Capacitor `C_(1)` of capacitance 1 `muF` and capacitor `C_(2)` of capacitance 2`muF` are separetely charged fully by a common battery.The two capacitors are then separately allowed to discharged thgrough eual resistores at time t=0

Options

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` losses 50% of its initial charge sooner than `C-2` loses 50% of its initial charge.

Answer

B, D

Explanation

b.,d.
During the decay of charge in RC circuit , `I = I_0e^(-t//RC)`, where
`I_0 = q_0//RC. When t = 0 , I= I_0 = q_0//RC`
Since potential difference between the plates is initially the same, I is the same in both the cases at t = 0 and is equal to
`I = q_0/(RC) = V/R. Also q = q_0e^(-t//RC)`
When `q_0 = q_0/2, then q_0/2 = q_0 e^(-t//RC)`

or `e^(+t//RC) = 2(t/(RC)) = log_e 2 or t = RC log_e or t prop C`
Therefore, time taken for the first capacitor `(1muF)` for
discharging `50%` of initial charge will be less.