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

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 $\mu$F are connected as shown in the figure. Then, the equivalent capacitance between A and B is

Choose the correct answer: