Question

If in the infinite series circuit, C = 9 $\mu$F and $C_1=6\mu F$ then the capacity across AB is

• A. $1.25\mu F$
• B. $6\mu F$
• C. $3\mu F$
• D. $12\mu F$

Answer 1

The correct option is C $3\mu F$


$\frac{1}{C_{AB}}=\frac{1}{c}+\frac{1}{c_1+x}+\frac{1}{c}$
$\frac{1}{x}=\frac{1}{9}+\frac{1}{6+x}+\frac{1}{9}$
$\frac{1}{x}-\frac{1}{6+x}=\frac{2}{9}$
$\frac{6+x-x}{x(6+x)}=\frac{2}{9}$
$27=x(6+x)$
$x=3\mu F$