PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

416 Practical MATLAB® Applications for Engineers

Example 4.13

The switch sw shown in the circuit diagram of Figure 4.64 has been opened for a long

time. At t = a = 0, the sw closes and remains closed for t ≥ 0. Assume that all the initial

conditions are zero. Determine by hand an expression for i(t). Create the script fi le analy-

sis_RLC that returns i(t) using the LT, and obtain plots of i(t) versus t for t ≥ 0, using a

numerical and symbolic approach.

Also obtain the symbolic expression fot i(t), for t ≥ 0, using Laplace for the case when

the sw closes at t = a = 1.

ANALYTICAL Solution

Zs R sL

sC

()
  ( )

1

total impedence

FIGURE 4.64
Circuit diagram of Example 4.13.

50 V

R = 2 Ω

L = 1 H

C = 0.1 F

sw closes at t = a

i(t)

0

0

01 2 3 4 5

0.5 1

1

0.5

−0.5

0

1

0.5

−0.5

− 1

1.5 2345 2.5 3.5 4.5

time (sec)

time (sec)

v 0 (t) versus t (symbolic solution)

v 0 (t) versus t (numerical solution)

Amplitude (volts)

Amplitude (volts)

FIGURE 4.63

Numerical and symbolic plots of v 0 (t) of Example 4.12.