
Five capacitors, each of capacitance 'C' are connected as shown in the figure. The ratio of equivalent…

- 1:4
- 2:3
- 3:1
- 5:2
Solution
Equivalent capacitance between P and R:
There are two parallel paths from P to R. The path P-Q-R consists of two series capacitors, with equivalent capacitance $\frac{C}{2}$. The path P-T-S-R consists of three series capacitors, with equivalent capacitance $\frac{C}{3}$. Combining these in parallel gives $C_{PR} = \frac{C}{2} + \frac{C}{3} = \frac{5C}{6}$.
Equivalent capacitance between P and Q:
There are two parallel paths from P to Q. The direct path is a single capacitor C. The alternate path P-T-S-R-Q consists of four series capacitors, with equivalent capacitance $\frac{C}{4}$. Combining these in parallel gives $C_{PQ} = C + \frac{C}{4} = \frac{5C}{4}$.
The ratio is $C_{PR} / C_{PQ} = \left( \frac{5C}{6} \right) / \left( \frac{5C}{4} \right) = \frac{2}{3}$, so the required ratio is 2:3.
$\boxed{2:3}$
Asked in: MHT CET 2025 (26 April Shift 2)