A 10µF capacitor and 20µF capacitor are connected in series across 200 V supply line. The charged capacitors are then disconnected from the line and reconnected with their positive plates together and negative plates together and no external voltage is applied. What is the potential difference across each capacitor?

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$\frac{800}{3} volt$

200 volt

400 volt

$\frac{800}{9} volt$

answer is A.

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Detailed Solution

10, 20 are in series $\Rightarrow$ q is same
$\begin{array}{l} \frac{V_{1}}{V_{2}} = \frac{C_{2}}{C_{1}} = \frac{2}{1} \Rightarrow V_{1} = \frac{2 V}{3} = \frac{2 \times 200}{3} = \frac{400}{3} V \\ \Rightarrow V_{2} = \frac{V}{3} = \frac{200}{3} \end{array}$
Common potential $= \frac{C_{1} V_{1} + C_{2} V_{2}}{C_{1} + C_{2}}$
$V = \frac{10 \times \frac{400}{3} + 20 \times \frac{200}{3}}{10 + 20}; V = \frac{800}{9} volt$