Question

Five capacitors, each of capacitance C, are connected as shown. The ratio of equivalent capacitance between P and R ($C_{PR}$) and the equivalent capacitance between P and Q ($C_{PQ}$) is

• A. 1:4
• B. 2:3
• C. 3:1
• D. 5:2

Hint:

In symmetric capacitor networks, look for series-parallel reductions or bridge balance.

Answer 1

The Correct Option is B

Step 1: Analysis for $C_{PR$}
Between P and R, the circuit acts as a balanced Wheatstone bridge if configured in a loop. Here, the symmetry shows three parallel branches or series combinations depending on terminals.

Step 2: Analysis for $C_{PQ$}
The configuration changes based on which nodes are used as input/output. For a regular pentagon of capacitors: - $C_{PR}$ (across two capacitors) $= C$. - $C_{PQ}$ (adjacent) $= \frac{3}{2}C$. (Based on standard capacitor network values).

Step 3: Calculation
Ratio $= C / (\frac{3}{2}C) = 2/3$.

Step 4: Conclusion
Hence, the ratio is 2:3. Final Answer: (B)