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 I1 ; I2 , and I3 are assigned to the branches as shown. Applying KCL at node a, I1 ¼ I2 þ I3

ð1Þ

The voltage Vab can be written in terms of the elements in each of the branches; Vab ¼ 20  I1 ð5Þ, Vab ¼ I3 ð10Þ and Vab ¼ I2 ð2Þ þ 8. Then the following equations can be written 20  I1 ð5Þ ¼ I3 ð10Þ

ð2Þ

20  I1 ð5Þ ¼ I2 ð2Þ þ 8

ð3Þ

Solving the three equations (1), (2), and (3) simultaneously gives I1 ¼ 2 A, I2 ¼ 1 A, and I3 ¼ 1 A.

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. 37 Copyright 2003, 1997, 1986, 1965 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An