Question

Charge on $6\mu F$ capacitor is.

• A. $8\mu C$
• B. $10\mu C$
• C. $4\mu C$
• D. $3.5\mu C$

Answer 1

The correct option is A $8\mu C$


Let charges on $2\mu F$ & $4\mu F$ be $q_2$ and $q_1$ respectively.
By charge conservation, charge on $6\mu F$ will be $(q_1-q_2)$.
Using $KVL$,
$\frac{q_1}{4}+\frac{(q_1-q_2)}{6}=\frac{q_2}{2}$
$\Rightarrow \frac{3q_1+2q_1-2q_2}{12}=\frac{q_2}{2}$
$\Rightarrow 5q_1=8q_2$

Again, $\frac{q_1}{4}+\frac{q_2}{2}=12=\frac{q_1+2q_2}{4}$
$48=\frac{8}{5}{q}_2+2q_2\Rightarrow q_2=\frac{48\times 5}{18}$
and $q_1=\frac{8}{5}\times \frac{48\times 5}{18}$
$q_1-q_2=8\mu C$