Question

The potential difference that must be applied across the parallel and series combination of three identical capacitors such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is

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

Hint:

Parallel capacitance is 9 times the series capacitance.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Energy stored in a capacitor is \(U=\tfrac12C_{eq}V^2\). We find the equivalent capacitance in each arrangement.

Step 2: Equivalent capacitances:
Parallel: \(C_p=3C\). Series: \(C_s=\dfrac C3\).

Step 3: Equal energy:
\[ \tfrac12(3C)V_p^2=\tfrac12\left(\frac C3\right)V_s^2 \]
\[ 3V_p^2=\frac{V_s^2}3\ \Rightarrow\ \frac{V_p^2}{V_s^2}=\frac19 \]

Step 4: Ratio:
\[ \frac{V_p}{V_s}=\frac13 \]
The ratio is \(1:3\), option (A).

Final Answer:
The potential difference ratio is 1 : 3. \[ \boxed{1:3} \]