Introduction to Electric Circuits

Ro

Figure 3.15

A

IL

Rt.

3.6 Thevenin's theorem 49

9 Step 3: to calculate E0 remove the resistor R L in Fig. 3.14 to give the circuit
of Fig. 3.16 and determine the potential difference between the
terminals A and B (say VAB).

I 10~ 40~

I I I

9v 12v

T
Figure 3.16

To calculate VAB we take a trip from A to B adding the potential drops as we

go. We therefore need to calculate the current I. Applying KVL to the circuit

and taking the clockwise direction to be positive, we have

9 - 10I- 40I + 12 = 0

501 = 21

and

I = 21/50 = 0.42 A

Now, going from A to B via the 9V battery we have that
-10 • 0.42 + 9 - 4.8 V. This means that the potential drop is positive so that
terminal A is at a higher potential than terminal B and so the current will flow
through RL from A to B.
To check, we can go from A to B via the 12 V battery in which case we have
that 40 • 0.42 - 12 = 16.8 - 12 = 4.8 V as before.

9 Step 4: to calculate R0, remove the resistor RL, replace the batteries by short
circuits to give the circuit of Fig. 3.17 on the following page and
determine the resistance between the terminals A and B.
The 10 1) and the 40 1) resistors are in parallel so the equivalent
resistance between A and B is given by
Ro- (10 • 40)/(10 + 40) = 8 12