PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Direct Current and Transient Analysis 121

R.2.83 Let us gain some experience by using the different network theorems and tech-

niques just presented by solving the following example.

For the circuit shown in Figure 2.15, fi nd the voltage across RL = 5 Ω (Va a’) by

hand calculation by using

a. Loop equations

b. Node equations

c. Source transformation—voltage to current source

d. Source transformation—current to voltage source

e. Superposition

f. Thevenin’s theorem

g. Norton’s theorem

FIGURE 2.14

Thevenin’s source transformation into a Norton’s equivalent circuit.

RTH

IN = VTH/RTH

RTH

VTH

a

a′ a

a

FIGURE 2.15

Network of R.2.83.

RL = 5 Ω

R = 15 Ω

Is = 12 A

Vs = 60 V

a

a′

ANALYTICAL Solutions

a. The loop equation solution is illustrated in the circuit diagram of Figure 2.16. The

loop currents I 1 and I 2 are indicated in Figure 2.16. Then the loop equation for loop

# 1 is given by

60 V = 20 I 1 − 5 I 2

and since

I 2 = −12 A