a current-carrying loop.

40. A circular loop with 10 turns of radius 2 cm carries current 5 A in a uniform magnetic field of 0.5 T. The angle between normal to plane and field is 30°. What is magnitude of torque experienced?

a) 0.0157 Nm

b) 0.0314 Nm

c) 0.00785 Nm

d) 0.0236 Nm

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Category: Moving-Coil Galvanometer

41. What is the formula for current sensitivity ($I$) of a moving-coil galvanometer?

a) $I = N A B \phi$

b) $I = \frac{N A B}{c \phi}$

c) $I = \frac{\phi}{N A B c}$

d) $I = \frac{c \phi}{N A B}$

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Category: Construction and working of a moving-coil galvanometer.

42. A moving-coil galvanometer has a coil with 100 turns, area $2 \times 10^{-4} \, \text{m}^2$, and is placed in a radial magnetic field of strength 0.5 T. The torsional constant of the suspension is $2 \times 10^{-9} \, \text{Nm/rad}$. What current through the coil will produce a deflection of 30°?

a) $1.05 \times 10^{-6} \, \text{A}$

b) $1.05 \times 10^{-7} \, \text{A}$

c) $2.1 \times 10^{-7} \, \text{A}$

d) $5.25 \times 10^{-8} \, \text{A}$

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Category: Sensitivity of a Moving-Coil Galvanometer

43. A moving-coil galvanometer has 150 turns, coil area $2 \times 10^{-3} \, \text{m}^2$, magnetic field $0.25 \, \text{T}$, and torsional constant $1.2 \times 10^{-6} \, \text{Nm/degree}$. If its coil resistance is $50 \, \Omega$, what is its voltage sensitivity?

a) 125 degrees/V

b) 250 degrees/V

c) 1250 degrees/V

d) 2500 degrees/V

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Category: Magnetic Moment and Torque

44. A circular coil has 50 turns, each with a radius of $0.1\,m$ and carries a current of $2\,A$. What is its magnetic moment?

a) $0.5\pi\,A \cdot m^2$

b) $\pi\,A \cdot m^2$

c) $2\pi\,A \cdot m^2$

d) $0.1\pi\,A \cdot m^2$

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Category: Moving-Coil Galvanometer

45. A moving-coil galvanometer has 100 turns, a coil area of $2 \times 10^{-4} \, \text{m}^2$, and is placed in a radial magnetic field of magnitude 0.1 T. If the torsional constant of the suspension is $5 \times 10^{-7} \, \text{Nm/degree}$, what current will produce a deflection of 20 degrees?

a) 1 mA

b) 3 mA

c) 5 mA

d) 10 mA

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Category: Sensitivity of a Moving-Coil Galvanometer

46. In a moving-coil galvanometer with a radial magnetic field, why is the deflection angle directly proportional to the current?

a) The magnetic field strength varies with angle

b) The coil's moment of inertia changes with current

c) The coil resistance adjusts to maintain linearity

d) The deflecting torque is independent of coil orientation

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Category: Torque on a Current-Loop in a Uniform Magnetic Field

47. A circular coil of radius 0.05 m with 20 turns carries a current of 3 A. It is placed in a magnetic field of 0.2 T such that the angle between the normal to the plane of the coil and the field is 90\textdegree. Calculate the torque.

a) 0.0471 Nm

b) 0.0942 Nm

c) 0.1884 Nm

d) 0.3768 Nm

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Category: Conversion to Ammeter and Voltmeter

48. (A) A galvanometer can be converted into an ammeter by connecting a low resistance shunt in parallel with it.
(R) The shunt resistance ensures that most of the current bypasses the galvanometer coil, protecting it from damage.

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: Conversion of Galvanometer to Ammeter and Voltmeter

49. A galvanometer with a resistance of $30 \, \Omega$ requires $3 \, \text{mA}$ current for full-scale deflection. It is to be converted into both an ammeter of range $0$ to $1.5 \, \text{A}$ and a voltmeter of range $0$ to $45 \, \text{V}$. What are the values of the shunt resistance ($S$) for the ammeter and series resistance ($R$) for the voltmeter?

a) $50 \, \text{m}\Omega$ and $15000 \, \Omega$

b) $60 \, \text{m}\Omega$ and $14970 \, \Omega$

c) $70 \, \text{m}\Omega$ and $14800 \, \Omega$

d) $80 \, \text{m}\Omega$ and $14700 \, \Omega$

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Category: Conversion of Galvanometer in Voltmeter

50. (A) To convert a galvanometer into a voltmeter, a high resistance must be connected in series with the galvanometer.
(R) The resistance of an ideal voltmeter should be infinite to ensure it does not draw any current from 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.

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Category: Conversion of Galvanometer in Voltmeter

51. What should be the resistance of an ideal voltmeter?

a) Zero

b) Equal to the galvanometer resistance

c) Very low compared to the circuit resistance

d) Infinite

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Category: Voltage sensitivity.

52. Which factor can increase the voltage sensitivity of a galvanometer?

a) Decreasing the number of turns ($N$)

b) Increasing the resistance of the coil ($R$)

c) Increasing the torsional constant ($c$)

d) Using a stronger magnetic field ($B$)

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Category: Current and Voltage Sensitivity

53. Which of the following changes will NOT increase the voltage sensitivity of a moving-coil galvanometer?

a) Reducing the torsion constant of the suspension

b) Decreasing the area of the coil

c) Increasing the number of turns in the coil

d) Using a stronger magnetic field

54 / 288

Category: Moving-Coil Galvanometer

54. (A) The sensitivity of a suspended-coil galvanometer is higher than that of a pivoted-coil galvanometer.

(R) In a suspended-coil galvanometer, the coil is suspended by a thin phosphor-bronze strip which offers less resistance to rotation compared to the springs in a pivoted-coil galvanometer.

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: Radial Magnetic Field

55. (A) For a current-carrying coil placed in a radial magnetic field, increasing the number of turns $N$ will always increase the angular deflection $\theta$ at equilibrium for a given current $I$.
(R) The restoring torque provided by hair springs depends only on the torsional constant $k$ and is independent of the number of turns $N$.

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.

56 / 288

Category: Formulae for both sensitivities.

56. What is the formula for current sensitivity of a galvanometer?

a) $\frac{\phi}{V} = \frac{N A B}{c R}$

b) $\frac{\phi}{I} = \frac{N A B}{c}$

c) $\frac{I}{\phi} = \frac{c}{N A B}$

d) $\frac{V}{\phi} = \frac{R c}{N A B}$

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Category: Definition of magnetic moment.

57. What is the formula for magnetic moment (\$m\$) of a current-carrying coil with \$N\$ turns, area \$A\$, and current \$I\$?

a) $m = N + I + A$

b) $m = \frac{N I}{A}$

c) $m = N I A$

d) $m = N I A B \sin \theta$

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Category: Moving-Coil Galvanometer Principle

58. A moving-coil galvanometer has a coil with 100 turns, area $10^{-4} \text{m}^2$, and is placed in a radial magnetic field of 0.1 T. The torsional constant of the suspension is $10^{-6}$ Nm/rad. If the deflection observed on the scale placed 2 m away is 20 cm, what is the current flowing through the galvanometer?

a) $25 \mu\text{A}$

b) $50 \mu\text{A}$

c) $75 \mu\text{A}$

d) $100 \mu\text{A}$

59 / 288

Category: Current sensitivity.

59. Which of the following will increase the current sensitivity of a galvanometer?

a) Increasing the torsional constant $c$

b) Decreasing the number of turns $N$

c) Reducing the area of the coil $A$

d) Increasing the magnetic field strength $B$

60 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

60. At what angle $\theta$ between the normal to the plane of the loop and the magnetic field is the torque on the loop maximum?

a) $0^\circ$

b) $30^\circ$

c) $45^\circ$

d) $90^\circ$

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Category: Conversion of Galvanometer to Ammeter and Voltmeter

61. Why is a high resistance connected in series with a galvanometer when converting it into a voltmeter instead of a shunt as in an ammeter?

a) To minimize power loss

b) To ensure accurate voltage measurement without significantly affecting the circuit

c) To allow more current to flow through the galvanometer

d) To protect the galvanometer from damage

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Category: Sensitivity of Galvanometer

62. (A) Increasing the number of turns ($N$) in a moving coil galvanometer will always increase its voltage sensitivity.
(R) Voltage sensitivity is inversely proportional to the resistance of the galvanometer coil.

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.

63 / 288

Category: Conversion of Galvanometer in Voltmeter

63. A galvanometer with $20 \Omega$ resistance and $2$ mA full-scale deflection is converted into a voltmeter with ranges $0-10$ V and $0-30$ V. If it mistakenly uses $R = 4500 \Omega$ for the $0-30$ V range, what error occurs at $15$ V?

a) $3.6$ V overreading

b) $5.96$ V underreading

c) No error

d) $7.2$ V overreading

64 / 288

Category: Moving-Coil Galvanometer

64. In a moving-coil galvanometer, the torsional constant of the suspension strip is $2 \times 10^{-6} \, \text{Nm/degree}$. The number of turns is 200, the area of the coil is $1.2 \times 10^{-3} \, \text{m}^2$, and the magnetic field is 0.15 T. What is the current sensitivity of the galvanometer if it shows a deflection of 20 degrees?

a) $0.55 \, \text{mA}$

b) $1.11 \, \text{mA}$

c) $2.22 \, \text{mA}$

d) $4.44 \, \text{mA}$

65 / 288

Category: Principle of operation.

65. (A) In a moving-coil galvanometer with a radial magnetic field, the deflecting torque is maximum when the plane of the coil is parallel to the magnetic field lines.
(R) For a radial magnetic field, $\theta = 90^\circ$, which maximizes $\sin \theta$ in the deflecting torque equation $\tau = N I A B \sin \theta$.

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.

66 / 288

Category: Current sensitivity.

66. The figure of merit of a galvanometer is defined as:

a) The product of current and deflection.

b) The ratio of current to deflection.

c) The product of resistance and current.

d) The ratio of deflection to current.

67 / 288

Category: Formulae for both sensitivities.

67. A galvanometer has 100 turns, a coil area of 0.01 m$^2$, a magnetic field strength of 0.5 T, and a torsional constant of $2 \times 10^{-4}$ Nm/rad. What is its current sensitivity?

a) 250 rad/A

b) 500 rad/A

c) 2500 rad/A

d) 5000 rad/A

68 / 288

Category: Moving-Coil Galvanometer Principle

68. A moving-coil galvanometer has a coil with 50 turns, an area of $0.02 \text{ m}^2$, and is placed in a radial magnetic field of strength $0.5 \text{ T}$. If the current passing through the coil is $10 \text{ mA}$, what is the deflecting torque acting on the coil?

a) $0.001 \text{ Nm}$

b) $0.005 \text{ Nm}$

c) $0.01 \text{ Nm}$

d) $0.05 \text{ Nm}$

69 / 288

Category: Voltage sensitivity.

69. Which of the following changes will NOT increase the voltage sensitivity of a galvanometer?

a) Increasing the number of turns ($N$) in the coil

b) Decreasing the torsional constant ($c$) of the suspension

c) Increasing the resistance ($R$) of the coil

d) Using a stronger magnetic field ($B$)

70 / 288

Category: Conversion of Galvanometer to Ammeter and Voltmeter

70. A galvanometer with a resistance of $20 \, \Omega$ shows full-scale deflection for a current of $10 \, \text{mA}$. If a shunt of $0.04 \, \Omega$ is connected, what will be the maximum current that can be measured by this modified ammeter?

a) $4.90 \, \text{A}$

b) $5.00 \, \text{A}$

c) $5.01 \, \text{A}$

d) $5.10 \, \text{A}$

71 / 288

Category: Conversion of Galvanometer in Ammeter

71. (A) The resistance of an ammeter must be very low to minimize its impact on the measured current.
(R) A galvanometer is converted into an ammeter by connecting a high resistance in series with 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.

