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

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4.) Steady state charge in capacitors $C$ and $2 C$ are in the ratio of $1 : 2$ .

1. Rate of increase of charge is same in both the capacitors

3.Time constants of both the capacitors are equal

2. Ratio of charge stored in capacitors $C$ and $2 C$ at any time $t$ would be $1 : 2$

answer is B, C, D.

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Detailed Solution

$τ_{c_{1}} = τ_{c_{2}} = 2 C R = τ_{C (S a y)}$

$q_{1} = (E C) [1 - e^{- \frac{t}{2 R C}}]$

$q_{2} = 2 (E C) [1 - e^{- \frac{t}{2 R C}}]$

$\frac{q_{1}}{q_{2}} = \frac{1}{2} (a t a n y t i m e)$

The ratio of steady state charge is also $1 : 2$

$\frac{d q_{1}}{d t} = \frac{E}{2 R} e^{- \frac{t}{2 R C}}$

$\frac{d q_{2}}{d t} = \frac{E}{R} e^{- \frac{t}{2 R C}}$

The option $(1)$ is wrong.

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