The switch `S` is closed at `t=0` . the capacitor `C` is uncharged but `C_0` has a charge `Q_0=2muC` at `t=0`. If `=100Ommega` , `C=2muF` , `C_0=2muF,E=4V`. Calculate `i (t)` in the circuit.

Answer

A, C, D

Explanation

At `t=0` capacitor `C_0` is like a battery of
emf `=Q_0/C_0=1V`
Net emf of the circfuit `=4-1=3V`
total resistance is `R=100Omega`
`:.` Initial current `3/100=0.03A`
This current will decrease exponentially to zero.
`:. i=0.03e^((-t)/(tau_C)`
Here, `tau_C=C_(n et)R=(1xx10^-6)(100)`
`=10^-4s`
`:. i=0.03e^(-10^4t)`