72 / 288

Category: Sensitivity of Galvanometer

72. Which of the following formulas represents the voltage sensitivity of a galvanometer?

a) $\frac{\phi}{I}$

b) $\frac{I}{\phi}$

c) $\frac{NAB}{cR}$

d) $\frac{NAB}{c}$

73 / 288

Category: Torque on Current-Loop

73. (A) The torque on a current-carrying loop is maximum when the plane of the loop is perpendicular to the magnetic field.
(R) The torque $\tau$ is given by $\tau = N I A B \sin \theta$, where $\theta$ is the angle between the normal to the plane of the loop and the magnetic 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.

74 / 288

Category: Construction and working of a moving-coil galvanometer.

74. (A) In a moving-coil galvanometer, the magnetic field is made radial to ensure that the plane of the coil remains parallel to the magnetic field lines.
(R) A radial magnetic field ensures that $\theta = 90^\circ$ and $\sin \theta = 1$, maximizing the deflecting torque for any current passing through the coil.

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.

75 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

75. To increase the current sensitivity of a galvanometer by 40\% without changing its coil resistance or magnetic field, which modification is most effective?

a) Doubling the number of turns ($N$)

b) Halving the coil area ($A$)

c) Using a stronger magnetic field ($B$)

d) Reducing torsional constant ($c$) by 40\%

76 / 288

Category: Moving-Coil Galvanometer

76. (A) The sensitivity of a moving-coil galvanometer can be increased by increasing the number of turns in the coil.
(R) Increasing the number of turns increases the deflecting torque for the same 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.

77 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

77. A rectangular coil with 10 turns, length $l = 0.05 \, \text{m}$, width $w = 0.03 \, \text{m}$ carries a current of $5 \, \text{A}$. It is placed in a uniform magnetic field of strength $0.2 \, \text{T}$ at an angle $\theta = 30^\circ$ to the normal of the plane of the coil. Calculate the torque experienced by the coil.

a) $3.75 \times 10^{-3} \, \text{N m}$

b) $7.5 \times 10^{-3} \, \text{N m}$

c) $15 \times 10^{-3} \, \text{N m}$

d) $22.5 \times 10^{-3} \, \text{N m}$

78 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

78. The voltage sensitivity of a galvanometer with current sensitivity $\frac{50 \, \text{rad}}{\text{A}}$ and coil resistance $25 \, \Omega$ is:

a) 1 rad/V

b) 2 rad/V

c) 3 rad/V

d) 4 rad/V

79 / 288

Category: Current sensitivity.

79. (A) Increasing the number of turns ($N$) in a galvanometer coil increases its current sensitivity.
(R) The current sensitivity is directly proportional to the number of turns in the coil, as given by $\frac{\phi}{I} = \frac{N A B}{c}$.

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 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

80. A moving-coil galvanometer has 150 turns, coil area $2 \times 10^{-3} \, \text{m}^2$, magnetic field strength 0.15 T, and torsional constant $1.2 \times 10^{-6} \, \text{Nm/degree}$. What current is required to produce a deflection of 20°?

a) 0.433 mA

b) 0.533 mA

c) 0.633 mA

d) 0.733 mA

81 / 288

Category: Current and Voltage Sensitivity

81. A moving-coil galvanometer has a current sensitivity of 10 rad/A and a voltage sensitivity of 0.5 rad/V. If the number of turns in the coil is doubled while keeping all other parameters constant, what will be the new voltage sensitivity?

a) 0.25 rad/V

b) 0.5 rad/V

c) 1 rad/V

d) 2 rad/V

82 / 288

Category: Principle of operation.

82. A moving-coil galvanometer works based on the torque produced due to current flowing through a coil in a magnetic field. What is the expression for the instantaneous deflecting torque $\tau$ acting on the coil?

a) $\tau = N I A B \cos \theta$

b) $\tau = N I B \sin \theta$

c) $\tau = N I A B \sin \theta$

d) $\tau = N A B \sin \theta$

83 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

83. A rectangular loop with dimensions 8 cm \times 6 cm, 15 turns, and carrying a current of 10 A is placed in a magnetic field of 0.5 T. What should be the orientation of the loop to achieve maximum torque?

a) Plane of loop at 30$^\circ$ to the magnetic field

b) Plane of loop at 45$^\circ$ to the magnetic field

c) Normal to the plane perpendicular to the magnetic field

d) Normal to the plane parallel to the magnetic field

84 / 288

Category: Radial Magnetic Field

84. A square coil of side 0.2 m and 200 turns rotates at 300 rpm in a radial magnetic field of 0.1 T. If the resistance of the coil is 10 Ω, what is the power dissipated as heat?

a) $1.6\pi^2 \, \text{W}$

b) $3.2\pi^2 \, \text{W}$

c) $6.4\pi^2 \, \text{W}$

d) $12.8\pi^2 \, \text{W}$

85 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

85. A circular coil of radius 5 cm, 50 turns, and carrying a current of 2 A is placed in a uniform magnetic field of 0.8 T. At what angle between the normal to the plane of the coil and the magnetic field will the torque be zero?

a) 30$^\circ$

b) 45$^\circ$

c) 90$^\circ$

d) 0$^\circ$

86 / 288

Category: Torque on Current-Loop

86. Under which condition will the torque on a current-carrying loop in a uniform magnetic field be zero?

a) When the loop is perpendicular to the magnetic field

b) When the loop is at $45^\circ$ to the magnetic field

c) When the loop is parallel to the magnetic field

d) When the loop is at $90^\circ$ to the magnetic field

87 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

87. If the number of turns in a galvanometer is doubled while keeping other parameters constant, how does the current sensitivity change?

a) It becomes half

b) It remains the same

c) It doubles

d) It quadruples

88 / 288

Category: Principle of operation.

88. In equilibrium, which condition holds true for a moving-coil galvanometer when the magnetic field is radial?

a) $N I A B \sin \theta = c \phi$

b) $N I A B = \frac{c}{\phi}$

c) $N I A B = c \phi$

d) $N I A B \tan \theta = c \phi$

89 / 288

Category: Definition of magnetic moment.

89. A circular coil of radius 5 cm having 100 turns carries a current of 0.5 A. Calculate the magnetic moment of the coil when placed in a uniform magnetic field of 0.2 T at an angle of $30^\circ$ to the field.

a) $0.125\pi \, \text{A} \cdot \text{m}^2$

b) $0.25\pi \, \text{A} \cdot \text{m}^2$

c) $0.5\pi \, \text{A} \cdot \text{m}^2$

d) $\pi \, \text{A} \cdot \text{m}^2$

90 / 288

Category: Moving-Coil Galvanometer Principle

90. In a moving-coil galvanometer, if the number of turns of the coil is doubled and the magnetic field strength is halved while keeping other parameters constant, how does the deflection change for the same current?

a) Becomes half

b) Doubles

c) Remains unchanged

d) Becomes four times

91 / 288

Category: Current and Voltage Sensitivity

91. Which of the following will NOT increase the current sensitivity of a galvanometer?

a) Increasing the number of turns $N$

b) Increasing the area $A$ of the coil

c) Decreasing the torsion constant $c$

d) Increasing the coil resistance $R$

92 / 288

Category: Construction and working of a moving-coil galvanometer.

92. Which of the following does NOT enhance the sensitivity of a moving-coil galvanometer?

a) Increasing the number of turns of the coil

b) Using a stronger magnetic field

c) Decreasing the number of turns of the coil

d) Reducing the torsional constant of the suspension strip

93 / 288

Category: Formulae for both sensitivities.

93. (A) Increasing the number of turns $N$ in the galvanometer coil will always increase both its current sensitivity and voltage sensitivity.
(R) The current sensitivity formula is $\frac{\phi}{I} = \frac{N A B}{c}$, and the voltage sensitivity formula is $\frac{\phi}{V} = \frac{N A B}{c R}$, both directly proportional to $N$.

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.

94 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

94. A square loop of side length 10 cm carrying a current of 5 A has 20 turns and is placed in a uniform magnetic field of 0.4 T. If the plane of the loop makes an angle of 30$^\circ$ with the direction of the magnetic field, what is the torque experienced by the loop?

a) 0.1 N m

b) 0.2 N m

c) 0.3 N m

d) 0.4 N m

95 / 288

Category: Sensitivity of Galvanometer

95. The figure of merit of a galvanometer is $0.2\,\text{rad/A}$. What current produces a deflection of $0.8\,\text{rad}$?

a) 0.04 A

b) 0.08 A

c) 0.10 A

d) 0.16 A

96 / 288

Category: Conversion of Galvanometer in Ammeter

96. A galvanometer has a resistance of 50 $\Omega$ and gives full-scale deflection for a current of 10 mA. What should be the value of the shunt resistance to convert it into an ammeter of range 0 to 2 A?

a) 0.251 $\Omega$

b) 0.502 $\Omega$

c) 1.00 $\Omega$

d) 0.125 $\Omega$

97 / 288

Category: Formulae for both sensitivities.

97. A galvanometer has a current sensitivity of 1500 rad/A, and the resistance of its coil is 50 $\Omega$. What is its voltage sensitivity?

a) 15 rad/V

b) 30 rad/V

c) 45 rad/V

d) 60 rad/V

98 / 288

Category: Sensitivity and factors affecting it.

98. A galvanometer coil of area $A = 4 \times 10^{-3} \, \text{m}^2$ and 30 turns is placed in a magnetic field $B = 0.15 \, \text{T}$. If the torsional constant $c$ is $2 \times 10^{-6} \, \text{Nm/rad}$, what current is needed to produce a deflection of $45^\circ$ ($\pi/4$ rad)?

a) 58.9 $\mu$A

b) 87.3 $\mu$A

c) 43.6 $\mu$A

d) 112.5 $\mu$A

99 / 288

Category: Principle of operation.

99. (A) In a moving-coil galvanometer, the current flowing through the coil is directly proportional to the deflection angle of the coil.
(R) The deflecting torque in the galvanometer is given by $\tau = N I A B$, and at equilibrium, it equals the restoring torque $c \phi$.

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 / 288

Category: Current and Voltage Sensitivity

100. (A) Increasing the number of turns $N$ in a galvanometer coil will always increase both its current sensitivity and voltage sensitivity.
(R) The voltage sensitivity formula $\frac{\phi}{V} = \frac{N A B}{c R}$ shows that increasing $N$ increases the numerator while keeping other parameters 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.

