Chapter 7: Energy Storage Elements
Example Problems
dv C
dt
di
=
vL L L
dt
=
iC C
=
W
1
2
2
=
Cv
=
W
1
2
Li2
q2
=
2C
1
2
qv
1 i dt
v C=
(t) v(t o ) + C
∫C
=
iL (t) iL (t o ) + L1 ∫ v L dt
Example 7.1
Determine vC(t) for t ≥ 0 for the circuit when vC(0) = −4 V.
Example 7.2
The current iL(t) in a 5-H inductor is
0
t≤0

iL (t) = 
t≥0
4 sin 2t
where the units of time and current are seconds and amps. Determine the power, p(t),
absorbed by the inductor and the energy, w(t), stored in the inductor.
Hint: 2 cos A ⋅ sinB
= sin(A + B) + sin(A − B)
7-1
Example 7.3
Assume steady state has occurred when the switch opens at time t = 0. Determine all
the voltages and currents of all elements for t = 0+.
Example 7.4
The circuit is at steady state when the switch closes at time t = 0. Determine v1(0−),
v1(0+), i2(0−), and i2(0+).
7-2