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Question #43415

Difficulty: 8/10 | 🟢 Free

The Question

A charged capacitor of capacitance $C = 1 \ \mu\text{F}$ is connected across a parallel combination of a pure shunt resistor $S$ and a galvanometer. The galvanometer coil has a resistance $G = 20 \ \Omega$ and a self-inductance $L_g = 0.1 \ \text{mH}$ . For what range of values of $S$ will the voltage across the capacitor exhibit underdamped electromagnetic oscillations?

Options

A.
$S > 2.5 \ \Omega$
B.
$S > 0 \ \Omega$
C.
$S < 2.5 \ \Omega$
D.
$S > 20 \ \Omega$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Shunt Resistance Conversion|LC Circuit Oscillations|Resistor Phase Invariance

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to analyze transient responses in complex RLC networks, specifically avoiding the trap of treating a shunted inductor as a simple equivalent DC resistance.

Students commonly misapply the standard series RLC damping condition ( $R < 2\sqrt{L/C}$ ) by calculating an effective DC resistance $R_{eff} = \frac{GS}{G+S}$ .

Since $\frac{20S}{20+S} < 20 \ \Omega$ for all $S > 0$ , this flawed logic leads to the incorrect conclusion that the circuit is always oscillatory (Option B).

The correct approach requires deriving the characteristic equation from Kirchhoff's laws, revealing that the shunt resistor actually introduces a damping term inversely proportional to $S$ , making the circuit overdamped for small values of $S$ .

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