101 / 288

Category: Definition of Magnetic Moment of a Coil

101. What is the SI unit of the magnetic moment $\vec{m}$ of a coil?

a) $T \cdot m^2$

b) $A \cdot m^2$

c) $N \cdot m$

d) $A \cdot s$

102 / 288

Category: Conversion of Galvanometer to Ammeter and Voltmeter

102. A galvanometer has a resistance of $20 \, \Omega$ and gives full-scale deflection for a current of $5 \, \text{mA}$. What shunt resistance is required to convert it into an ammeter with a range of $0$ to $10 \, \text{A}$?

a) $15 \, \text{m}\Omega$

b) $20 \, \text{m}\Omega$

c) $10 \, \text{m}\Omega$

d) $25 \, \text{m}\Omega$

103 / 288

Category: Conversion of Galvanometer in Voltmeter

103. A voltmeter has a resistance of $2000 \Omega$ and measures up to $5 \text{ V}$. What additional resistance is required to extend its range to $50 \text{ V}$?

a) 10000 $\Omega$

b) 15000 $\Omega$

c) 18000 $\Omega$

d) 20000 $\Omega$

104 / 288

Category: Conversion of Galvanometer to Ammeter and Voltmeter

104. What is the purpose of connecting a shunt resistance in parallel with a galvanometer when converting it into an ammeter?

a) To increase the voltage across the galvanometer

b) To decrease the overall resistance of the circuit

c) To reduce the current passing through the galvanometer

d) To amplify the deflection of the galvanometer

105 / 288

Category: Formulae for both sensitivities.

105. (A) Increasing the number of turns $N$ in a galvanometer coil will always increase its voltage sensitivity.
(R) Voltage sensitivity $\frac{\phi}{V}$ depends on $\frac{N A B}{c R}$, and increasing $N$ increases the numerator but may also increase resistance $R$, reducing the overall effect.

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.

106 / 288

Category: Current sensitivity.

106. Which of the following modifications will NOT increase the current sensitivity of a galvanometer?

a) Using a stronger magnet

b) Increasing the number of turns in the coil

c) Increasing the resistance of the coil

d) Using a suspension strip with a smaller torsion constant

107 / 288

Category: Current and Voltage Sensitivity

107. Two galvanometers, $M_1$ and $M_2$, have parameters $(N_1 = 25, A_1 = 2.0 \times 10^{-3} \, \text{m}^2, B_1 = 0.20 \, \text{T}, R_1 = 15 \, \Omega)$ and $(N_2 = 40, A_2 = 3.0 \times 10^{-3} \, \text{m}^2, B_2 = 0.30 \, \text{T}, R_2 = 25 \, \Omega)$. What is the ratio of their voltage sensitivities ($\frac{S_{V2}}{S_{V1}}$)?

a) 0.8

b) 1.44

c) 2.16

d) 3.6

108 / 288

Category: Moving-Coil Galvanometer

108. What is the minimum detectable current for a suspended-coil galvanometer with a torsional constant of $1.5 \times 10^{-6} \, \text{Nm/degree}$, 150 turns, a coil area of $1 \times 10^{-3} \, \text{m}^2$, and a magnetic field of 0.2 T if the smallest measurable deflection is 0.05 degrees?

a) $1.25 \, \mu \text{A}$

b) $2.5 \, \mu \text{A}$

c) $5 \, \mu \text{A}$

d) $10 \, \mu \text{A}$

109 / 288

Category: Principle of operation.

109. (A) In a moving-coil galvanometer, the deflecting torque is maximum when the plane of the coil is parallel to the magnetic field.
(R) The deflecting torque in a moving-coil galvanometer is given by $\tau = N I A B \sin \theta$, which becomes maximum when $\theta = 90^\circ$.

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 / 288

Category: Moving-Coil Galvanometer

110. A galvanometer with a coil resistance of $50 \, \Omega$ and full-scale deflection current of $1 \, \text{mA}$ is to be converted into an ammeter measuring up to $1 \, \text{A}$. What shunt resistance is required?

a) $0.01 \, \Omega$

b) $0.02 \, \Omega$

c) $0.05 \, \Omega$

d) $0.10 \, \Omega$

111 / 288

Category: Conversion of Galvanometer in Ammeter

111. (A) A galvanometer can be converted into an ammeter by connecting a high resistance in series with it.
(R) The shunt resistance connected in parallel reduces the overall resistance of the galvanometer, allowing it to measure higher currents.

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.

112 / 288

Category: Principle of operation.

112. What is the relationship between the current $I$ and the displacement $d$ of the light spot in a moving-coil galvanometer?

a) $I \propto d^2$

b) $I \propto \sqrt{d}$

c) $I \propto \frac{1}{d}$

d) $I \propto d$

113 / 288

Category: Conversion of Galvanometer in Voltmeter

113. What is the formula to calculate the series resistance $R$ required to convert a galvanometer into a voltmeter measuring potential difference up to $V$, given the galvanometer resistance $G$ and full-scale deflection current $I_g$?

a) $\frac{V}{G} - I_g$

b) $\frac{G}{V} + I_g$

c) $\frac{V}{I_g} - G$

d) $\frac{I_g}{V} - G$

114 / 288

Category: Conversion of Galvanometer in Ammeter

114. A galvanometer with resistance 25 Ω and full-scale deflection current 10 mA is to be converted simultaneously into two ammeter ranges: 0-2 A and 0-10 A using two separate shunts. What is the ratio of the two shunt resistances ($S_1/S_2$) required for these ranges?

a) 4.00

b) 5.02

c) 6.50

d) 7.25

115 / 288

Category: Definition of magnetic moment.

115. A coil with 200 turns, each of area $0.01 \, \text{m}^2$, carries a current of 0.2 A. If it is placed in a magnetic field of 0.5 T such that the angle between the normal to the coil and the field is $45^\circ$, what is the torque acting on the coil?

a) $0.1 \, \text{N} \cdot \text{m}$

b) $0.1\sqrt{2} \, \text{N} \cdot \text{m}$

c) $0.2 \, \text{N} \cdot \text{m}$

d) $0.2\sqrt{2} \, \text{N} \cdot \text{m}$

116 / 288

Category: Torque on Current-Loop

116. A rectangular coil of 50 turns with dimensions 0.3 m $\times$ 0.4 m carries a current of 5 A. It is placed in a uniform magnetic field of 0.2 T such that the angle between the normal to the plane of the coil and the magnetic field is $30^\circ$. Calculate the torque acting on the coil.

a) 1.5 Nm

b) 3 Nm

c) 6 Nm

d) 7.5 Nm

117 / 288

Category: Definition of Magnetic Moment of a Coil

117. (A) The magnetic moment of a coil is defined as the product of current, number of turns, and area of the coil.
(R) The direction of the magnetic moment is along the normal to the plane of the coil.

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 / 288

Category: Definition of Magnetic Moment of a Coil

118. A square coil of side 0.2 m has 100 turns and carries a current of 1.5 A. The coil is placed in a magnetic field of 0.3 T with its plane parallel to the field. What is the direction of the torque experienced by the coil?

a) Along the direction of the magnetic field

b) Perpendicular to both the magnetic moment and the field

c) Opposite to the magnetic moment

d) Along the plane of the coil

119 / 288

Category: Sensitivity and factors affecting it.

119. How can the sensitivity of a galvanometer be increased?

a) By increasing resistance ($R$)

b) By decreasing the number of turns ($N$)

c) By using a stronger magnet (higher $B$)

d) By increasing the torsional constant ($c$)

120 / 288

Category: Voltage sensitivity.

120. What is the expression for voltage sensitivity of a galvanometer, given that $N$ is the number of turns, $A$ is the area of the coil, $B$ is the magnetic field, $c$ is the torsional constant, and $R$ is the resistance of the coil?

a) $\frac{N A B}{c}$

b) $\frac{A B}{c R}$

c) $\frac{N A B}{c R}$

d) $\frac{N B}{c R}$

121 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

121. An irregularly shaped planar loop of area $5 \times 10^{-4} \, \text{m}^2$ carrying a current of 4 A is placed in a uniform magnetic field of 2 T. The angle between the normal to the loop and the magnetic field is $60^\circ$. If the torque acting on this loop is equivalent to that on a square loop of side length $L$ under the same conditions, find $L$ (assuming both loops have the same number of turns).

a) 1.58 cm

b) 2.24 cm

c) 3.16 cm

d) 4.47 cm

122 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

122. (A) Increasing the number of turns ($N$) in a moving-coil galvanometer always increases its voltage sensitivity.
(R) Voltage sensitivity is directly proportional to the number of turns and inversely proportional to the resistance of the coil.

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.

123 / 288

Category: Conversion to Ammeter and Voltmeter

123. A galvanometer has a resistance of $50 \, \Omega$ and a full-scale deflection current of $10 \, \text{mA}$. What shunt resistance is required to convert it into an ammeter with a range of $0$ to $5 \, \text{A}$?

a) $0.05 \, \Omega$

b) $0.1 \, \Omega$

c) $0.15 \, \Omega$

d) $0.2 \, \Omega$

124 / 288

Category: Magnetic Moment and Torque

124. A triangular loop ABC (AB = BC = CA = 0.4 m) carries a current of 3 A and is placed in a uniform magnetic field of 0.8 T acting along the +x-axis. If side AB lies along the x-axis, what is the net force and torque on the loop?

a) Net force: 0 N; Torque: 0.166 N $\cdot$ m

b) Net force: 0.166 N; Torque: 0 N $\cdot$ m

c) Net force: 0.208 N; Torque: 0 N $\cdot$ m

d) Net force: 0 N; Torque: 0.208 N $\cdot$ m

125 / 288

Category: Voltage sensitivity.

125. (A) Increasing the number of turns ($N$) in a moving-coil galvanometer will always increase its voltage sensitivity.
(R) Voltage sensitivity is given by $\frac{\phi}{V} = \frac{N A B}{c R}$, where increasing $N$ increases the numerator but may also increase $R$ disproportionately.

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.

126 / 288

Category: Current and Voltage Sensitivity

126. The current sensitivity of a galvanometer is defined as:

a) The voltage drop across the galvanometer per unit current

b) The deflection produced per unit current

c) The resistance of the galvanometer per unit voltage

d) The torsion constant of the suspension per unit area

127 / 288

Category: Construction and working of a moving-coil galvanometer.

127. (A) The deflection of the coil in a moving-coil galvanometer is directly proportional to the current passing through it only when the magnetic field is radial.
(R) In a radial magnetic field, the plane of the coil always remains parallel to the magnetic field lines, ensuring $\sin \theta = 1$ and making the deflecting torque independent of the coil's angular position.

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.

128 / 288

Category: Radial Magnetic Field

128. A coil of 30 turns and area $4 \times 10^{-4} \, \text{m}^2$ is placed in a radial magnetic field of $0.04 \, \text{T}$. If the torsional constant of the hair springs is $2 \times 10^{-5} \, \text{Nm/rad}$, what current is required to produce an angular deflection of $10^\circ$?

a) $0.5 \, \text{mA}$

b) $0.727 \, \text{mA}$

c) $1.0 \, \text{mA}$

d) $1.5 \, \text{mA}$

129 / 288

Category: Conversion of Galvanometer to Ammeter and Voltmeter

129. A galvanometer has a resistance of $50 \, \Omega$ and shows full-scale deflection for a current of $2 \, \text{mA}$. What series resistance is required to convert it into a voltmeter with a range of $0$ to $50 \, \text{V}$?

a) $24500 \, \Omega$

b) $24950 \, \Omega$

c) $25000 \, \Omega$

d) $25500 \, \Omega$

130 / 288

Category: Construction and working of a moving-coil galvanometer.

