Question

In the circuit shown in the figure, switch S is closed at time $t=0$. Select the correct statements

• A. Rate of increase of charge is same in both the capacitors
• B. Ratio of charge stored in capacitors C and 2C at any time t would be 1 : 2
• C. Time constants of both the capacitors are equal
• D. Steady state charge in capacitors C and 2C are in the ratio of 1 : 2

Answer 1

Answer: (B), (C), (D)

The correct options are
B Ratio of charge stored in capacitors C and 2C at any time t would be 1 : 2
C Time constants of both the capacitors are equal
D Steady state charge in capacitors C and 2C are in the ratio of 1 : 2

In steady state , charge on C is $q_{10}=CE$ and charge on 2C is $q_{20}=2CE$
$\therefore \frac{q_{10}}{q_{20}}=\frac{CE}{2CE}=1/2=1:2$
Charge on C at time t is $q_1\left(t\right)=q_{10}(1-e^{-t/C\left(2R\right)})=CE(1-e^{-t/2RC})$
Charge on 2C at time t is $q_2\left(t\right)=q_{20}(1-e^{-t/\left(2C\right)R)})=2CE(1-e^{-t/2RC})$
Thus, $\frac{q_1}{q_2}=1/2=1:2$ and time constant of both is $\tau =2RC$