Question

Four identical capacitors are connected as shown in diagram. When a battery of $6\, V$ is connected between $A$ and $B$, the charge stored is found to be $1.5\, \mu C$. The value of $C_{1}$ is

• A. $2.5\, \mu F$
• B. $15\, \mu F$
• C. $1.5\, \mu F$
• D. $0.1\, \mu F$

Answer 1

Answer: (D)

The capacitance across $A$ and $B$
$=\frac{C_{1}}{2}+C_{1}+C_{1}=\frac{5}{2} C_{1}$
As $Q=C V$,
$1.5\, \mu C =\frac{5}{2} C_{1} \times 6$
$\Rightarrow C_{1}=\frac{1.5}{15} \times 10^{-6}$
$=0.1 \times 10^{-6} F =0.1\, \mu F$