130. In a moving-coil galvanometer, at equilibrium, the deflecting torque equals the restoring torque. If $K$ is the torsional constant of the suspension and $\phi$ is the deflection angle, what is the relationship between current $I$ and deflection $\phi$?

a) $\phi = \frac{N A B}{K} I$

b) $I = \frac{N A B}{K} \phi$

c) $I = \left( \frac{K}{N A B} \right) \phi$

d) $\phi = \left( \frac{K}{N A B} \right) I$

131 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

131. A square coil of side 4 cm has 100 turns carrying 2A current. It experiences maximum torque when placed in magnetic field of 0.1T. What is magnetic moment vector's direction relative to field at this instant?

a) Parallel to field

b) At 45° to field

c) Perpendicular to field

d) Anti-parallel to field

132 / 288

Category: Radial Magnetic Field

132. What is the deflecting torque acting on a 50-turn coil with an area of $2 \times 10^{-4} \, \text{m}^2$ carrying a current of $3 \times 10^{-4} \, \text{A}$ placed in a radial magnetic field of $80 \, \text{G}$? ($1 \, \text{G} = 10^{-4} \, \text{T}$)

a) $12 \times 10^{-8} \, \text{Nm}$

b) $18 \times 10^{-8} \, \text{Nm}$

c) $24 \times 10^{-8} \, \text{Nm}$

d) $30 \times 10^{-8} \, \text{Nm}$

133 / 288

Category: Current sensitivity.

133. (A) Increasing the number of turns ($N$) in a galvanometer coil always increases its voltage sensitivity.

(R) Voltage sensitivity is given by $\frac{\phi}{V} = \frac{N A B}{c R}$, where increasing $N$ directly increases the numerator.

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.

134 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

134. (A) The torque on a current-carrying loop in a uniform magnetic field is maximum when the plane of the loop is perpendicular to the magnetic field.
(R) The torque $\tau = N I A B \sin \theta$ is maximum when $\theta = 90^\circ$.

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 / 288

Category: Construction and working of a moving-coil galvanometer.

135. (A) The deflection of the coil in a moving-coil galvanometer is proportional to the current passing through it.

(R) In a radial magnetic field, the deflecting torque on the coil is directly proportional to 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.

136 / 288

Category: Definition of Magnetic Moment of a Coil

136. (A) The magnetic moment of a coil is independent of the number of turns in the coil.
(R) The torque acting on a coil placed in a uniform magnetic field depends only on the current passing through the coil and not on its geometry.

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 / 288

Category: Conversion to Ammeter and Voltmeter

137. A galvanometer has a resistance of $20 \, \Omega$ and a full-scale deflection current of $5 \, \text{mA}$. What series resistance is needed to convert it into a voltmeter with a range of 0 to 10 V?

a) 2000 $\Omega$

b) 1800 $\Omega$

c) 1980 $\Omega$

d) 2200 $\Omega$

138 / 288

Category: Conversion to Ammeter and Voltmeter

138. A galvanometer has a resistance of $20 \, \Omega$ and a full-scale deflection current of $2 \, \text{mA}$. What series resistance is needed to convert it into a voltmeter with a range of $0$ to $50 \, \text{V}$?

a) $24 \, \text{k}\Omega$

b) $25 \, \text{k}\Omega$

c) $24980 \, \Omega$

d) $30 \, \text{k}\Omega$

139 / 288

Category: Radial Magnetic Field

139. What is the net force acting on a planar current-loop placed in a uniform magnetic field?

a) Zero

b) Depends on the loop's orientation

c) Equal to the torque

d) Proportional to the current

140 / 288

Category: Definition of magnetic moment.

140. A rectangular coil with length 10 cm and width 5 cm has 50 turns and carries a current of 1 A. The plane of the coil makes an angle of $60^\circ$ with the direction of a uniform magnetic field. What is the direction of the magnetic moment?

a) Along the length of the coil

b) Along the width of the coil

c) Perpendicular to the plane of the coil

d) Parallel to the magnetic field

141 / 288

Category: Moving-Coil Galvanometer

141. A moving-coil galvanometer has a coil with 100 turns and area $1 \times 10^{-3} \, \text{m}^2$. It is placed in a radial magnetic field of 0.1 T. If the current passing through the coil is 5 mA, what is the deflecting torque acting on the coil?

a) $2.5 \times 10^{-5} \, \text{Nm}$

b) $5 \times 10^{-5} \, \text{Nm}$

c) $1 \times 10^{-4} \, \text{Nm}$

d) $2 \times 10^{-4} \, \text{Nm}$

142 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

142. A rectangular coil of area $0.2 \, \text{m}^2$ carrying a current of 5 A is placed in a uniform magnetic field of 0.4 T. The angle between the normal to the plane of the coil and the magnetic field is 30\textdegree. What is the torque acting on the coil if it has 10 turns?

a) 1 Nm

b) 2 Nm

c) 4 Nm

d) 8 Nm

143 / 288

Category: Conversion of Galvanometer in Voltmeter

143. (A) A high resistance is connected in series with a galvanometer to convert it into a voltmeter.
(R) The resistance of a voltmeter must be very high to prevent it from drawing current from 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.

144 / 288

Category: Moving-Coil Galvanometer

144. A moving-coil galvanometer has a coil of area $2 \times 10^{-3} \, \text{m}^2$, 100 turns, and a torsional constant of $5 \times 10^{-7} \, \text{Nm/degree}$. If the magnetic field is 0.1 T, what deflection occurs when a current of 0.2 mA passes through the coil?

a) 4 degrees

b) 6 degrees

c) 8 degrees

d) 10 degrees

145 / 288

Category: Conversion to Ammeter and Voltmeter

145. A galvanometer with $G = 30 \, \Omega$ is converted into an ammeter using a shunt resistance of $0.06 \, \Omega$. What is the effective resistance of the ammeter?

a) $0.03 \, \Omega$

b) $0.06 \, \Omega$

c) $0.09 \, \Omega$

d) $0.12 \, \Omega$

146 / 288

Category: Current sensitivity.

146. A galvanometer shows a deflection of 30 radians when a current of 15 microamperes is passed through it. What is the figure of merit of this galvanometer?

a) $5 \times 10^{-7}$ A/rad

b) $2 \times 10^6$ A/rad

c) $3 \times 10^{-6}$ A/rad

d) $7.5 \times 10^{-6}$ A/rad

147 / 288

Category: Radial Magnetic Field

147. A rectangular coil of 40 turns and area $3 \times 10^{-4} \, \text{m}^2$ is placed in a radial magnetic field of $0.03 \, \text{T}$. When a current of $1 \, \text{mA}$ flows, it produces an angular deflection of $12^\circ$. What is the torsional constant of the hair springs connected to the coil?

a) $3.6 \times 10^{-6} \, \text{Nm/rad}$

b) $1.72 \times 10^{-5} \, \text{Nm/rad}$

c) $5.4 \times 10^{-5} \, \text{Nm/rad}$

d) $3.14 \times 10^{-5} \, \text{Nm/rad}$

148 / 288

Category: Sensitivity and factors affecting it.

148. (A) Increasing the number of turns in the coil of a galvanometer increases its current sensitivity.
(R) The current sensitivity is directly proportional to the number of turns in the coil.

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.

149 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

149. What is the expression for torque $\tau$ on a rectangular current-carrying loop of area $A$, with $N$ turns, carrying current $I$ placed in a uniform magnetic field $\vec{B}$ at an angle $\theta$?

a) $\tau = N \cdot I \cdot A \cdot B \cdot \cos \theta$

b) $\tau = I \cdot A \cdot B \cdot \sin \theta$

c) $\tau = N \cdot I \cdot A \cdot B \cdot \sin \theta$

d) $\tau = N \cdot I \cdot A \cdot B$

150 / 288

Category: Magnetic Moment and Torque

150. (A) The torque acting on a current-carrying coil in a uniform magnetic field is maximum when the plane of the coil is perpendicular to the direction of the magnetic field.
(R) The torque $\tau$ on a coil is given by $\tau = mB \sin \theta$, where $\theta$ is the angle between the magnetic moment $\vec{m}$ and the magnetic field $\vec{B}$, and it reaches its maximum value when $\theta = 90^\circ$.

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 / 288

Category: Principle of operation.

151. What is the instantaneous deflecting torque acting on a moving-coil galvanometer when the normal to the plane of the coil makes an angle $\theta$ with the direction of the magnetic field?

a) $\tau = N I A B$

b) $\tau = N I A B \cos \theta$

c) $\tau = N I A B \sin \theta$

d) $\tau = \frac{c \phi}{N A B}$

152 / 288

Category: Magnetic Moment and Torque

152. The torque acting on a magnetic dipole of moment $\vec{m} = 4\,\hat{k}\,A \cdot m^2$ placed in a magnetic field $\vec{B} = 2\,\hat{i}\,T$ is:

a) $8\,\hat{i}\,N \cdot m$

b) $-8\,\hat{j}\,N \cdot m$

c) $8\,\hat{k}\,N \cdot m$

d) $8\,\hat{j}\,N \cdot m$

153 / 288

Category: Definition of Magnetic Moment of a Coil

153. A solenoid with 200 turns, length 0.5 m, and radius 0.05 m carries a current of 3 A. It is placed in a magnetic field of 0.8 T. Under what orientation will the solenoid experience maximum torque?

a) When the solenoid axis is at 45° to the field

b) When the solenoid axis is parallel to the field

c) When the solenoid's plane is parallel to the field

d) When the solenoid axis is perpendicular to the field

154 / 288

Category: Sensitivity and factors affecting it.

154. (A) Increasing the number of turns ($N$) in the coil of a galvanometer will always increase its voltage sensitivity.
(R) Voltage sensitivity depends on $\frac{N A B}{c R}$, where increasing $N$ increases the numerator but may also increase $R$, affecting the overall value.

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 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

155. Why is the magnetic field in a moving-coil galvanometer made radial?

a) To increase the number of turns (\$N\$)

b) To ensure constant torque for all coil positions

c) To reduce the resistance (\$R\$) of the coil

d) To decrease the magnetic field strength (\$B\$)

156 / 288

Category: Definition of Magnetic Moment of a Coil

156. When the plane of a coil is parallel to a uniform magnetic field $\vec{B}$, what is the torque $\tau$ acting on the coil with magnetic moment $\vec{m}$?

a) $\tau = 0$

b) $\tau = m B \cos 90°$

c) $\tau = m B$

d) $\tau = m B \sin 0°$

157 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

157. A circular loop of radius 8 cm, having 100 turns and carrying a current of 5 A, is placed in a uniform magnetic field of 0.8 T. What should be the orientation of the loop so that the torque acting on it is maximized?

a) Normal perpendicular to the magnetic field ($90^\circ$)

b) Normal parallel to the magnetic field ($0^\circ$)

c) Normal at $45^\circ$ to the magnetic field

d) Normal antiparallel to the magnetic field ($180^\circ$)

158 / 288

Category: Magnetic Moment and Torque

158. A circular coil of 50 turns with radius 0.10 m carries a current of 5.0 A. It is placed in a uniform magnetic field of 0.20 T such that the angle between the normal to the plane of the coil and the magnetic field is $60^{\circ}$. What is the torque acting on the coil?

a) 0.68 N$\cdot$m

b) 1.36 N$\cdot$m

c) 2.72 N$\cdot$m

d) 0.34 N$\cdot$m

159 / 288

Category: Formulae for both sensitivities.

159. If the number of turns in a galvanometer coil is doubled while keeping all other parameters constant, how does it affect the current sensitivity and voltage sensitivity?

a) Both sensitivities double

b) Current sensitivity doubles, voltage sensitivity remains same

c) Current sensitivity remains same, voltage sensitivity doubles

d) Both sensitivities remain same

160 / 288

Category: Conversion of Galvanometer to Ammeter and Voltmeter

160. (A) A galvanometer with resistance $G$ and full-scale deflection current $I_g$ can be converted into an ammeter of range $0$ to $I$ by connecting a shunt resistance $S = \frac{I_g}{I - I_g} \times G$ in parallel.

