Question

Rs 100Ω resistor C- 10 uF capacitor L- 120 mH inductor Write the impedance Z [Q] equation for the circuit shown in Figure 1. This formula should be in term of the frequency (f), not for angular frequency (). (using MATLAB) 1. From the above formula, plot power factor versus frequency over the frequency range 0 Hz to 1000 Hz. You may use a MATLAB program to do the plotting. 2. Find the frequencies for; Maximum power factor, Minimum power factor, and Minimum impedance magnitude | Z (f) 3. 4. Please include the MATLAB script 10uF 120 mH 1000 VR Figure 1: RLC Circuit

Answer 1

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define R L and C parameters
R = 100;
L = 120e-3;
C = 10e-6;

% Impedance as a function of f is given below
% define f as below
f = logspace(-3,7,1000);
Z = R + 1j*2*pi*f*L + 1./(1j*2*pi*f*C);

% plot the impedance as a function of f
figure;
semilogx(f,abs(Z));grid on;
xlabel('Hz');ylabel('ohm');
title('Impedance in omhs');

% power factor
f = logspace(-3,3,1000);
Z = R + 1j*2*pi*f*L + 1./(1j*2*pi*f*C);
p = R./abs(Z);

% plot the power factor
figure;
semilogx(f,p);grid on;
xlabel('Hz');ylabel('');
title('power factor');

The impedance as a function of f is plotted below.

x106 16 Impedance in omhs 14 12 10 6 4 2 0 10 100 10 101010 -2 6 100 10% Hz

From the above figure, it is observed that the impedance is highest at low frequencies and high frequencies.

The minimum impedance is observed at frequency 146.3 Hz and the value of impedance is 100 ohms.

Power factor is plotted below.

power factor 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 02 10 10-3 02 10 10101

power factor X: 146.3 Y: 0.9999 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 02 10 10-3 02 10 10101 Hz

From the above figure, it is observed that the power factor is highest at a frequency 146.3 Hz and lowest at frequencies less than 0.1Hz and greater than 10^5Hz.