Question

In the circuit shown, $C_1=C_2=2\mu F$. Capacitor $C_1$ is charged to $50V$ and $C_2$ is charged to $20V$. After charging, they are connected as shown. When $S_1,S_2$ and $S_3$ are closed :

• A. $70\mu C$ of charge will pass through $S_1$
• B. $100\mu C$ of charge will pass through $S_1$
• C. $70\mu C$ of charge will pass through $S_3$
• D. $40\mu C$ of charge will pass through $S_3$

Answer 1

Answer: (A), (C)

$70\mu C$ of charge will pass through $S_1$
$70\mu C$ of charge will pass through $S_3$

When switches are open, charges on the capacitor are $Q_1=50\times 2=100\mu C$ and $Q_2=20\times 2=40\mu C$
when switches are closed, both capacitor will be in parallel
so potential and capacitance for both capacitor will be same. Hence Q will also be same
$Q_1=Q_2$
let charge $x\mu C$ flowing from $C_{1}to{C}_2$
$-(Q_1-x)=Q_2-x$
$-(100-x)=40-x$
$2x=140$ $x=70\mu C$
$70\mu C$ charge will flow in the circuit. Hence charge passing through $S_1,S_2$ and $S_3$ is $70\mu C$.