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Capacitor C1 of capacitance 1 micro-fara...

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 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.

Text Solution

Verified by Experts

The correct Answer is:
B, D
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.
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