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

Five capacitors, each of capacitance 'C' are connected as shown in the figure. The ratio of equivalent capacitance between $P$ and $R$ and the equivalent capacitance between $P$ and $Q$ is
  1. 1:4
  2. 2:3
  3. 3:1
  4. 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)

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