Explanation

(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 it’s initial charge (steady state charge).
In figure (i) $PN$ junction diode is in forward bias, so current will flow the circuit $i.e.,$ charge on the capacitor decrease and in time $t$ it becomes $Q = \frac{1}{e}\left( Q_{o} \right);$ where
$Q_{o} = CV \Rightarrow Q = \frac{CV}{e}$
In figure (ii) $P$-$N$ junction diode is in reverse bias, so no current will flow through the circuit hence change on capacitor will not decay and it remains same, $i.e.,\ CV$ after time $t$