Question

Two identical capacitors $A$ and $B$ of capacitance $C$ each, are charged to the same potential $V$ and are connected in two circuits at $t=0$ , as shown in the figure $\left(i\right)$ and $\left(ii\right)$ respectively. The charge on the capacitors at time $t=CR$ are respectively

• A. $VC,VC$
• B. $\frac{VC}{e},VC$
• C. $VC,\frac{VC}{e}$
• D. $\frac{VC}{e},\frac{VC}{e}$

Answer 1

Answer: (B)

Time $t=CR$ is known as time constant. It is time in which charge on the capacitor decreases to $\frac{1}{e}$ times of its initial charge (steady-state charge).
In figure $\left(i\right)$ PN junction diode is in forward bias, so current will flow in the circuit, i.e., charge on the capacitor decrease and in time $t=CR$ , it becomes $Q=\frac{1}{e}\left(Q_o\right)$ ,
where,
$Q_0=CV\Rightarrow Q=\frac{CV}{e}$
In figure $\left(ii\right)$ P-N junction diode is in reverse bias, so no current will flow through the circuit hence charge on the capacitor will not decay, and it remains same, i.e. $CV$ after time $t$ .