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: Understanding the Concept:
Three identical capacitors, each of capacitance \(C\), are arranged once in series and once in parallel, and each arrangement is connected to the same source of voltage \(V\).

Step 2: Key Formula or Approach:
1. Series: \(C_s = \dfrac C3\).
2. Parallel: \(C_p = 3C\).
3. Energy at fixed voltage: \(U = \dfrac12C_{eq}V^2\).

Step 3: Detailed Explanation:
\[ \frac{U_s}{U_p} = \frac{C_s}{C_p} = \frac{C/3}{3C} = \frac19 \]
So the energy in the series arrangement is one ninth of that in the parallel arrangement.
Option (D) 9:1 is the inverse ratio. Option (A) 1:3 and (B) 3:1 would arise from comparing \(C/3\) with \(C\), or \(3C\) with \(C\), instead of comparing the two arrangements with each other.

Final Answer:
The ratio of energies is 1:9, option (C). \[ \boxed{1:9 \text{ (C)}} \]