Electrostatics 6 Question 6
6. Capacitor $C _1$ of capacitance $1 \mu F$ and capacitor $C _2$ of capacitance $2 \mu F$ are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time $t=0 . \quad(1989,2 M)$
(a) The current in each of the two discharging circuits is zero at $t=0$
(b) The currents in the two discharging circuits at $t=0$ are equal but not zero
(c) The currents in the two discharging circuits at $t=0$ are unequal
(d) Capacitor $C _1$, loses $50 %$ of its initial charge sooner than $C _2$ loses $50 %$ of its initial charge
Integer Answer Type Questions
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Solution:
- The discharging current in the circuit is,
Here, $i _0=$ initial current $=\frac{V}{R}$
Here, $V$ is the potential with which capacitor was charged.
Since, $V$ and $R$ for both the capacitors are same, initial discharging current will be same but non-zero.
$\therefore$ Correct option is (b).
Further, $\tau _c=C R \Rightarrow C _1<C _2$ or $\tau _{C _1}<\tau _{C _2}$ or $C _1$ loses its $50 %$ of initial charge sooner than $C _2$.
$\therefore$ Option (d) is also correct .
