EE210.02
08.04.2009
HOMEWORK #5
1) In the circuit in Figure 1, the voltage and current expressions are
v  250e 60t V, t  0  ;
i  6e 60t A, t  0
Find
a)R; b)  (in milliseconds). c) L, d) the initial energy stored in the inductor. e) the time
(in milliseconds) it takes to dissipate 80 % of the initial stored energy.
Figure1
2) The current in a 15 mH inductor is known to be
i  1 A,
t  0;
4.000t
6.000t
i  A1e
 A2 e
A, t  0
The voltage across the inductor (passive sign convention) is 60 V at t = 0.
a) Find the expression for the voltage across the inductor for t > 0.
b) Find the time, greater than zero, when the power at the terminals of the inductor is
zero.
3) The current shown in Figure 2 is applied to a 0.75µF capacitor. The initial voltage on
the capacitor is zero.
a) Find the charge on the capacitor at t = 30 µs.
b) Find the voltage on the capacitor at t = 50 µs.
c) How much energy is stored in the capacitor by this current ?
Figure 2
4) The three inductors in the circuit in Figure 3 are connected across the terminals of a
black box at t = 0. The resulting voltage for t > 0 is known to be
v0  1250e 25t V.
If i1(0) = 10 A and i2(0) = -5A, find
a) i0(0);
b)i0(t), t  0;
c) i1(t), t  0,
d) i2(t), t  0;
e) the initial energy stored in the three inductors;
f) the total energy delivered to the black box, and g) the energy trapped in the ideal
inductors. i1 i2 i0
Figure 3
5) In the circuit in Figure 4 the voltage and current expressions are
v  100e 1000t V, t  0;
i  5e 1000t mA,
t  0 .
Find
a)R; b) C. c)  (in milliseconds).
c) L,
d) the initial energy stored in the capacitor.
e) how many microseconds it takes to dissipate 80 % of the initial energy stored in the
capacitor.
Figure 4