Question

2) The switch in the circuit below has been closed a long time. At t=0, it is opened.

Answer 1

Answer:

  il(t) = e^(-100t)

Explanation:

The current from the source when the switch is closed is the current through an equivalent load of 15 + 50║50 = 15+25 = 40 ohms. That is, it is 80/40 = 2 amperes. That current is split evenly between the two parallel 50-ohm resistors, so the initial inductor current is 2/2 = 1 ampere.

The time constant is L/R = 0.20/20 = 0.01 seconds. Then the decaying current is described by ...

  il(t) = e^(-t/.01)

  il(t) = e^(-100t) . . . amperes