Question 9: Electrostatics & Capacitance

Question

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
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m3o0ctfm/6922ef2d-e6e7-4d9a-8d72-f362528218c2/41c48e20-a636-11ef-a300-b723d4598e73/file-jaoe38c1m3o0ctfn.png?format=png)

Accepted Answer

This combination forms a GP,
$s=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\ldots$
Sum of infinite GP,$\$
$\begin{aligned}
& s=\frac{a}{1-r} \
& s=\frac{1}{1-\frac{1}{2}} \
& s=\frac{1}{\frac{1}{2}} \
	herefore \quad & s=2
\end{aligned}$
$\$Hence, capacitance of the combination
$C_{\infty}=2 	imes 1 \mu \mathrm{F}=2 \mu \mathrm{F}$

Answer

$1 \mu \mathrm{F}$

Answer

$2 \mu \mathrm{F}$

Answer

$\frac{1}{2} \mu \mathrm{F}$

Answer

$\infty$

Electrostatics & Capacitance

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

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