Problem 4-26

a) In the circuit below find v1 and the power developed by the 25 volt source using nodal analysis. Note that the node labels (in Blue) were not on the original diagram, but are part of step 1: label all essential nodes.

There are no dependent sources, so that part of the algorithm can be skipped.

There is a voltage source directly connecting nodes 1 and 2, so equate the difference in the node voltages to the voltage source and form a supernode. The circuit is copied below with the supernode marked.

V1 - V2 = 25 (equation a)

This is one of the two equations we need.

Now write KCL at the supernode.

2 + V1 / 50 + V2 / 150 + V2 / 75 = 0

Multiply by 150

300 + 3V1 + V2 + 2 V2 = 0

Collect terms

3V1 + 3 V2 = - 300 (equation b)

Now solve the two equations (a and b)

Solving equation b for V2 gives

V2 = - 100 - V1

Inserting this into equation a gives

V1 - (- 100 - V1) = 25

Collecting terms gives

2 V1 = -75

thus

V1 = - 37.5

The power developed by the 25 volt source is

P25 = 25 (2 + V1 / 50) = 25 (2 - 37.5 / 50) = 25 (1.25)
P25 = 31.25 W

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