Question

Three identical capacitors connected in series have net capacitance '\(x\)'. Then they are connected in parallel. The ratio of energy stored in series configuration to that in parallel configuration is (if both configurations are connected to the same source)

• A. \(1:3\)
• B. \(3:1\)
• C. \(1:9\)
• D. \(9:1\)

Hint:

Same voltage: U = (1/2) C V^2, so the energy ratio equals the ratio of the equivalent capacitances.

Answer 1

The Correct Option is C

Step 1: Use the series capacitance given as x:
The series net capacitance is $x = C/3$, so $C = 3x$. The parallel capacitance is $3C = 9x$.

Step 2: Energy at the same source:
$U\propto C_{eq}$ when $V$ is fixed. So $\dfrac{U_s}{U_p} = \dfrac{x}{9x} = \dfrac19$.

Step 3: Interpretation:
For the same voltage, parallel stores more energy because it has more capacitance. The factor 9 comes from $3\times3$, one 3 from the series reduction and one from the parallel increase.

Final Answer:
1:9, option (C). \[ \boxed{1:9 \text{ (C)}} \]