(R) The shunt resistance ensures that most of the current flows through the shunt, leaving only a small fraction $I_g$ to pass through the galvanometer coil, thereby protecting it from damage.

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.

161 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

161. Which of the following factors directly affects the voltage sensitivity of a moving-coil galvanometer?

a) Only torsional constant (\$c\$)

b) Resistance of the coil (\$R\$)

c) Both \$N\$ and \$R\$

d) All of the above

162 / 288

Category: Voltage sensitivity.

162. If the current sensitivity of a galvanometer increases but its resistance increases more than the increase in current sensitivity, what happens to its voltage sensitivity?

a) Increases

b) Decreases

c) Remains unchanged

d) Cannot be determined

163 / 288

Category: Moving-Coil Galvanometer

163. A moving-coil galvanometer has a coil with 100 turns, an area of $2 \times 10^{-4} \, \text{m}^2$, and is placed in a radial magnetic field of 0.15 T. If the torsional constant of the suspension is $5 \times 10^{-7} \, \text{Nm/degree}$, what current will produce a deflection of $20^\circ$?

a) $1.67 \times 10^{-3} \, \text{A}$

b) $2.50 \times 10^{-3} \, \text{A}$

c) $3.33 \times 10^{-3} \, \text{A}$

d) $5.00 \times 10^{-3} \, \text{A}$

164 / 288

Category: Voltage sensitivity.

164. (A) Increasing the number of turns ($N$) in a galvanometer coil always increases its voltage sensitivity.

(R) Voltage sensitivity is given by $\frac{\phi}{V} = \frac{N A B}{c R}$, where increasing $N$ directly increases the numerator.

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.

165 / 288

Category: Moving-Coil Galvanometer Principle

165. In a moving-coil galvanometer, the current passing through the coil is directly proportional to which of the following?

a) Deflection angle ($\phi$)

b) Number of turns ($N$)

c) Magnetic field strength ($B$)

d) Area of the coil ($A$)

166 / 288

Category: Conversion to Ammeter and Voltmeter

166. A galvanometer with a resistance of $30 \Omega$ and a full-scale deflection current of $1 \text{ mA}$ is converted into an ammeter of range $0$ to $10 \text{ A}$ using a shunt resistance $S$. What is the effective resistance of the converted ammeter?

a) $0.002 \Omega$

b) $0.003 \Omega$

c) $0.004 \Omega$

d) $0.005 \Omega$

167 / 288

Category: Principle of operation.

167. For a moving-coil galvanometer with a radial magnetic field, how is the current $I$ related to the deflection $\phi$?

a) $I \propto \phi^2$

b) $I \propto \sqrt{\phi}$

c) $I \propto \phi$

d) $I \propto \frac{1}{\phi}$

168 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

168. What is the maximum torque experienced by a rectangular loop with 50 turns, area $0.02 \ m^2$, carrying a current of 5 A, placed in a uniform magnetic field of 0.5 T?

a) 1.0 Nm

b) 2.5 Nm

c) 0.5 Nm

d) 5.0 Nm

169 / 288

Category: Moving-Coil Galvanometer

169. (A) The suspended-coil galvanometer is more sensitive than the pivoted-coil galvanometer.
(R) The suspension strip in a suspended-coil galvanometer offers negligible resistance to the rotation of the coil, allowing for greater deflection with smaller currents.

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.

170 / 288

Category: Conversion of Galvanometer to Ammeter and Voltmeter

170. A galvanometer has a coil resistance of $50 \, \Omega$ and requires a current of $2 \, \text{mA}$ for full-scale deflection. What series resistance $R$ is needed to convert it into a voltmeter with a range of $0$ to $10 \, \text{V}$?

a) $4900 \, \Omega$

b) $4950 \, \Omega$

c) $5000 \, \Omega$

d) $5050 \, \Omega$

171 / 288

Category: Definition of magnetic moment.

171. How is the direction of the magnetic moment vector (\$\vec{m}\$) determined for a current-carrying loop?

a) Along the tangent to the loop

b) Opposite to the direction of the current

c) Perpendicular to the plane of the loop (right-hand rule)

d) Parallel to the magnetic field

172 / 288

Category: Conversion of Galvanometer in Ammeter

172. A moving-coil galvanometer has a resistance of 25 $\Omega$ and shows full-scale deflection at a current of 2 mA. If we want to use it as an ammeter to measure currents up to 1 A, what should be the shunt resistance connected in parallel?

a) 0.0501 $\Omega$

b) 0.0250 $\Omega$

c) 0.1002 $\Omega$

d) 0.2004 $\Omega$

173 / 288

Category: Conversion of Galvanometer in Ammeter

173. A galvanometer has a resistance of 20 $\Omega$ and gives full-scale deflection for a current of 5 mA. What should be the shunt resistance to convert it into an ammeter of range 0 to 1 A?

a) 0.05 $\Omega$

b) 0.10 $\Omega$

c) 0.15 $\Omega$

d) 0.20 $\Omega$

174 / 288

Category: Principle of operation.

174. The plane of a 100-turn galvanometer coil (area = 3 cm$^2$) initially makes 30$^\circ$ angle with a uniform 0.25 T magnetic field. If the torsional constant is $8 \times 10^{-7}$ Nm/rad and current is 200 μA, what will be the equilibrium deflection?

a) 26.85$^\circ$

b) 37.12$^\circ$

c) 53.71$^\circ$

d) 60.00$^\circ$

175 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

175. (A) The torque on a current-carrying loop is maximum when the angle between the normal to the plane of the loop and the magnetic field is $90^\circ$.
(R) The torque is given by $\tau = N I A B \sin \theta$, and $\sin 90^\circ$ equals 1, which gives the maximum value of torque.

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.

176 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

176. A circular coil of radius 0.1 m has 100 turns and carries a current of 2 A. What is the magnitude of its magnetic moment?

a) 3.14 A$\cdot$m$^2$

b) 6.28 A$\cdot$m$^2$

c) 12.56 A$\cdot$m$^2$

d) 1.57 A$\cdot$m$^2$

177 / 288

Category: Sensitivity and factors affecting it.

177. What is the current sensitivity of a galvanometer given by?

a) $\frac{N A B}{c}$

b) $\frac{N A B}{c R}$

c) $\frac{\phi}{V}$

d) $\frac{c}{N A B}$

178 / 288

Category: Conversion of Galvanometer in Voltmeter

178. A galvanometer has a resistance of $50 \Omega$ and gives full-scale deflection for $1$ mA. It is converted into a voltmeter with a range of $0$ to $50$ V. Later, the range needs to be extended to $150$ V. What additional series resistance is required?

a) $50000 \Omega$

b) $75000 \Omega$

c) $100000 \Omega$

d) $125000 \Omega$

179 / 288

Category: Moving-Coil Galvanometer

179. Why is an aluminium frame used in the construction of a moving-coil galvanometer?

a) To increase the magnetic field strength

b) To reduce the weight and provide damping via eddy currents

c) To make the coil more conductive

d) To enhance the torsional constant of the suspension

180 / 288

Category: Current and Voltage Sensitivity

180. (A) Increasing the number of turns in a galvanometer coil increases both its current sensitivity and voltage sensitivity.
(R) The voltage sensitivity is inversely proportional to the resistance of the coil.

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.

181 / 288

Category: Sensitivity of Galvanometer

181. A galvanometer has 50 turns, a coil area of $1.5 \times 10^{-3} \, \text{m}^2$, a magnetic field strength of 0.30 T, and a resistance of 20 $\Omega$. If the current sensitivity is increased by 20\% by increasing the number of turns, what will be the new voltage sensitivity if the resistance becomes 25 $\Omega$?

a) 95\% of the original

b) 96\% of the original

c) 100\% of the original

d) 104\% of the original

182 / 288

Category: Definition of magnetic moment.

182. A rectangular coil of 50 turns, each with an area of $0.02 \, \text{m}^2$, carries a current of $4 \, \text{A}$. The coil is placed in a uniform magnetic field of $0.5 \, \text{T}$ such that the angle between the normal to the plane of the coil and the magnetic field is $30^\circ$. What is the magnitude of the torque acting on the coil?

a) $0.5 \, \text{N} \cdot \text{m}$

b) $1.0 \, \text{N} \cdot \text{m}$

c) $2.0 \, \text{N} \cdot \text{m}$

d) $4.0 \, \text{N} \cdot \text{m}$

183 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

183. What is the unit of current sensitivity for a moving-coil galvanometer?

a) radian/volt

b) ampere/radian

c) volt/radian

d) radian/ampere

184 / 288

Category: Sensitivity of Galvanometer

184. Which of the following changes will increase the voltage sensitivity of a galvanometer?

a) Increase the number of turns in the coil

b) Increase the torsional constant of the suspension

c) Use a stronger magnetic field

d) Decrease the area of the coil

185 / 288

Category: Conversion to Ammeter and Voltmeter

185. A galvanometer with a resistance of $50 \Omega$ and a full-scale deflection current of $2 \text{ mA}$ is to be converted into an ammeter capable of measuring up to $1 \text{ A}$. What should be the value of the shunt resistance $S$?

a) $0.05 \Omega$

b) $0.1 \Omega$

c) $0.5 \Omega$

d) $1 \Omega$

186 / 288

Category: Definition of Magnetic Moment of a Coil

186. A circular coil of 50 turns with radius 0.1 m carries a current of 2 A. It is placed in a uniform magnetic field of 0.5 T such that the plane of the coil makes an angle of 30° with the field direction. What is the magnitude of torque acting on the coil?

a) 0.68 N$\cdot$m

b) 1.36 N$\cdot$m

c) 2.72 N$\cdot$m

d) 0.34 N$\cdot$m

187 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

187. (A) The torque acting on a planar current-loop in a uniform magnetic field is given by $\tau = N I A B \sin \theta$.
(R) The net force on a planar current-loop in a uniform magnetic field 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.

188 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

188. (A) The torque on a current-carrying loop in a magnetic field is maximum when the plane of the loop is perpendicular to the magnetic field direction.
(R) The torque $\tau$ acting on a current-carrying loop in a magnetic field is given by $\tau = N I A B \sin \theta$, and $\sin \theta$ attains its maximum value of 1 when $\theta = 90^\circ$.

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.

189 / 288

Category: Sensitivity of Galvanometer

189. A moving-coil galvanometer has a current sensitivity of $4 \times 10^{-3}$ rad/A. If the magnetic field strength is doubled and all other parameters remain unchanged, what will be the new current sensitivity?

a) $2 \times 10^{-3}$ rad/A

b) $4 \times 10^{-3}$ rad/A

c) $6 \times 10^{-3}$ rad/A

d) $8 \times 10^{-3}$ rad/A

190 / 288

Category: Voltage sensitivity.

190. If the current sensitivity of a galvanometer is increased by increasing the number of turns ($N$), what could be a possible effect on its voltage sensitivity?

a) Voltage sensitivity always increases

b) Voltage sensitivity remains unchanged

c) Voltage sensitivity may decrease

d) Voltage sensitivity becomes zero

191 / 288

Category: Voltage sensitivity.

