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
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
20 I1 ð5Þ ¼ I2 ð2Þ þ 8
Solving the three equations (1), (2), and (3) simultaneously gives I1 ¼ 2 A, I2 ¼ 1 A, and I3 ¼ 1 A.
Published on May 10, 2013