Question

In the figure shown below, if the charge on the left plate of the $10\mu F$ capacitor is $-30\mu C$ , then the charge on the right plate of the $6\mu F$ capacitor should be ____ $\mu C$ .

Answer 1

Let $q_{1}$ and $q_{2}$ be charge on $6\mu F$ and $4\mu F$ respectively.
$q_{1}+q_{2}=q\ldots \left(i\right)$
Also, $\frac{q_{1}}{C_{1}}=\frac{q_{2}}{C_{2}} \ldots$ (ii)
$\cdots\left[\because C_{1}\right.$ and $C_{2}$ are in parallel combination $]$
$\Rightarrow q_{2}=\frac{C_{2}}{C_{1}}q_{1}$
$=\frac{4}{6}q_{1}\ldots \left(iii\right)$
Using $\left(i\right)$ and $\left(ii\right)$ ,
$\frac{10}{6}q_{1}=q$
$\therefore q=\frac{5}{3}q_{1}$
$\Rightarrow q_{1}=\frac{3}{5}\times 30=18\mu C$