Question

If a battery is placed between $\text{A}$ and $\text{B}$, with what capacitor you can replace the combination of capacitors?

• A. $8\mu \text{F}$
• B. $6\mu \text{F}$
• C. $26\mu \text{F}$
• D. $10/3\mu \text{F}$

Answer 1

The correct option is A $8\mu \text{F}$

As we can see from the circuit, the capacitors present in the top and bottom branches are in series, and the three branches are in parallel.

$\therefore$ Capacitance of the top branch $=$ Capacitance of the bottom branch $=\frac{4\times 4}{4+4}=2\mu \text{F}$


Now, equivalent capacitance across $\text{AB}$ is given by

$C_{eq}=C_{top}+C_{middle}+C_{bottom}$

$\Rightarrow C_{eq}=2\mu \text{F}+4\mu \text{F}+2\mu \text{F}=8\mu \text{F}$

Hence, option $\left(a\right)$ is correct.