Question

Find the equivalent capacitance of the infinite ladder shown in the figure between points $\text{P}$ & $\text{Q}$.

• A. $6\mu \text{F}$
• B. $24\mu \text{F}$
• C. $15\mu \text{F}$
• D. $12\mu \text{F}$

Answer 1

The correct option is D $12\mu \text{F}$


As we can see, in the given circuit a symmetric element is repeating infinite times i.e., between $\text{RS}$

Hence, let the equivalent capacitance across $\text{RS}$ i.e., $C_{RS}=C$ and similarly capacitance across $\text{PQ}$ i.e., $C_{PQ}=C$

$\therefore$ The given circuit can be redrawn as follows,


$\Downarrow$


$\therefore$ Equivalent resistance of the given circuit is,

$C_{PQ}=C=8+\frac{6C}{C+6}$

$C^2-8C-48=0$

$(C-12)(C+4)=0$

$\therefore C=12\text{or}-4$

Capacitance cannot be negative.

$\therefore C=12\mu \text{F}$

Hence, option $\left(d\right)$ is the correct answer.