W9_parallel_resonance.eps

Week 9: Alternating Current Circuits 301

Problem 9.

R L

R

V

S t = 0

I (0)

I(0)

0

1

I (0) 2

In the circuit above, switchShas been closed for a very long time. At timet= 0 the switch is
opened. Find:

a) The currentsI(0),I 1 (0), andI 2 (0) att= 0 at the instant before the switch is opened.

b) Using Kirchhoff’s voltage rule, find (derive) and solve the differential equation forI 2 (t). Draw

a qualitative plot of this function.

c) Write an expression for the energy stored on the inductor as a function of time, using your

answer to b). Draw a qualitative plot of this function.