Question

Capacitor `C_1` of capacitance 1 micro-farad and capacitor `C_2` of capacitance 2 microfarad 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`
B. The current in the two discharging circuits at `t=0` are equal but not zero
C. The currents in the two discharging circuits at `t=0` unequl
D. Capacitor `C_(1)`, loses `50%` of its initial charge sooner than `C_(2)` loses `50%` of its initial charge

Answer 1

Correct Answer - B
The discharging current in the circuit is
`i=i_(0)e^((-t)/(CR))` Here, `i_(0)=` initial current `=(V)/(R)`
Here, V is the potential with which capacitor was charged since, V and R for both te capacitors are same, initial discharging current will be sae but non-zero further `tau_(c)=CR`
`C_(1)ltC_(2)` or `tau_(C_(1))lttau_(C_(2))`
or `C_(1)` loses its `50%` of initial charge sooner than `C_(2)`