Six identical capacitors, each of capacitance C , are connected along the four edges and two diagonals of a square ABCD. An ideal conducting wire is then connected directly between corners A and B. The equivalent capacitance of the network

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Six identical capacitors, each of capacitance C , are connected along the four edges and two diagonals of a square ABCD. An ideal conducting wire is then connected directly between corners A and B. The equivalent capacitance of the network across corners C and D is

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Correct answer: B. 2C

When an ideal conducting wire connects corners A and B, they become an equipotential node (let us call it node M). The capacitor along the edge AB is connected between node M and node M, so it is short-circuited and stores no charge. Now, let us redraw the circuit between terminals C and D. The capacitors along BC and AC are both connected between node C and node M. They are in parallel, giving an equivalent capacitance of C + C = 2C . Similarly, the capacitors along AD and BD are both connected between node D and

Six identical capacitors, each of capacitance C , are connected along the four edges and two diagonals of a square ABCD. An ideal conducting wire is then connected directly between corners A and B. The equivalent capacitance of the network across corners C and D is

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