In Fig. the switch is closed and steady-state conditions are established. The switch is thrown open at `t = 0`.
a. Find the initial voltage `E_(0)` across `L` just after `t = 0`. Which end of the coil is at the heigher potential : `a` or `b`?
b. Make freehand graphs of the current in `R_(1)` and `R_(2)` as a funtion of time, treating the steady-state directions as positive. Show values before and after `t = 0`.
c. How long after `t = 0` does the current in `R_(2)` have the value `2 mA`?

Explanation

a. `b` shell be at a higher potential
`E_(0) = I_(0)(R_(1) + R_(2)) = 9 xx 8 = 72 V`
b. `I = I_(0)e^(-((R_(1)+R_(2))t)/(L))` for `t = gt 0`
`I` through `R_(1)`

`I` through `R_(2)`

c. `I = 9 e^((-8t)/(0.4))`
`2 xx 10^(-3) = 9 e^(-20t) rArr e^(20t) = (9 xx 10^(3))/(2)`
`20t = In (4.5 xx 10^(3))`
`t = (1)/(20) In (4.5 xx 10^(3))s`