Introduction to Electric Circuits

3.6 Thevenin's theorem 51

and B at either end of the resistor, r. To calculate E0 we first remove the resistor

r in the circuit of Fig. 3.18 to give the circuit of Fig. 3.20.

To calculate the potential difference between A and B we need to determine

(~20V

I 20s

I oA

lOV

~

lOfl

oB

Figure 3.20

the current I. Applying KVL to the closed path and taking the clockwise

direction to be positive

20- 51- 101- 10 = 0

151 = 10

I = 0.67 A

The potential drop between A and B is then given by

VAB -- IR 2 -Jr V 2 .~- 0.67 • 10 + 10 = 16.7 V

Since this turns out to be positive, then the potential of terminal A is higher

than that of terminal B and the current IL flOWS from A to B.

In accordance with Thevenin's theorem, VAB = E0.

To calculate R0 we remove the resistor r in Fig. 3.18 and replace the batteries

20~

-4 ] oA

.•5•

[~10~

oB

Figure 3.21

by short circuits to give the diagram of Fig. 3.21. R0 is the resistance between A

and B and is given by

RAB- R3 + R1R2//(R1 + R2)
= 20 + 50/15
= 23.33 11

Now from the Thevenin equivalent circuit of Fig. 3.19, putting in the values for
E0 and R0,