Question

Three capacitors each having capacitance $C=2\mu F$ are connected to battery of emf 30 V as shown in the figure. When the switch is closed.

• A. The amount of charge that flows through the battery is $20\mu C$.
• B. Heat generated in the circuit is $0.6mJ$.
• C. Work done by the battery is $0.6mJ$.
• D. The charge flowing through the switch is $60\mu C$.

Answer 1

Answer: (A), (C), (D)

The correct options are
A The amount of charge that flows through the battery is $20\mu C$.
C Work done by the battery is $0.6mJ$.
D The charge flowing through the switch is $60\mu C$.

When the switch is open, the equivalent capacitance $C_1=\left(\frac{4}{2}\right)\mu F$
Charge flown through the battery $=\frac{4}{3}\times 30=40\mu C$
When switch is close
$C_1^{\prime }=2\mu F$
$q_1=2\times 30=60\mu C$
Hence, $20\mu C$ extra charge flows when S is closed
Work done by the battery $=20\times {10}^{-6}\times 30=0.6mJ$
When switch is closed, it is short circuited. Hence all the charge flows through S.