In the circuit shown, find C if the effective capacitance of the...

In the circuit shown, find $C$ if the effective capacitance of the whole circuit is to be $0.5\muF .$ All values in the circuit are in $\muF .$

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 . All values in the circuit

Options

A $\dfrac{7}{10}\muF$
B $4\muF$
C $\dfrac{7}{11}\muF$
D $\dfrac{6}{5}\muF$

Correct answer

C. $\dfrac{7}{11}\muF$

Step-by-step solution

Let us take the equivalent circuit one by one.

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 . All values in the circuit

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 . All values in the circuit

$∴ {C}_{eq} = \dfrac{C \times \dfrac{7}{3}}{C + \dfrac{7}{3}}$ = 0.5 $⇒ \dfrac{7}{3}C = \dfrac{C}{2} + \dfrac{7}{6}$

$⇒ \dfrac{11}{6}C = \dfrac{7}{6} ⇒ C = \dfrac{7}{11}\muF$

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