Question

A capacitor C1 of capacitance 1 μF and a capacitor C2 of capacitance 2 μF are separately charged by a common battery for a long time. The two capacitors are then separately discharged through equal resistors. Both the discharge circuits are connected at t = 0.
(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) C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge.

Answer 1

(b) The currents in the two discharging circuits at t = 0 are equal but not zero.

(d) C1 loses 50% of its initial charge sooner than C2 loses 50% of its initial charge" .

Both (b) and (d) are correct.

Explanation:

• From the statement given, both the capacitors are connected to the same battery from long time and also connected to an equal resistors separately at t=0.

• Now, the capacitors are started discharging at the same time, where the current in discharging circuits are equal but not zero.

• The range of capacitors are in the ratio 1:2. So, C1 loses 50% of its initial charge sooner than C2 loss 50% of its initial charge.

• Hence connected to the same resistance separately then the currents in the two discharging circuits at t = 0 are equal but not zero and C1 loses 50% of its initial charge sooner than C2 loss 50% of its initial charge.