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Elastic Potential Energy

Two capacitor...

Question

Two capacitors $C_{1}$ and $C_{2}$ have equal amount of energy stored in them. What is the ratio of potential differences across their plates.

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Solution

$E_{1} = \frac{1}{2} C_{1} V_{1}^{2} E_{2} = \frac{1}{2} C_{2} V_{2}^{2} E_{1} = E_{2}$
So,
$C_{1} V_{1}^{2} = C_{2} V_{2}^{2} \frac{V_{2}}{V_{1}} = \sqrt{\frac{C_{2}}{C_{1}}}$

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