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Question #43036

Difficulty: 8/10 | 🟢 Free

The Question

A moving coil galvanometer consists of a coil with $N = 100$ turns, each of area $A = 2 \times 10^{-4} \text{ m}^2$ , and has a moment of inertia $I = 10^{-6} \text{ kg m}^2$ about its axis of rotation. The coil is placed in a uniform radial magnetic field $B = 0.5 \text{ T}$ . The torsional constant of the suspension spring is $C = 10^{-6} \text{ N m rad}^{-1}$ . The resistance of the galvanometer coil is $R_g = 40 \ \Omega$ . The galvanometer is disconnected from any external circuit, and its terminals are shorted using a shunt resistance $R_s$ . What should be the value of $R_s$ so that if the coil is slightly displaced and released, it returns to its equilibrium position without oscillating (i.e., the system is critically damped)? Ignore mechanical friction and air drag.

Options

A.
$10 \ \Omega$
B.
$50 \ \Omega$
C.
$60 \ \Omega$
D.
$100 \ \Omega$

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

Shunt Resistance Conversion|Torque on Current Loop|Damped Oscillation Equation

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of the dynamic behavior of a galvanometer, specifically electromagnetic damping.

Students often memorize the static current sensitivity formula ( $C\theta = NiAB$ ) and treat the shunt merely as a static current divider for range extension.

They fail to recognize that a moving coil in a magnetic field acts as a generator, and the closed loop formed by the shunt allows an induced current to flow, creating a velocity-dependent damping torque ( $\tau \propto \dot{\theta}$ ).

By asking for the critical damping condition, the problem forces students to set up the second-order differential equation for a damped harmonic oscillator and correctly identify the electromagnetic damping coefficient $c = (NAB)^2 / (R_g + R_s)$ .

Common traps include ignoring the coil's own resistance $R_g$ (leading to $50 \ \Omega$ ) or missing the factor of 2 in the critical damping condition (leading to $60 \ \Omega$ or $100 \ \Omega$ ).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Moving Charges and Magnetism - Class 12
Concept	Shunt Resistance Conversion
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free