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Question: Three capacitors of capacity \(C_{1}, C_{2}C_{3}\) are connected in series. Their total capacity wil...

Three capacitors of capacity C1,C2C3C_{1}, C_{2}C_{3} are connected in series. Their total capacity will be

A

(a) C1+C2+C3C_{1} + C_{2} + C_{3}

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(b) 1/(C1+C2+C3)1/(C_{1} + C_{2} + C_{3})

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(c) (C1−1+C2−1+C3−1)−1(C_{1}^{- 1} + C_{2}^{- 1} + C_{3}^{- 1})^{- 1}

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(d) None of these

Explanation

Solution

(c)

Sol. 1CR=1C1+1C2+1C3\frac{1}{C_{R}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}} ⇒ CR=(C1−1+C2−1+C3−1)−1C_{R} = (C_{1}^{- 1} + C_{2}^{- 1} + C_{3}^{- 1})^{- 1}