Page 48 - Schaum's Outline of Theory and Problems of Electric Circuits

Analysis Methods

4.1 THE BRANCH CURRENT METHOD
In the branch current method a current is assigned to each branch in an active network. Then
Kirchhoff’s current law is applied at the principal nodes and the voltages between the nodes employed to
relate the currents. This produces a set of simultaneous equations which can be solved to obtain the
currents.

EXAMPLE 4.1 Obtain the current in each branch of the network shown in Fig. 4-1 using the branch current
method.

Fig. 4-1

Currents I 1 ; I 2 , and I 3 are assigned to the branches as shown. Applying KCL at node a,

ð1Þ
I 1 ¼ I 2 þ I 3
The voltage V ab can be written in terms of the elements in each of the branches; V ab ¼ 20 I 1 ð5Þ, V ab ¼ I 3 ð10Þ and
V ab ¼ I 2 ð2Þþ 8. Then the following equations can be written
20 I 1 ð5Þ¼ I 3 ð10Þ ð2Þ
20 I 1 ð5Þ¼ I 2 ð2Þþ 8 ð3Þ

Solving the three equations (1), (2), and (3) simultaneously gives I 1 ¼ 2A, I 2 ¼ 1 A, and I 3 ¼ 1A.
Other directions may be chosen for the branch currents and the answers will simply include the
appropriate sign. In a more complex network, the branch current method is difficult to apply because it
does not suggest either a starting point or a logical progression through the network to produce the
necessary equations. It also results in more independent equations than either the mesh current or node
voltage method requires.

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