An infinite number of identical capacitors each of capacitance 1 μ F are connected as shown in figu

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1. Electric Charges and Fields

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An infinite number of identical capacitors each of capacitance $1 \mu F$ are connected as shown in the figure. Then, the equivalent capacitance between $A$ and $B$ is .......... $\mu F$

A

$1$

B

$2$

C

$0.5$

D

$\infty$

Solution

This combination forms a $G P$,

$s=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots$

Sun of infinite $G P$,

$s=\frac{a}{1-r}$

$s=\frac{1}{1-\frac{1}{2}}$

$s=\frac{1}{\frac{1}{2}}$

$\therefore s=2$

Hence, capacitance of the combination

$C_{\infty}=2 \times 1 \mu F=2 \mu F$

Standard 12

Physics

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