Introduction to Electric Circuits

3.5 The principle of superposition 47

batteries are in the circuit together is therefore, according to the principle of
superposition, given by

IL -- ILl "q- /L2 -- 0.45 + 0.9 = 1.35 A flowing from A to B

Note that if the battery V2 were connected in the opposite sense (i.e. with its
negative plate connected to the load terminal A and its positive plate connected
to B) then IL2 would flow from B to A and the load current IL would be
0.45 - 0.9 - -0.45 A flowing from A to B (i.e. +0.45 A flowing from B to A).

Example 3.4

Determine the current flowing in the 8fl resistor (R~) in the circuit of
Fig. 3.11.

R2 = 4~

t J

I = 3AI R1 = 8~ V = 6V

/

Figure 3.11

Solution

First we replace the current source I by an open circuit, giving the diagram of

Fig. 3.12.

4~

i J

Ia

8o ()6v

Figure 3.12

From this circuit we see that the current Ia- V/(R1 + R2)= 6/12- 0.5 A.
Next we reconnect the current source and replace the battery V by a short
circuit to give the circuit of Fig. 3.13 shown overleaf.

By current division we obtain

Ib = [4/(4 + 8)1I- 4 • 3/12 = 1 A

When both sources are acting
R a - Ia + lb -- 0.5 + 1 = 1.5 A

together the current through