A `1 -k Omega` resistor is connected in series with a `10-mH` inductor, a `30 V` battery and an open switch. At time `t= 0`, the switch is suddenly closed.
a. What is the maximum current in this circuit and when does it occur?
b. What are the voltage drops across the inductor and across the resistor `20 mu s` after the switch is closed?
c. On a single set of axes, sketch the voltage across the resistor and the voltage across the inductor as functions of time. Also, sketch a graph of the current in the circuit as s function of time.

Explanation

a. `i_(max) = (30 V)/(1000 Omega) = 0.030 A = 30 mA`, long time after closing the switch.
b. `I = imax (1 - e^(-t//(L//R))) = 0.030 (1-e^(-(20mus)/(10mus))) = 0.0259 A`
`V_(R ) = Ri = (1000 Omega)(0.0259 A) = 26 v`
`V_(L) = epsilon_("Battery") - V_(R ) = 30 V - 26 V = 4.0 V`
(or could use `V_(L) = L(di)/(dt)` at `t = 20 mu s`)
c.