Question

Two capacitors, \(C_1\) and \(C_2\) have their capacitances in the ratio 1:2. \(V_s\) and \(V_p\) are the potential differences applied across the series and parallel combination of \(C_1\) and \(C_2\) respectively, so that the energy stored in the two cases becomes same. The ratio \(V_s\) to \(V_p\) is

• A. \(\sqrt{2}:3\)
• B. \(3:\sqrt{2}\)
• C. \(2:\sqrt{3}\)
• D. \(\sqrt{3}:2\)

Hint:

Energy is \(\frac12C_{eq}V^2\); equate for the two combinations.

Answer 1

The Correct Option is B

Step 1: Write the voltage from the energy
$V=\sqrt{\dfrac{2U}{C_{eq}}}$, so for the same $U$, $V\propto\dfrac{1}{\sqrt{C_{eq}}}$.

Step 2: Compare
$\dfrac{V_s}{V_p}=\sqrt{\dfrac{C_p}{C_s}}=\sqrt{\dfrac92}=\dfrac{3}{\sqrt2}$, option (B).

Final Answer:
$V_s:V_p=3:\sqrt2$, option (B). \[ \boxed{3:\sqrt2} \]