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)

$1.0 \, \mu F$

Answer 2

An infinite number of capacitors $2\, \mu F ,\, 4\, \mu F$,
$8 \mu F ,\, 16 \mu F , \ldots \ldots \ldots . .$ are connected in series.
As we know, $\frac{1}{C_{\text {series }}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\ldots \ldots . .$
$C_{\text {series }}=\frac{C_{1} C_{2} C_{3} \ldots \ldots . \infty}{C_{1}+C_{2}+C_{3}+\ldots \ldots \ldots \infty}$
Equivalent capacitance of the system $=1\, \mu F$