PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 305

Example 3.20

Let the current in the series RLC circuit diagram shown in Figure 3.84 be given by

i(t) = t^3 + t^2 – 12t A.

Create the script fi le sym_analysis_RLC that returns the following plots using sym-

bolic techniques:

1. i(t) versus t


2. i^2 (t) versus t


3. ∫i(t)dt versus t


4. (di(t))/dt versus t


5. vR(t) versus t, where vR(t) = R i(t)


6. vL(t) versus t, where vL(t) = L di/dt


7. vC(t) versus t, where vC(t) = 1/C ∫i(t)dt


8. [vL(t) + vR(t)] ver su s t


9. [vC(t) + vR(t)] ver su s t


10. pR(t) versus t, where pR(t) = i^2 (t)R


11. pL(t) versus t


12. pC(t) versus t

and the instantaneous expressions of i(t), VR(t), VL(t), VC(t), VRL(t) = VR(t) + VL(t), VRC(t) =

VR(t) + VC(t), PR(t), PL(t), and PC(t).

MATLAB Solution

% Script file : sym _ analysis _ RLC

% Analysis of an RLC series circuit

% where the current isiamps=t^3+t^2-12*t

% R=1000 Ohms, L=30 mH, and C=0.5 microF

echo off;

syms t;

iamps=t^3+t^2-12*t;

figure(1)

subplot(2,2,1)

ezplot(iamps)

title(‘i(t) vs.t’);

ylabel(‘Amplitude (amps)’);

grid on

isquare=iamps^2;

subplot(2,2,2)

ezplot(isquare)

C = 0.5 μF

L = 30 mH

i(t)

R = 1000 Ω

FIGURE 3.84

Network of Example 3.20.