question_answer

Directions: Two capacitors of capacity 6\[\mu F\]and 3\[\mu F\]are charged to 100 V and 50 V separately and connected as shown. Now all the three switches \[{{S}_{1}},{{S}_{2}}\]and\[{{S}_{3}}\]are closed.

Charges on both the capacitors in steady state will be on \[6\mu F\] first

A)  \[400\mu C,400\mu C\]         

B)  \[700\mu C,250\mu C\]

C)  \[800\mu C,350\mu C\]         

D)  \[300\mu C,450\mu C\]

Correct Answer: B

Solution :

Before closing the switch the charges are as shown in figure .  When switches are open [b] when switches are closed Let \[q(\mu C)\] charges goes from the battery. Then charges on both will increase by q. Applying Kirchhoff's second law in figure [b] after closing the switch. \[200-\left( \frac{600+q}{6} \right)-\left( \frac{150+q}{3} \right)=0\]or\[q=100\mu C\] \[\therefore \] Charge on \[6\mu F\] is \[700\mu C\] and on \[3\mu F\]is\[250\mu C\].