Question

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

• A. $1 \mu F$
• B. $2 \mu F$
• C. $\frac{1}{2} \mu F$
• D. $\infty$

Answer 1

Answer: (B)

This combination forms a $G.P. S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8} \ldots \ldots .$
Sum of infinite $G.P. S=\frac{a}{1-r}$
Here $a=$ first term $=1$ and $r=$ common ratio $=\frac{1}{2}$
$\Rightarrow S=\frac{1}{1-\frac{1}{2}}=2$
$ \Rightarrow C_{e q}=2 \mu F$