Question

Problem 3 Impedance matching concept in electrical circuits states that the maximum power to a loa when the load resistance is matched to the internal resistance of the source. Show that this is true by plotting the power to the load RL and that it is maximum when is equal to the source resistance Rs for a source of 10 v DC and internal resistance Rs of load RL in series. Fit the power vs resistance to a second order polynomial and use Matlab function to fi power value and the resistance RL at maximum power Use the following equations: V/R total Total current to the circuit I Power to the load is IRL See circuit on the board
matlab problem

Answer 1

Solution:

3.

T

k
Rs 1 6 Эт 2

%%--------------- MATLAB CODE -----------------%%

%the range of load resistance RL
RL=0:0.001:20
P=100*RL ./(8+RL).^2;
%plot the power vs resistance
plot(RL,P,'k')
%specify the axis
axis([0 20 0 4]);
grid on ;
%label the asises
xlabel('Load resistance');
ylabel('Power');
%name the plot
title('Maximum Power')

%%--------------------- END ------------------------%%

Simulation:

Maximum Power 3.5 2.5 2 1.5 0.5 0 2468 10 12 1416 18 20 Load resistance

From the plot it is clearly seen that the power dissipated by the RL is maximum when RL=8ohm(i.e Rs=RL).

N.B: Copy the code save it in a mfile and rum in MATLAB simulator to have the best result.