Question

An infinite number of capacitors $2.0\mu F,4.0\mu F,8.0\mu F,16.0\mu F$, ............ are connected in series. The equivalent capacitance of the system is

• A. $\infty$
• B. $0.25\mu F$
• C. $0.5\mu F$
• D. $1.0\mu F$

Answer 1

Answer: (D)

An infinite number of capacitors $2\mu F,4\mu F$,
$8\mu F,16\mu F,\dots \dots \dots ..$ are connected in series.
As we know, $\frac{1}{C_{\text{series }}}=\frac{1}{C_1}+\frac{1}{C_2}+\dots \dots ..$
$C_{\text{series }}=\frac{C_1{C}_2{C}_3\dots \dots .\infty }{C_1+C_2+C_3+\dots \dots \dots \infty }$
Equivalent capacitance of the system $=1\mu F$