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Parallel and Series Combination of Capacitors

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Question

Find the potential difference between the points A and B $(V_{A} - V_{B})$ as shown in figure. (Initially all the capacitors are uncharged).

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Solution

$V_{A B} = \frac{\frac{V_{1}}{R_{1}} + \frac{V_{2}}{R_{2}} + \frac{V_{3}}{R_{3}}}{\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}}$

By this analogy;

$V_{A B} = \frac{V_{1} C_{1} + V_{2} C_{2} + V_{3} C_{3}}{C_{1} + C_{2} + C_{3}}$

$V_{A B} = \frac{10 \times 6 + 20 \times 4 + 30 \times 10}{20} = 22 V$

$V_{A B} = 22 V$

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