Question

Two identical capacitors each of capacitance $ C $ are charged to the same potential $ V $ and are connected in two circuits (i) and (ii) at $ t = 0 $ as shown. The charged on the capacitor at $ t = CR $ are

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

Answer 1

Answer: (C)

In Fig. (i) the $p-n$ junction diode is forward biased and represents a very low resistance, the capacitor, therefore discharges itself through resistor $R$ according to relation.
$q =q_{0} e^{-t / C R} $
and $ q_{0} =C V$ at $t=C R $
$ \therefore \,\, q =q_{0} e^{-1}=\frac{C V}{e} $
In Fig. (ii), the $p-n$ junction diode is reverse biased, the capacitor, therefore holds the charge intact.
$\therefore q=q_{0}=C V$