Question

In the figure shown below, the charge on the left plate of the $10\, \mu F$ capacitor is $-30 \,\mu C$. The charge on the right plate of the $6\, \mu F$ capacitor is _______$\mu C$.

Answer 1

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