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Question #42692

Difficulty: 8/10 | 🟢 Free

The Question

A capacitor of capacitance $C$ is initially charged to a potential difference $V_0$ . It is connected in a series circuit containing an open switch $S$ , an uncharged capacitor of capacitance $2C$ , and an ideal solenoid of self-inductance $L$ . The ohmic resistance of the circuit is negligible. If the switch $S$ is closed at $t = 0$ , what is the maximum potential difference developed across the initially uncharged capacitor during the subsequent LC oscillations?

Options

A.
$\frac{V_0}{3}$
B.
$\frac{2V_0}{3}$
C.
$\frac{V_0}{2}$
D.
V_0

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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

Common Potential Redistribution|Self-Inductance of Solenoid|Average Power over Cycle|Differential Equations

Why This Question Is Tricky

Common Mistakes

This question tests the 'instantaneous charge equalization' fallacy.

Students often incorrectly apply electrostatic charge redistribution, assuming the capacitors simply reach a common potential $V = \frac{C V_0}{C + 2C} = \frac{V_0}{3}$ .

They fail to recognize that the solenoid's self-inductance creates a back-EMF ( $L \frac{di}{dt}$ ) that governs the transient dynamics.

Instead of settling instantly, the system forms an LC oscillator.

The magnetic inertia of the inductor causes the charge transfer to overshoot the electrostatic equilibrium point, reaching exactly twice the equilibrium charge before the current reverses, resulting in a maximum potential difference of $\frac{2V_0}{3}$ .

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