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Question #42784

Difficulty: 8/10 | 🟢 Free

The Question

A capacitor of capacitance $C_1 = 2 \text{ \mu F}$ is initially charged to a potential difference $V_0 = 30 \text{ V}$ . It is then connected in a closed series loop with an uncharged capacitor of capacitance $C_2 = 4 \text{ \mu F}$ , an ideal inductor of inductance $L = 5 \text{ mH}$ , and an open switch. If the switch is closed at $t = 0$ , what is the maximum potential difference across the capacitor $C_2$ during the subsequent oscillations? Assume the circuit has zero electrical resistance.

Options

A.
$10 \text{ V}$
B.
$15 \text{ V}$
C.
$20 \text{ V}$
D.
$30 \text{ V}$

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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

Common Potential Redistribution|L-C Circuit Analogy|Vector Calculus

Why This Question Is Tricky

Common Mistakes

This question tests the critical distinction between static charge redistribution and dynamic LC oscillations.

A common trap is applying the static 'common potential' formula $V = \frac{C_1 V_1 + C_2 V_2}{C_1 + C_2}$ , which yields $10 \text{ V}$ .

This static approach implicitly assumes the 'missing' electrostatic energy is permanently dissipated as heat.

However, in an ideal circuit with an inductor, this energy is temporarily stored in the magnetic field and drives the charge past the equilibrium point, causing the potential to oscillate symmetrically and reach a maximum of twice the equilibrium value.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electrostatic Potential and Capacitance - Class 12
Concept	Common Potential Redistribution
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free