Question

Five equal capacitors each with capacitance \(C\) are connected as shown in the figure. Then, the equivalent capacitance between \(A\) and \(B\) is:

• A. \(5C\)
• B. \( \frac{C}{5} \)
• C. \(3C\)
• D. \(C\)

Hint:

In symmetric capacitor bridges, the central branch often carries no charge — remove it to simplify.

Answer 1

The Correct Option is D

Concept:
• Capacitors in series: \( \frac{1}{C_{eq}} = \sum \frac{1}{C} \)
• Capacitors in parallel: \( C_{eq} = \sum C \)

Step 1: Identify structure.
The circuit forms a bridge-like symmetric network.

Step 2: Use symmetry.
Due to symmetry, the potential at middle junctions becomes equal. Hence, no charge flows through the central bridge capacitor.

Step 3: Simplify circuit.
The network reduces to simple series-parallel combination:
• Left two capacitors combine
• Right two capacitors combine

Step 4: Final reduction.
After simplification: \[ C_{eq} = C \]