AIIMS2017Physics-Electrostatics

AIIMS 2017 Physics Capacitors MCQ Question

Type: MCQ-conceptual-Medium-Class 12

A parallel plate capacitor of capacitance CC is connected to a battery and charged to the potential difference VV. Another capacitor of capacitance 2C2C is connected to another battery and is charged to a potential difference 2V2V. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

A

Zero

B

25CV26\frac{25CV^2}{6}

C

3CV22\frac{3CV^2}{2}

D

9CV22\frac{9CV^2}{2}

Correct Answer

Option C

Detailed Explanation

Option C is correct because it correctly calculates the energy stored in a capacitor with an equivalent capacitance Ceq=3CC_{eq} = 3C when connected in parallel, leading to the expression U=12(3C)V2=32CV2U = \frac{1}{2} (3C) V^2 = \frac{3}{2} CV^2. Option A is misleading because it does not account for the correct equivalent capacitance when capacitors are in parallel. Option B incorrectly states the equivalent capacitance without proper context, as it should clarify that the capacitors are connected in parallel. Understanding these relationships is essential for analyzing circuits involving capacitors.

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