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Question #43035

Difficulty: 8/10 | 🟢 Free

The Question

A moving coil galvanometer consists of a coil with moment of inertia $I$ , torsional constant $k$ , $N$ turns, and cross-sectional area $A$ . It is placed in a uniform radial magnetic field of magnitude $B$ . The galvanometer is connected in a closed circuit to an ideal AC voltage source given by $V(t) = V_0 \sin(\omega t)$ . The total electrical resistance of the circuit is $R$ . Assume mechanical friction and air drag are completely absent. If the angular frequency $\omega$ of the voltage source is tuned exactly to the natural angular frequency of the galvanometer ( $\omega = \sqrt{k/I}$ ), what is the steady-state amplitude of the angular deflection of the coil?

Options

A.
$\frac{V_0}{NAB} \sqrt{\frac{I}{k}}$
B.
$\frac{V_0 NAB}{R k}$
C.
$\frac{V_0 R}{(NAB)^3} \sqrt{k I}$
D.
$\infty$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Galvanometer Sensitivity Logic|Driven Oscillations and Resonance|Physical Pendulum Inertia

Why This Question Is Tricky

Common Mistakes

This question tests the transition from static galvanometer logic to dynamic driven oscillations, specifically targeting the misconception that zero mechanical friction implies infinite amplitude at resonance.

Students often incorrectly assume the current is simply $i = V_0/R$ and apply the static deflection formula, or they recognize the resonance but ignore the back-EMF.

The trap lies in neglecting Electromagnetic Damping: the oscillating coil generates a velocity-dependent back-EMF ( $e = NAB \dot{\theta}$ ) which acts as a non-conservative damping force.

This internal electro-mechanical feedback limits the resonant amplitude to a finite value that is surprisingly independent of the circuit's electrical resistance.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Moving Charges and Magnetism - Class 12
Concept	Galvanometer Sensitivity Logic
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free