PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

154 Practical MATLAB® Applications for Engineers

Example 2.13

Using two loop equations and one node equation, and the matrix operations I =

inv(R) * V (where R is the [equivalent] impedance matrix of the network and V the

voltage vector), solve for the three branch currents—I 1 , I 2 , and I 3 —shown in the circuit

diagram of Figure 2.52.

ANALYTICAL Solution

The node and the two loop equations are shown as follows:

Node A; −I 1 + I 2 + I 3 = 0

Loop# 1; (^10) I 1 + (^5) I 2 = 10
Loop# 2; − (^5) I 2 + (10 + 20) I 3 = 0
The preceding equations in matrix form is given by


11 1
10 5 0
0530
0
10
0
1
2
3































• I
  I
  I
  
  
  Then the 3 × 3 matrix becomes the resistance matrix R, and the voltage V is given by the
  column vector [0 10 0]T as illustrated by the following matrix equation:
  []RI V[] [ ]
  
  then
  I = inv (R) V
  FIGURE 2.51
  Plots of Example 2.12.
  2
  1.5
  Current IL 1
  Power of RL
  0.5 05
  IL versus RL VL versus RL
  8
  6
  4
  Voltage VL 2
  0
  8
  6
  IL,VL,P = IL
  ∗VL
  IL,VL,P versus RL
  IL
  4
  2
  0
  Power versus RL
  Load Resistance RL Load Resistance RL
  Load Resistance RL
  Load Resistance RL
  10 0 5 10
  0 0510
  0
  1
  2
  3
  4
  5
  510
  P
  VL