PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 285

Example 3.11

Write a MATLAB program that returns

1. The phasor diagram of the voltages V(Applied), VL, VC, and VR of the circuit shown in
   Figure 3.65


2. The angle between the I and V


3. Verify KVL, that is, V = VL + VC + VR

R = 100 Ω

I

C = 40 μF

V = 220, f = 60 Hz L = 0.5 H

FIGURE 3.65

Network of Example 3.11.

MATLAB Solution

>> V = 220;

>> R = 100;

>> C = 40e-6;

>> L = .5;

>> Omega = 2*pi*60;

>> Z = R+j*((L*Omega)-1/(C*Omega));

>> Magnitude = abs(Z);

>> Phase = 180*angle(Z)/pi;

>> I = V/Z;

>> I = abs(I);

>> VR = I*R;

>> VL = j*L*Omega*I;

>> VC = -j*I/(C*Omega);

>> Vapplied = VR+VL+VC; % the result should be 220 (KVL)

>> Check _ KVL = abs(VApplied)

Check _ KVL =

220.0000

>> phase _ in _ deg = 180*angle(VApplied)/pi

phase _ in _ deg =

50.7011

>> % construction of the phasor diagram

>> L(1) = 0;

>> L(2) = VR;

>> L(3) = VR+VL;

>> L(4) = VR+VC;

>> Voltage = [0 VApplied];

>> axis(‘square’)

>> plot(real(L), imag(L), real(Voltage), imag(Voltage))

>> grid on

>> xlabel(‘Real Axis’), ylabel(‘Imaginary Axis’)

>> title(‘Phasor Diagram’) (Figure 3.66)