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  4. 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 (i) and (ii) respectively. The charge on the capacitors at time t=CR are respectively <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-zjz6m1tp7adyjwql.jpg />

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Q. 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
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NTA AbhyasNTA Abhyas 2022

Solution:

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,
$Q_{0}=CV\Rightarrow Q=\frac{C V}{e}$
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 $t$ .