Question

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

• A. $1\mu F$
• B. $2\mu F$
• C. $1/2\mu F$
• D. $\infty$

Answer 1

The correct option is B $2\mu F$

$Ceq=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...={\sum }_{n=0}^{\infty }1(\frac{1}{2}{)}^n=\frac{1}{1-\frac{1}{2}}=2\mu F$