Question

In the circuit shown in the figure-$3.370$, 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 $2 C$ 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 $2 C$ are in the ratio of $1: 2$

Answer 1

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

In steady state
$q_{C}=E C $ and $ q_{2 C}=2 EC$
Time constant is same for both the circuits $\tau_{C}=2 RC$.
At time $t$ charge on the two capacitors is given as
$q_{C}=E C\left(1-e^{t / \tau}\right)$
$q_{2 C}=2 E C\left(1-e^{t / \tau}\right)$
$\Rightarrow \frac{q_{C}}{q_{2 C}}=\frac{1}{2}$