Electric Circuits and Networks, Ist Edition by Pearson

87

3.2 THE INDUCTOR

SOLUTION

Only an impulse voltage can change the inductor current over [0

–

, 0

+

]. The current at

t  0

+

is read from the given i

L

waveform as 2 A. Therefore, the initial current in 2 H

inductor at t  0

–

 2 A.

We use v(t)  L(di/dt) to work out the v(t) waveform. i(t) is a piecewise linear

function. The slope of current is 1 A/s in the (0 s, 2 s) interval, 0 A/s in (2 s, 4 s) interval

and –1 A/s in the (4 s, 8 s) interval. Note that all intervals are open intervals. This is so

because the current waveform is not differentiable at the end points of the intervals

and hence the endpoints will have to be excluded from the domain of the derivative ...