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Parallel and Series Combination of Capacitors

Question

Find equivalent capacitance between points A and B :

$\frac{5 C}{3}$
$\frac{4 C}{3}$
$2 C$
$C$

A

C

B

2 C

C

\frac{5 C}{3}

D

\frac{4 C}{3}

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Solution

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The corresponding equivalent circuit is as shown in figure.
The all capacitors on top are in series so the equivalent capacitance for top part is $C_{t} = (1 / C + 1 / C + 1 / C)^{- 1} = C / 3$
Now this capacitance $C_{t}$ and bottom capacitance $C$ are in parallel.
So the equivalent capacitance $C_{A B} = C_{t} + C = C / 3 + C = 4 C / 3$

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