191. What is the unit of voltage sensitivity of a galvanometer?

a) volt/radian

b) ampere/radian

c) radian/volt

d) newtonm/volt

192 / 288

Category: Torque on Current-Loop

192. A rectangular loop of wire with dimensions 0.1 m by 0.2 m carries a current of 3 A and is placed in a uniform magnetic field of 0.5 T. The angle between the normal to the plane of the loop and the magnetic field is 30°. What is the torque acting on the loop?

a) $0.005\ \text{Nm}$

b) $0.010\ \text{Nm}$

c) $0.015\ \text{Nm}$

d) $0.020\ \text{Nm}$

193 / 288

Category: Radial Magnetic Field

193. A rectangular coil of 100 turns and area $8 \times 10^{-4} \, \text{m}^2$ is placed in a radial magnetic field of 0.05 T. If the torsional constant of the hair springs connected to the coil is $2 \times 10^{-5} \, \text{N m rad}^{-1}$, what current through the coil will produce an angular deflection of $30^\circ$?

a) $\frac{\pi}{60} \, \text{A}$

b) $\frac{\pi}{120} \, \text{A}$

c) $\frac{\pi}{240} \, \text{A}$

d) $\frac{\pi}{480} \, \text{A}$

194 / 288

Category: Moving-Coil Galvanometer

194. Why is a radial magnetic field used in a pivoted-coil galvanometer?

a) To increase the resistance of the coil

b) To make the field uniform and ensure constant torque

c) To reduce the effect of external magnetic fields

d) To minimize heat dissipation in the coil

195 / 288

Category: Moving-Coil Galvanometer Principle

195. (A) In a moving-coil galvanometer, the deflecting torque is maximized when the plane of the coil is parallel to the magnetic field.
(R) The deflecting torque $\tau$ is given by $N I A B \sin \theta$, which becomes maximum when $\theta = 90^\circ$.

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.

196 / 288

Category: Sensitivity of Galvanometer

196. Increasing which of the following will NOT increase the voltage sensitivity of a galvanometer?

a) Number of turns ($N$) in the coil

b) Magnetic field strength ($B$)

c) Area of the coil ($A$)

d) Torsional constant ($c$)

197 / 288

Category: Voltage sensitivity.

197. A galvanometer has a voltage sensitivity of 2 rad/V and a coil resistance of 50 Ω. What is its current sensitivity?

a) 25 rad/A

b) 50 rad/A

c) 100 rad/A

d) 200 rad/A

198 / 288

Category: Conversion to Ammeter and Voltmeter

198. A galvanometer with a resistance of $30 \, \Omega$ is converted into an ammeter using a shunt resistance of $0.03 \, \Omega$. What is the effective resistance of the converted ammeter?

a) 0.03 $\Omega$

b) 0.06 $\Omega$

c) 0.09 $\Omega$

d) 0.12 $\Omega$

199 / 288

Category: Radial Magnetic Field

199. If the current in the coil is doubled while keeping other parameters constant, how does the angular deflection change in a radial magnetic field?

a) Remains the same

b) Doubles

c) Halves

d) Quadruples

200 / 288

Category: Moving-Coil Galvanometer

200. Why is a radial magnetic field used in a pivoted-coil (Weston) galvanometer?

a) To reduce the weight of the coil

b) To ensure $\sin \theta = 1$ for constant torque

c) To eliminate the need for a soft-iron core

d) To decrease the resistance of the coil

201 / 288

Category: Construction and working of a moving-coil galvanometer.

201. If the number of turns in the coil of a moving-coil galvanometer is doubled and the area of the coil is halved while keeping all other parameters constant, how does the sensitivity of the galvanometer change?

a) It doubles

b) It halves

c) It remains the same

d) It becomes four times

202 / 288

Category: Conversion of Galvanometer in Voltmeter

202. A galvanometer has a resistance of $50 \Omega$ and requires a current of $5 \text{ mA}$ for full-scale deflection. What series resistance is needed to convert it into a voltmeter with a range of $10 \text{ V}$?

a) 1000 $\Omega$

b) 1500 $\Omega$

c) 1950 $\Omega$

d) 2000 $\Omega$

203 / 288

Category: Magnetic Moment and Torque

203. A rectangular loop of dimensions 0.2 m × 0.3 m carries a current of 2 A and is placed in a magnetic field of 1 T. The normal to the loop is initially perpendicular to the magnetic field. What work must be done to rotate the loop so that its plane becomes parallel to the magnetic field?

a) 0 J

b) 0.06 J

c) 0.12 J

d) 0.24 J

204 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

204. In which of the following cases will a circular loop of radius $r$ carrying current $I$ experience maximum torque when placed in a uniform magnetic field $B$?

a) When the magnetic field is perpendicular to the plane of the loop ($\theta = 0^\circ$)

b) When the magnetic field is parallel to the plane of the loop ($\theta = 90^\circ$)

c) When the magnetic field is at $45^\circ$ to the plane of the loop

d) When the magnetic field is anti-parallel to the plane of the loop ($\theta = 180^\circ$)

205 / 288

Category: Moving-Coil Galvanometer

205. Why is a soft-iron core used in a moving-coil galvanometer?

a) To increase the resistance of the coil

b) To decrease the current sensitivity

c) To make the magnetic field radial and concentrate magnetic lines

d) To reduce the number of turns in the coil

206 / 288

Category: Sensitivity of Galvanometer

206. A galvanometer has a voltage sensitivity of $2 \times 10^{-3}$ rad/V and a coil resistance of 15 $\Omega$. If the resistance is reduced to 10 $\Omega$ without changing any other parameter, what will be the new voltage sensitivity?

a) $1 \times 10^{-3}$ rad/V

b) $2 \times 10^{-3}$ rad/V

c) $3 \times 10^{-3}$ rad/V

d) $4 \times 10^{-3}$ rad/V

207 / 288

Category: Definition of magnetic moment.

207. A circular loop of radius $0.1 \, \text{m}$ carries a current of $2 \, \text{A}$. The direction of the magnetic moment vector associated with this loop is:

a) Along the tangent to the loop at any point

b) Radially outward from the center of the loop

c) Perpendicular to the plane of the loop

d) Opposite to the direction of current flow

208 / 288

Category: Radial Magnetic Field

208. A circular coil of 50 turns and radius 0.1 m carries a current of 0.5 A and is placed in a radial magnetic field of 0.2 T. What work must be done to rotate the coil by $90^\circ$ against the field?

a) $0.0125\pi^2 \, \text{J}$

b) $0.025\pi^2 \, \text{J}$

c) $0.05\pi^2 \, \text{J}$

d) $0.1\pi^2 \, \text{J}$

209 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

209. (A) For a current-carrying loop placed in a uniform magnetic field, the torque is maximum when the plane of the loop is parallel to the magnetic field.
(R) The torque $\tau$ on a current-loop depends on $\sin \theta$, where $\theta$ is the angle between the magnetic moment and the magnetic 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.

210 / 288

Category: Current sensitivity.

210. (A) Increasing the number of turns $N$ in a moving-coil galvanometer increases its current sensitivity but decreases its figure of merit.
(R) The figure of merit is inversely proportional to the current sensitivity of the galvanometer.

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.

211 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

211. (A) The net torque on a planar current-carrying loop placed in a uniform magnetic field is zero when the plane of the loop is perpendicular to the magnetic field.
(R) When the angle between $\vec{A}$ and $\vec{B}$ is $0^\circ$ or $180^\circ$, the torque becomes 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.

212 / 288

Category: Conversion of Galvanometer to Ammeter and Voltmeter

212. Which formula is used to calculate the series resistance required to convert a galvanometer into a voltmeter?

a) $S = \frac{I_g}{I - I_g} \times G$

b) $R = \frac{V}{I_g} + G$

c) $R = \frac{V}{I_g} - G$

d) $S = \frac{G}{I_g}$

213 / 288

Category: Conversion of Galvanometer in Ammeter

213. A galvanometer has a coil resistance of 60 $\Omega$ and requires a current of 8 mA for full-scale deflection. To convert it into an ammeter reading up to 3 A, calculate the shunt resistance needed.

a) 0.3208 $\Omega$

b) 0.0802 $\Omega$

c) 0.1604 $\Omega$

d) 0.2406 $\Omega$

214 / 288

Category: Torque on Current-Loop

214. (A) A current-carrying loop in a uniform magnetic field attains stable equilibrium when its plane is perpendicular to the magnetic field.
(R) The torque on the loop is zero in stable equilibrium because the magnetic moment $\vec{M}$ and the magnetic field $\vec{B}$ are parallel.

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.

215 / 288

Category: Conversion of Galvanometer in Voltmeter

215. A voltmeter graded as $4000 \Omega/V$ reads $5$ V at full scale. What is its resistance when measuring a $20$ V range after modification, and how does its sensitivity compare?

a) $5000 \Omega/V$, more sensitive

b) $4000 \Omega/V$, same sensitivity

c) $3000 \Omega/V$, less sensitive

d) $2000 \Omega/V$, half sensitive

216 / 288

Category: Moving-Coil Galvanometer

216. The current sensitivity of a moving-coil galvanometer can be increased by:

a) Decreasing the number of turns in the coil

b) Using a suspension strip with a higher torsional constant

c) Increasing the magnetic field strength

d) Reducing the area of the coil

217 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

217. (A) The torque acting on a planar current-carrying loop in a uniform magnetic field is zero when the plane of the loop is perpendicular to the magnetic field.
(R) In this orientation, the angle $\theta$ between the normal to the loop and the magnetic field is $0^\circ$, making $\sin \theta = 0$.

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.

218 / 288

Category: Torque on Current-Loop

218. A square coil of side 0.1 m has 50 turns and carries a current of 2 A. It is placed in a magnetic field such that the torque experienced is $0.04\ \text{Nm}$. What is the magnetic field strength if the angle between the normal to the plane of the coil and the magnetic field is $60^\circ$?

a) $0.0231\ \text{T}$

b) $0.0462\ \text{T}$

c) $0.0924\ \text{T}$

d) $0.1848\ \text{T}$

219 / 288

Category: Radial Magnetic Field

219. A circular coil of 50 turns with an area of $2 \times 10^{-4} \, \text{m}^2$ is placed in a radial magnetic field of $0.02 \, \text{T}$. If the current flowing through the coil is $0.5 \, \text{A}$, what is the deflecting torque acting on the coil?

a) $0.5 \times 10^{-4} \, \text{Nm}$

b) $1 \times 10^{-4} \, \text{Nm}$

c) $2 \times 10^{-4} \, \text{Nm}$

d) $4 \times 10^{-4} \, \text{Nm}$

220 / 288

Category: Current sensitivity.

220. Which of the following changes will decrease the current sensitivity of a moving-coil galvanometer?

a) Decreasing the number of turns ($N$) in the coil.

b) Increasing the area ($A$) of the coil.

c) Increasing the magnetic field strength ($B$).

d) Increasing the torsional constant ($c$) of the suspension.

221 / 288

Category: Current sensitivity.

221. The current sensitivity of a galvanometer is given by $\frac{\phi}{I} = \frac{N A B}{c}$. If the number of turns ($N$) is doubled while keeping all other parameters constant, how does the current sensitivity change?

a) It remains unchanged.

b) It becomes half.

c) It doubles.

d) It becomes four times.

222 / 288

Category: Conversion of Galvanometer in Ammeter

222. (A) A galvanometer can be converted into an ammeter by connecting a high resistance in series with it.
(R) The purpose of the shunt is to bypass most of the current, allowing only a small fraction to pass through the galvanometer coil.

