Question

An infinite no. of capacitors, having capacitances $1\mu F,2\mu F,\mu F,8\mu F$,.......... are connected in series. The equivalent of the system is

• A. Infinite
• B. $0.25\mu F$
• C. $0.5\mu F$
• D. $2\mu F$

Answer 1

The correct option is D $2\mu F$

$C$ equivalent $=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}+\frac{1}{C_4}$

$=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}$

$=\frac{1}{(1-1/2)}=\frac{1}{1/2}=2\mu$ farad.