Question

Consider the circuit given below with capacitors and resistances. Switch $S$ is closed at time $t=0$. Select the correct statement (s).

• A. Rate of increase of charge is same for both the capacitors
• B. ratio of charge stored in capacitors $2C$ and $4C$ at any time t will be 1:2
• C. Time constant for both the capacitors are equal
• D. steady state charge in capacitoe $2C$ and $4C$ are in the ratio 1 :2

Answer 1

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

The correct options are
B ratio of charge stored in capacitors $2C$ and $4C$ at any time t will be 1:2
C Time constant for both the capacitors are equal
D steady state charge in capacitoe $2C$ and $4C$ are in the ratio 1 :2

${\tau }_{c_1}={\tau }_{c_2}=8RC={\tau }_c\left(\text{say}\right)\begin{array}{cc}{q}_1=E\left(2C\right)[1-e^{-t/{\tau }_c}]& \\ q_2=E\left(4C\right)[1-e^{-t/{\tau }_c}]& \end{array}\}\Rightarrow \frac{q_1}{q_2}=\frac{1}{2}$
Threfore, $\frac{\frac{d{q}_1}{dt}}{\frac{d{q}_2}{dt}}=\frac{1}{2}$
So, ratio of rate of change in charge at any time is $1:2$ and the ratio of steady state charge is also $1:2$