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 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

223. A circular loop of radius $r$ carrying current $I$ is placed in a uniform magnetic field $B$. What is the net force acting on the loop?

a) $I B r$

b) $2 \pi r I B$

c) Zero

d) $\pi r^2 I B$

224 / 288

Category: Sensitivity of Galvanometer

224. (A) Increasing the number of turns in the coil of a galvanometer increases its current sensitivity.
(R) Current sensitivity is directly proportional to the number of turns $N$ in the coil.

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.

225 / 288

Category: Moving-Coil Galvanometer Principle

225. What is the expression for the deflecting torque acting on a moving-coil galvanometer when the coil is placed in a radial magnetic field?

a) $\tau = N I A B$

b) $\tau = N I A B \sin \theta$

c) $\tau = \frac{N I A}{\sin \theta}$

d) $\tau = \frac{c \phi}{N I A B}$

226 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

226. For a current-carrying loop in a uniform magnetic field, at what angle between the normal to the plane of the loop and the magnetic field will the torque be maximum?

a) $0^\circ$

b) $30^\circ$

c) $45^\circ$

d) $90^\circ$

227 / 288

Category: Magnetic Moment and Torque

227. (A) The torque on a current-carrying coil is maximum when the plane of the coil is parallel to the magnetic field.
(R) The torque $\tau$ depends on $\sin \theta$, where $\theta$ is the angle between the normal to the plane of the coil and the magnetic 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.

228 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

228. A rectangular loop with 50 turns, carrying a current of 2 A, is placed in a uniform magnetic field of 0.5 T. The dimensions of the loop are 10 cm × 20 cm. What is the torque acting on the loop when the angle between the normal to the plane of the loop and the magnetic field is 30°?

a) 0.25 Nm

b) 0.5 Nm

c) 1.0 Nm

d) 0.75 Nm

229 / 288

Category: Conversion of Galvanometer in Ammeter

229. A galvanometer has a coil resistance of 30 $\Omega$ and requires 2 mA for full-scale deflection. To convert it into an ammeter measuring 0 to 500 mA, what is the required shunt resistance?

a) 0.10 $\Omega$

b) 0.12 $\Omega$

c) 0.15 $\Omega$

d) 0.18 $\Omega$

230 / 288

Category: Construction and working of a moving-coil galvanometer.

230. In a moving-coil galvanometer, the deflecting torque $\tau$ acting on the coil is given by:

a) $\tau = N I A B \sin \theta$

b) $\tau = N I A B$

c) $\tau = k \phi$

d) $\tau = \frac{k}{N A B}$

231 / 288

Category: Conversion of Galvanometer to Ammeter and Voltmeter

231. A galvanometer with resistance $G = 30 \, \Omega$ gives full-scale deflection for a current of $5 \, \text{mA}$. What shunt resistance $S$ is required to convert it into an ammeter measuring up to $1 \, \text{A}$?

a) $0.15 \, \Omega$

b) $0.25 \, \Omega$

c) $0.35 \, \Omega$

d) $0.45 \, \Omega$

232 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

232. A square loop of side 0.1 m carrying a current of 2 A is placed in a uniform magnetic field of 0.5 T. What is the net force acting on the loop?

a) 0.1 N

b) 0.2 N

c) 0.5 N

d) 0 N

233 / 288

Category: Principle of operation.

233. In a moving-coil galvanometer, what condition holds true when the coil is in equilibrium?

a) Deflecting torque > Restoring torque

b) Deflecting torque < Restoring torque

c) Deflecting torque = Restoring torque

d) No torque acts on the coil

234 / 288

Category: Magnetic Moment and Torque

234. A solenoid has 200 turns, each of radius 0.05 m, and carries a current of 3.0 A. It is placed in a uniform magnetic field of 0.10 T such that the angle between the axis of the solenoid and the magnetic field is $45^{\circ}$. Determine the torque experienced by the solenoid.

a) 0.166 N$\cdot$m

b) 0.333 N$\cdot$m

c) 0.666 N$\cdot$m

d) 0.083 N$\cdot$m

235 / 288

Category: Conversion to Ammeter and Voltmeter

235. (A) A galvanometer with a high resistance $G$ converts more accurately into an ammeter when a shunt resistance $S$ is connected in parallel, as it minimizes the voltage drop across the galvanometer.
(R) For accurate current measurement, the resistance of the ammeter must be very low to avoid significant voltage drop.

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.

236 / 288

Category: Construction and working of a moving-coil galvanometer.

236. What is the deflecting torque acting on a moving-coil galvanometer when a current $I$ flows through it, given that the coil has $N$ turns, area $A$, and the magnetic field strength is $B$? Assume the angle between the normal to the coil and the magnetic field is $90^\circ$.

a) $N I / A B$

b) $\frac{N A B}{I}$

c) $N I A B$

d) $N I + A B$

237 / 288

Category: Moving-Coil Galvanometer Principle

237. A galvanometer has a reduction factor $K = 2 \times 10^{-4} \text{ A/rad}$. If the deflection measured on the scale is $15 \text{ cm}$ and the distance from the mirror to the scale is $3 \text{ m}$, what is the current flowing through the galvanometer?

a) $2.5 \times 10^{-6} \text{ A}$

b) $5 \times 10^{-6} \text{ A}$

c) $7.5 \times 10^{-6} \text{ A}$

d) $1 \times 10^{-5} \text{ A}$

238 / 288

Category: Principle of operation.

238. In a galvanometer with reduction factor K = 2 μA/mm, the scale is placed 1.5 m from the mirror. If a current causes 15 cm displacement of light spot, what is the value of current?

a) 7.5 μA

b) 30 μA

c) 300 μA

d) 150 μA

239 / 288

Category: Sensitivity and factors affecting it.

239. A galvanometer has its torsional constant $c$ reduced to half its original value while keeping all other parameters unchanged. How does this affect its current and voltage sensitivities?

a) Both decrease by half

b) Both remain unchanged

c) Both double

d) Only current sensitivity doubles

240 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

240. A rectangular loop (3cm × 5cm) with 50 turns carrying 0.5A is placed such that its normal makes 60° with 0.8T magnetic field. If only the length doubles while other parameters remain same, what happens to torque?

a) Becomes half

b) Remains same

c) Doubles

d) Quadruples

241 / 288

Category: Moving-Coil Galvanometer

241. What is the principle behind the working of a moving-coil galvanometer?

a) Deflection due to force on a stationary coil

b) Rotation caused by heating effect of current

c) Torque on a current-carrying coil in a magnetic field

d) Induction of emf due to changing magnetic flux

242 / 288

Category: Sensitivity of Galvanometer

242. A galvanometer has a current sensitivity of $5\,\text{rad/A}$ and a coil resistance of $20\,\Omega$. What is its voltage sensitivity?

a) 0.025 rad/V

b) 0.20 rad/V

c) 0.25 rad/V

d) 0.30 rad/V

243 / 288

Category: Voltage sensitivity.

243. The figure of merit of a galvanometer is 0.5 rad/A. If the coil resistance is 20 Ω, what is the voltage sensitivity of the galvanometer?

a) 0.025 rad/V

b) 0.05 rad/V

c) 0.1 rad/V

d) 0.2 rad/V

244 / 288

Category: Torque on Current-Loop

244. At what angle $\theta$ between the normal to the plane of a current-carrying loop and the magnetic field will the torque be maximum?

a) $0^\circ$

b) $30^\circ$

c) $60^\circ$

d) $90^\circ$

245 / 288

Category: Torque on Current-Loop

245. A circular loop of radius 0.05 m carries a current of 5 A and is placed in a magnetic field of 0.2 T. At what angle should the loop be oriented relative to the magnetic field to experience the maximum torque?

a) $0^\circ$

b) $30^\circ$

c) $45^\circ$

d) $90^\circ$

246 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

246. A rectangular coil with 50 turns, carrying a current of 2 A, has dimensions 10 cm $\times$ 20 cm and is placed in a uniform magnetic field of 1.5 T. The normal to the plane of the coil makes an angle of $30^\circ$ with the magnetic field. Calculate the torque acting on the coil.

a) 0.45 Nm

b) 1.5 Nm

c) 3.0 Nm

d) 6.0 Nm

247 / 288

Category: Conversion to Ammeter and Voltmeter

247. A galvanometer has a resistance of $20 \Omega$ and gives full-scale deflection for a current of $5 \text{ mA}$. What series resistance $R$ is needed to convert it into a voltmeter with a range of $0$ to $10 \text{ V}$?

a) $1000 \Omega$

b) $1500 \Omega$

c) $1980 \Omega$

d) $2000 \Omega$

248 / 288

Category: Formulae for both sensitivities.

248. In a moving-coil galvanometer, if the magnetic field strength is increased by 40\% and simultaneously the coil resistance is decreased by 30\%, what will be the percentage change in voltage sensitivity? (Assume other parameters remain unchanged)

a) 10\% increase

b) 100\% increase

c) 70\% increase

d) 58\% increase

249 / 288

Category: Current and Voltage Sensitivity

249. What happens to the voltage sensitivity of a galvanometer if its coil resistance $R$ is doubled while keeping other parameters constant?

a) It becomes double

b) It remains unchanged

c) It becomes half

d) It becomes four times

250 / 288

Category: Torque on Current-Loop

250. What is the torque acting on a single-turn rectangular coil of area 0.05 m$^2$, carrying a current of 3 A, placed in a magnetic field of 0.02 T when the angle between the normal to the plane of the coil and the magnetic field is 30$^\circ$?

a) $1.5 \times 10^{-4}$ Nm

b) $3.0 \times 10^{-3}$ Nm

c) $1.5 \times 10^{-3}$ Nm

d) $3.0 \times 10^{-4}$ Nm

251 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

251. (A) Increasing the number of turns ($N$) in a moving-coil galvanometer always increases its voltage sensitivity.
(R) The voltage sensitivity is inversely proportional to the resistance ($R$) of the coil, which increases with $N$.

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.

252 / 288

Category: Voltage sensitivity.

252. If the number of turns in a galvanometer coil is doubled while keeping all other parameters (area, magnetic field, torsional constant, resistance) the same, how does the voltage sensitivity change?

a) Remains the same

b) Halves

c) Doubles

d) Quadruples

253 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

253. Which of the following correctly represents the torque $\vec{\tau}$ on a current-carrying loop in a magnetic field $\vec{B}$ if the magnetic moment is $\vec{m}$?

a) $\vec{\tau} = \vec{B} \times \vec{m}$

b) $\vec{\tau} = \vec{m} \cdot \vec{B}$

c) $\vec{\tau} = \vec{m} \times \vec{B}$

d) $\vec{\tau} = \vec{B} / \vec{m}$

254 / 288

Category: Sensitivity and factors affecting it.

254. A moving-coil galvanometer has a current sensitivity of 5 rad/A and voltage sensitivity of 2 rad/V. If the number of turns is increased by 50\% while keeping other parameters constant except resistance which increases proportionally, what will be the new voltage sensitivity?

a) 1.33 rad/V

b) 3.00 rad/V

c) 2.22 rad/V

d) 1.50 rad/V

255 / 288

Category: Formulae for both sensitivities.

