Question

Consider the figure shown. Now, the switch is shifted to position $2$. The charge appearing on capacitor $C_3$ is :

• A. $225\mu C$
• B. $135\mu C$
• C. $270\mu C$
• D. $75\mu C$

Answer 1

The correct option is A $225\mu C$

When switch is in position 1,
Let charge $q$ is flowing in the circuit.
$30-\frac{q}{20}-\frac{q}{30}=0orq=360\mu C$

The switch is in position 2,
$q_1^{\prime }+q_3^{\prime }=360$

Loop $ABCD$,
$\frac{q_1^{\prime }}{20}-\frac{q_1^{\prime }}{30}+\frac{q_3}{20}=0$

$-3q_1^{\prime }-2q_1^{\prime }+3q_3=0$

$5q_1^{\prime }=3qor{q}_1^{\prime }=\frac{3}{5}{q}_3$

$\frac{8q_3}{5}=360$

$q_3=\frac{360\times 5}{8}=\frac{450}{2}\mu C=225\mu C$