Direct Current and Transient Analysis
187
Example 2.26
Steady-state conditions exist in the network shown in Figure 2.89 at t = 0
−
, when the
source V 2 = 10 V is connected to the RL circuit. At t = 0
+
, the switch is moved downward
and the source V 1 = 20 V is then connected to the RL circuit (while the source V 2 = 10 V
is disconnected), where it remains for t ≥ 0.
1. Write and solve the differential loop equation by hand for the current i(t) (through
RL), and the voltages v R (t) and v L (t), for t ≥ 0.
2. Create the script fi le RL_IC that returns the solutions for part 1 by using the MATLAB symbolic solver dsolve.
3. Repeat part 2 by using the MATLAB numerical solver ode45.
4. Also obtain the plots of
a. i(t) versus t
b. v R (t) versus t
c. v L (t) versus t
over the range 0 ≤ t ≤ 2 s, for parts 2 and 3 and compare their results.
5. By using MATLAB, verify the solution i(t) obtained in part 2 by applying KVL
around the loop consisting of V 1 , R, and L.
FIGURE 2.88
Transient current plots across R of Example 2.25.
Current i(t) for: R = 1, 2, and 5
11
10
9
8
7
6
currents
5
4
3
2
1
0
0
0.5
1
1.5
time t/sec
2
2.5
3
R = 1 ohm
R = 2 ohms
R = 5 ohms
FIGURE 2.89
Network of Example 2.26.
V 2 = 10 V
R = 2 Ω
Switch
L = 1 H
V 1 = 20 V
i(t )
t = 0
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7/23/2008 1:38:57 PM