PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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 con nected to t he 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 vR(t) and vL(t), for t ≥ 0.


2. Create the script fi le RL_IC that returns the solutions for part 1 by using the MAT-
   LAB 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. vR(t) versus t
   c. vL(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.

R = 2 Ω V 2 = 10 V

Switch

L = 1 H

i(t) V 1 = 20 V

t = 0