Question

An infinite number of identical capacitors, each of capacitance $1\mu \text{F}$ are connected as in the figure below. Find the equivalent capacitance between $\text{A}$ and $\text{B}$ is

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

Answer 1

The correct option is B $2\mu \text{F}$

In each row ,the capacitors are in series, and each row of capacitors are joined in parallel to infinity.

Therefore, total capacity,

$C_{eq}=C+\frac{C}{2}+\frac{C}{4}+\frac{C}{8}+\frac{C}{16}+...\infty$

$C_{eq}=C[1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...\infty ]$

Applying the formula of sum of infinite geometrical series we get,

$C_{eq}=C\left[\frac{1}{1-\frac{1}{2}}\right]=2\times 1\mu \text{F}=2\mu \text{F}$

Hence, option (b) is the correct answer.