0195136047.pdf

1.3 KIRCHHOFF’S LAWS 41

In a network consisting of one or more energy sources and one or more circuit elements,
thecause-and-effectrelationship incircuit theorycan be studied utilizing Kirchhoff’s laws and
volt-ampere relationships of the circuit elements. While the cause is usually the voltage or current
source exciting the circuit, the effect is the voltages and currents existing in various parts of
the network.

EXAMPLE 1.3.1

Consider the circuit shown in Figure E1.3.1 and determine the unknown currents using KCL.

iS = 10 A i 1 = 5 A

i 4 = 3 A i 5 =? i 2 = 4 A i 3 =?

+

−

Node a

Node b

Node c

Figure E1.3.1

Solution

Let us assign a+sign for currents entering the node and a−sign for currents leaving the node.
Applying KCL at nodea,weget

+iS−i 1 −i 4 −i 5 = 0

or

10 − 5 − 3 −i 5 =0ori 5 =2A

Applying KCL at nodeb,weget

+i 1 −i 2 −i 3 = 0

or

5 − 4 −i 3 =0ori 3 =1A

The student is encouraged to rework this problem by:

(a) Assigning a−sign for currents entering the node and a+sign for currents leaving the

node; and

(b) Applying the statement that the sum of the currents entering a node is equal to the sum

of the currents leaving that node.