If in the infinite series circuit, C = 9 μF and C1=6μF then the capacity acro

Question

If in the infinite series circuit, C = 9

μ

F and

C_{1} = 6 μ F

then the capacity across AB is

Options:

A . 1.25μF

B . 6μF

C . 3μF

D . 12μF

Answer: Option C
:
C

\frac{1}{C_{A B}} = \frac{1}{c} + \frac{1}{c_{1} + x} + \frac{1}{c}

\frac{1}{x} = \frac{1}{9} + \frac{1}{6 + x} + \frac{1}{9}

\frac{1}{x} - \frac{1}{6 + x} = \frac{2}{9}

\frac{6 + x - x}{x (6 + x)} = \frac{2}{9}

27 = x (6 + x)

x = 3 μ F

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