255. The figure of merit of a galvanometer is found to be $0.02 \text{ rad/A}$. If the area of the coil is increased by 50\% and the torsional constant is reduced by 20\% while keeping other parameters unchanged, what will be the new current sensitivity?

a) 62.5 rad/A

b) 60.0 rad/A

c) 93.75 rad/A

d) 83.33 rad/A

256 / 288

Category: Moving-Coil Galvanometer

256. What is the formula for the current sensitivity of a moving-coil galvanometer?

a) $\frac{N A B}{c}$

b) $\frac{c}{N A B}$

c) $\frac{I}{\phi}$

d) $\frac{\phi}{c}$

257 / 288

Category: Conversion of Galvanometer in Ammeter

257. A galvanometer has a resistance of 20 Ω and gives full-scale deflection for a current of 5 mA. What should be the value of the shunt resistance to convert it into an ammeter with a range of 0 to 10 A?

a) 0.005 Ω

b) 0.01 Ω

c) 0.02 Ω

d) 0.05 Ω

258 / 288

Category: Moving-Coil Galvanometer

258. What is the principle behind the working of a moving-coil galvanometer?

a) Deflection due to gravitational force

b) Torque acting on a current-carrying coil in a magnetic field

c) Electromagnetic induction

d) Heating effect of current

259 / 288

Category: Moving-Coil Galvanometer

259. (A) In a moving-coil galvanometer, the deflection of the coil is directly proportional to the current flowing through it only when the magnetic field is radial.
(R) A radial magnetic field ensures that the plane of the coil always remains parallel to the magnetic field lines, making $\sin \theta = 1$ and thus the deflecting torque becomes independent of the angle of rotation.

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.

260 / 288

Category: Formulae for both sensitivities.

260. A galvanometer has current sensitivity of $2 \text{ rad/A}$ and voltage sensitivity of $0.5 \text{ rad/V}$. If the number of turns in the coil is doubled while keeping all other parameters constant except resistance which increases by 2.5 times, what will be the new voltage sensitivity?

a) 1.0 rad/V

b) 0.4 rad/V

c) 0.8 rad/V

d) 0.25 rad/V

261 / 288

Category: Construction and working of a moving-coil galvanometer.

261. Which of the following modifications will increase the sensitivity of a moving-coil galvanometer?

a) Decreasing the number of turns in the coil

b) Using a weaker magnetic field

c) Increasing the torsional constant of the suspension

d) Increasing the area of the coil

262 / 288

Category: Conversion to Ammeter and Voltmeter

262. A galvanometer with a resistance of $100 \Omega$ and full-scale deflection current of $10 \, \text{mA}$ is to be converted into an ammeter of range 0 to 1 A. What should be the value of the shunt resistance?

a) 0.99 $\Omega$

b) 1.01 $\Omega$

c) 0.50 $\Omega$

d) 2.00 $\Omega$

263 / 288

Category: Definition of Magnetic Moment of a Coil

263. Which of the following correctly describes the direction of the magnetic moment of a current-carrying coil?

a) Opposite to the direction of the current

b) Along the tangent to the coil

c) Parallel to the plane of the coil

d) Perpendicular to the plane of the coil

264 / 288

Category: Magnetic Moment and Torque

264. A rectangular loop of dimensions 0.20 m $\times$ 0.30 m carries a current of 4.0 A. The loop is placed in a uniform magnetic field of 0.50 T such that the normal to the plane of the loop makes an angle of $30^{\circ}$ with the field. Calculate the magnetic moment of the loop.

a) 0.12 A$\cdot$m$^2$

b) 0.24 A$\cdot$m$^2$

c) 0.48 A$\cdot$m$^2$

d) 1.20 A$\cdot$m$^2$

265 / 288

Category: Moving-Coil Galvanometer Principle

265. In a moving-coil galvanometer with a radial magnetic field, which of the following factors does NOT affect the deflecting torque?

a) Number of turns in the coil

b) Current through the coil

c) Angle between coil and magnetic field

d) Area of the coil

266 / 288

Category: Sensitivity and factors affecting it.

266. For a moving-coil galvanometer, how does increasing the number of turns ($N$) while keeping other parameters constant affect its voltage sensitivity ($\frac{\phi}{V}$)?

a) It always increases

b) It remains unchanged

c) It may decrease

d) It becomes zero

267 / 288

Category: Definition of magnetic moment.

267. (A) The magnetic moment $\vec{m}$ of a coil is always parallel to the torque $\vec{\tau}$ experienced by the coil when placed in a uniform magnetic field $\vec{B}$.
(R) The torque acting on a current-carrying coil in a magnetic field is given by $\vec{\tau} = \vec{m} \times \vec{B}$, which implies that $\vec{\tau}$ is perpendicular to both $\vec{m}$ and $\vec{B}$.

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.

268 / 288

Category: Radial Magnetic Field

268. (A) The torque acting on a current-carrying coil in a radial magnetic field is given by $\tau = N I A B$.
(R) In a radial magnetic field, the plane of the coil always remains parallel to the field lines.

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.

269 / 288

Category: Conversion of Galvanometer in Voltmeter

269. A voltmeter is graded as $4000 \Omega/\text{V}$. If it reads $10 \text{ V}$ at full-scale deflection, what is the resistance of the voltmeter?

a) 400 $\Omega$

b) 4000 $\Omega$

c) 40000 $\Omega$

d) 50000 $\Omega$

270 / 288

Category: Conversion of Galvanometer in Voltmeter

270. Why is a high resistance connected in series with a galvanometer to convert it into a voltmeter?

a) To decrease the overall resistance of the voltmeter

b) To allow more current to flow through the galvanometer

c) To prevent the galvanometer from overheating

d) To ensure the voltmeter draws negligible current from the circuit

271 / 288

Category: Current and Voltage Sensitivity

271. Two galvanometers $G_1$ and $G_2$ have the same current sensitivity but $G_2$ has twice the resistance of $G_1$. What is the ratio of their voltage sensitivities ($S_{V1}/S_{V2}$)?

a) 0.5

b) 1

c) 2

d) 4

272 / 288

Category: Moving-Coil Galvanometer Principle

272. (A) The deflection of the coil in a moving-coil galvanometer is directly proportional to the current passing through it.
(R) In a radial magnetic field, the deflecting torque $\tau = N I A B$ is constant for all positions of the coil.

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.

273 / 288

Category: Voltage sensitivity.

273. (A) The voltage sensitivity of a galvanometer can be increased by decreasing the resistance of its coil.
(R) Voltage sensitivity is given by $\frac{\phi}{V} = \frac{N A B}{c R}$ where decreasing $R$ increases the sensitivity.

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.

274 / 288

Category: Magnetic Moment and Torque

274. A circular coil of radius 10 cm has 50 turns and carries a current of 5 A. It is placed in a uniform magnetic field of 0.5 T such that the plane of the coil makes an angle of 30° with the field direction. What is the magnitude of the torque experienced by the coil?

a) 1.96 N $\cdot$ m

b) 3.40 N $\cdot$ m

c) 5.89 N $\cdot$ m

d) 6.28 N $\cdot$ m

275 / 288

Category: Formulae for both sensitivities.

275. What is the unit of current sensitivity of a galvanometer?

a) radian/volt

b) ampere/radian

c) radian/ampere

d) volt/radian

276 / 288

Category: Sensitivity of a Moving-Coil Galvanometer

276. (A) Increasing the number of turns in a moving-coil galvanometer increases its current sensitivity.
(R) Current sensitivity is directly proportional to the number of turns $N$.

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.

277 / 288

Category: Construction and working of a moving-coil galvanometer.

277. A moving-coil galvanometer is mistakenly set up such that the magnetic field is not perfectly radial but makes an angle of 60° with the plane of the coil. If the coil has 50 turns, area $1 \times 10^{-4} \, \text{m}^2$, and carries a current of $10^{-5} \, \text{A}$ in a field of 0.2 T, what is the deflection angle when the restoring torque constant is $1 \times 10^{-8} \, \text{Nm/rad}$?

a) $14.32^\circ$

b) $28.65^\circ$

c) $45^\circ$

d) $57.30^\circ$

278 / 288

Category: Magnetic Moment and Torque

278. A current loop of area $0.05\,m^2$ carrying a current of $3\,A$ is placed in a uniform magnetic field of $0.2\,T$ at an angle of $30^\circ$. What is the torque acting on the loop?

a) $0.015\,N \cdot m$

b) $0.03\,N \cdot m$

c) $0.006\,N \cdot m$

d) $0.012\,N \cdot m$

279 / 288

Category: Current and Voltage Sensitivity

279. A galvanometer has $N = 50$ turns, $A = 1.5 \times 10^{-3} \, \text{m}^2$, $B = 0.15 \, \text{T}$, and a torsion constant $c = 2.5 \times 10^{-4} \, \text{N}\cdot\text{m/rad}$. What is its current sensitivity?

a) 30 rad/A

b) 45 rad/A

c) 60 rad/A

d) 75 rad/A

280 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

280. (A) The torque on a planar current-carrying loop in a uniform magnetic field depends on the angle between the normal to the plane of the loop and the magnetic field.
(R) The torque $\tau = N I A B \sin \theta$ where $\theta$ is the angle between the normal to the plane of the loop and the magnetic 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.

281 / 288

Category: Moving-Coil Galvanometer Principle

281. Which factor does NOT affect the sensitivity of a moving-coil galvanometer?

a) Number of turns ($N$)

b) Magnetic field strength ($B$)

c) Torsional constant ($c$) of the suspension

d) Color of the suspension strip

282 / 288

Category: Derivation of the expression for torque on a current-carrying loop.

282. Under what condition is the torque on a current-carrying loop zero in a uniform magnetic field?

a) When the loop is parallel to the magnetic field

b) When the loop is at $45^\circ$ to the magnetic field

c) When the loop is perpendicular to the magnetic field

d) When the loop carries no current

283 / 288

Category: Sensitivity and factors affecting it.

283. (A) Increasing the number of turns $N$ in a galvanometer coil always increases both current sensitivity and voltage sensitivity.
(R) The voltage sensitivity $\frac{\phi}{V} = \frac{N A B}{c R}$ depends inversely on the resistance $R$ of the coil.

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.

284 / 288

Category: Sensitivity of Galvanometer

284. (A) The current sensitivity of a galvanometer can be increased by increasing the number of turns in its coil.
(R) Increasing the number of turns increases the magnetic moment, thereby increasing the deflection for a given 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.

285 / 288

Category: Conversion of Galvanometer to Ammeter and Voltmeter

285. (A) A galvanometer can be converted into an ammeter by connecting a high resistance in series with it.
(R) An ammeter must have very low resistance to measure current accurately.

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.

286 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

286. A circular coil of 10 turns, radius $0.04\,m$, carrying a current of $5\,A$, is placed in a magnetic field of $0.5\,T$ at an angle of $30^\circ$ to the field. Calculate the torque acting on the coil.

a) $0.0314\,Nm$

b) $0.0628\,Nm$

c) $0.0942\,Nm$

d) $0.1257\,Nm$

287 / 288

Category: Torque on a Current-Loop in a Uniform Magnetic Field

287. Two loops, one square of side $a$ and another circular of radius $r$, carry the same current $I$ and have the same number of turns $N$. They are placed in the same uniform magnetic field $B$ at the same angle $\theta = 60^\circ$. If both loops enclose the same area, which loop experiences greater torque?

a) Square loop

b) Circular loop

c) Both experience the same torque

d) Cannot be determined without additional data

288 / 288

Category: Moving-Coil Galvanometer Principle

288. (A) In a moving-coil galvanometer, the deflection of the coil is directly proportional to the current passing through it.
(R) The deflecting torque acting on the coil is balanced by the restoring torque, which is proportional to the angle of deflection.

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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Class 12 Physics (Part 1) Chapter 8 Torque on a Current-Loop : Moving-Coil Galvanometer

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