4.
(Second Order Circuits, 35 points total)
Assume the following circuit configuration, with a current source of 2A, a 25 mH inductor,
a 62.5 µF capacitor, and a 12.5 ? resistor.
??
t=0 CEL
R
a) Derive the differential equation that describes the current through the inductor $i_L(t)$ in
this circuit.
b) Find the roots of the equation in (a). Is the solution overdamped, underdamped, or
critically damped?
Assume the initial inductor current $i_L(0)$ is 1 A and the initial voltage on the capacitor
is 0.5 V, where the upper terminal has positive polarity. Find $i_L(t)$ for $t \ge 0$.