For the circuit shown in figure, find
(a) the initial current through each resistor
(b) steady state current through each resistor
(c) final energy stored in the capacitor
(d) time constant of the circuit when switch is opened.

Answer

A, B, C

Explanation

a. At `t=0` equivalent resistance of capacitor is zero. `R_1` and `R_2` are in parallel across the battery `PD` across each is `E`.
`:. i_(R_1)=E/R_1`
`i_(R_2)=E/R_2`
b. In steady state, no current flow thruogh capacitor wire. `PD` acorss `R_1` is `E`.
`:. i_(R_1)=E/R_1` and `i_(R_2)=0`
c. In steady state, potential difference across capacitor is `E`.
`:. U=1/2CV^2=1/2CE^2`
d. When switch is opened capacitor is discharged throgh resistors `R_1` and `R_2`
`tau_C=CR_(n et)`
`=C(R_1+R_2)`