Question

An infinite number of capacitors of capacitances C, 2C, 4C, 8C, 16C, 32C, ..... are connected in series. The equivalent capacitance of arrangement between A and B is

• A. C
• B. $\frac{C}{2}$
• C. 2C
• D. Infinite

Answer 1

The correct option is B $\frac{C}{2}$

$\frac{1}{C^1}=\frac{1}{c}+\frac{1}{2c}+\frac{1}{4c}+\cdots \infty =\frac{1}{c}[1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+,\cdots \cdots \infty ]=\frac{1}{c}\left[\frac{1}{1-\frac{1}{2}}\right]=\frac{2}{c}\Rightarrow C^1=\frac{c}{2}$