Question

Two capacitors of capacity $6\mu F$ and $3\mu F$ are charged to $100V$ and $50V$ separately and connected as shown in figure. Now all the three switches $S_1,S_2$ and $S_3$ are closed. Suppose $q_1,q_2$ and $q_3$ be the magnitudes of charge flowing from switches $S_1,S_2$ and $S_3$ after they are closed. Then :

• A. $q_1=q_3$ and $q_2=0$
• B. $q_1=q_3=\frac{q_2}{2}$
• C. $q_1=q_3=2q_2$
• D. $q_1=q_2=q_3$

Answer 1

The correct option is D $q_1=q_2=q_3$

Total charge on plate 1 and 2 is $q=CV=600\mu C$ and total charge on plate 3 and 4 is $50\times 3=150\mu C$
Now charge $x\mu C$ is flowing in the circuit
$\frac{(150-x)}{3}+\frac{(600-x)}{6}-200=0$
$x=-100\mu C$

Hence, final charge on $6\mu F$ capacitor is
$q_2=150-x=150+100=250\mu C$

Plates 2 and 3 and plates 1 and 4 form isolated system.

Hence $q_2=q_3=q_1=x=-100\mu C$