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Question

# Find the equivalent capacitance across points A and B. All the capacitors have capacitance C.

A
7C8
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B
7C4
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C
9C2
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D
9C4
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Solution

## The correct option is A 7C8The uppermost capacitor of capacity C can be considered as the equivalent of two capacitors joined in series, each having a capacity of 2C. Now, the circuit diagram can be redrawn as shown below. This circuit is symmetrical about the perpendicular bisector XY of AB. Hence, point X and point Y are at the same potential. To the left side of (X,Y), 2C and C are parallel. So, their equivalent =2C+C=3C Similar case in the right part of the circuit. The circuit further reduces to a setup shown below. Now, C and 3C are in series. So their equivalent =C×3CC+3C=3C4 Now reduced form of circuit will be as shown below. Now, 3C4 and C are in parallel, so their equivalent capacitance will be C′=3C4+C=7C4 So equivalent capacitance of the given circuit will be Ceq=7C4×7C47C4+7C4=7C8 Therefore, option (A) is the correct choice. Why this question? Tip: For this type of question, check for symmetry pattern and use equipotential method to simplify circuit.

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