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: Plan:
Same energy needs $C_pV_p^2=C_sV_s^2$.

Step 2: Ratio of capacitances:
$\dfrac{C_p}{C_s}=\dfrac{3C}{C/3}=9$.

Step 3: Square root:
$\dfrac{V_p^2}{V_s^2}=\dfrac{C_s}{C_p}=\dfrac19$, so $V_p:V_s=1:3$. Option (A).

Final Answer:
The parallel set has 9 times the capacitance, so needs one third the voltage. \[ \boxed{A} \]