Capacitor C1 of capacitance 1 μ F and capacitor C2 of capacitance 2 μ 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.

Question

Capacitor C1 of capacitance 1 μ F and capacitor C2 of capacitance 2 μ 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. (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 C1, loses 50 % of its initial charge sooner than C2 loses 50 % of its initial charge

Tardigrade Admin · Accepted Answer

The discharging current in the circuit is,

i = i_{0} e^{- t / CR}

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.

∴

Correct option is (b).
Further,

τ_{c} = CR

C_{1} < C_{2}

or

τ_{C_{1}} < τ_{C_{2}}

or

C_{1}

loses its

50%

of initial charge sooner than

C_{2} .

Q. Capacitor $C_{1}$ of capacitance $1 μ F$ and capacitor $C_{2}$ of capacitance $2 μ F$ are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time $t = 0$ .

The current in each of the two discharging circuits is zero at t = 0

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

The currents in the two discharging circuits at t = 0 are unequal

Capacitor $C_{1},$ loses $50%$ of its initial charge sooner than $C_{2}$ loses $50%$ of its initial charge

Q. Capacitor C1​ of capacitance 1μF and capacitor C2​ of capacitance 2μF are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time t=0.

The current in each of the two discharging circuits is zero at t = 0

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

The currents in the two discharging circuits at t = 0 are unequal

Capacitor C1​, loses 50% of its initial charge sooner than C2​ loses 50% of its initial charge

Q. Capacitor $C_{1}$ of capacitance $1 μ F$ and capacitor $C_{2}$ of capacitance $2 μ F$ are separately charged fully by a common battery. The two capacitors are then separately allowed to discharge through equal resistors at time $t = 0$ .

Capacitor $C_{1},$ loses $50%$ of its initial charge sooner than $C_{2}$ loses $50%$ of its initial charge