Q134 / 180 · JIPMER 2017 · Physics

Capacitor $C_1$ of capacitance $1 \mu \mathrm{F}$ and capacitor $C_2$ of capacitance $2 \mu \mathrm{F}$ are separately charged fully by a common battery. The two capacitors are then separately allowed to discharged through equal resistors at time $t=0$

  • A
    the current in each of the two discharging circuits is zero at $t=0$
  • Correct answer
    B
    the currents in the two discharging circuits at $t=0$ are equal but non-zero
  • C
    the currents in the two discharging circuits at $t=0$
  • D
    Capacitor $C_1$ loses $40 \%$ of its initial charge sooner than $\mathrm{C}_2$ loses $40 \%$ of initial charge.

Solution

Here, $V_0$ and $R$ in the two $C R$ circuits are same, hence the currents in the two discharging circuits at $t=0\left(V_0 / R\right)$ will be same. We know that, time constant of a resistance and capacitance circuit is $C R$. Here, time constant of first circuit (capacity $C_1=1 \mu F$ ) is half of the time constant of second circuit (capacity $C_2=2 \mu F$ ). Hence, $C_1$ loses $50 \%$ its initial charge sooner.

Hence, the correct answer is option: 'B'.

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