Question

Determine the charge on the capacitor in the following circuit

• A. $200\mu \text{C}$
• B. $10\mu \text{C}$
• C. $2\mu \text{C}$
• D. $60\mu \text{C}$

Answer 1

The correct option is A $200\mu \text{C}$

At steady state, there is no current in capacitor.
$2\Omega \text{and}10\Omega$ are in series. There equivalent resistance is $12\Omega$. This $12\Omega$ is in parallel with $4\Omega$ and there combined resistance is $\frac{12\times 4}{(12+4)}$. This resistance is in series with $6\Omega$. Therefore, current drawn from battery
$i=\frac{V}{R}=\left(\frac{72}{6+\frac{12\times 4}{12+4}}\right)=8\text{A}$


Current in $10\Omega$ resistor is
$i^{\prime }=\left(\frac{4}{4+12}\right)8=2\text{A}$
PD across capacitor, $V=i^{\prime }R=2\times 10=20\text{V}$
$\therefore$ Charge on the capacitor, $q=CV$
$q=10\times 20=200\mu \text{C}$.