PHYS345 Electricity and Electronics

Example with Mixed Sources - Nodal Analysis

Textbook Circuit P3.8

Identify nodes and label accordingly.
Here I have grounded the central node.

Node voltage specified

Write the node equations.
There are three unknowns so three equations will be needed. Derive the first equation by considering the grounded node.

V1/2 - V2/4 - V3/4 = 0
2V1 +V2 + V3 = 0

The next two equations may be written quickly by inspection of the voltage sources connecting pairs of nodes.

V1 - V3 = 10
V3 - V2 = 12

Solve the equations to obtain the value of the unknowns.

V1 = 8 V
V2 = -14 V
V3 = -2 V

Finally, to find the current through the 12 V course, apply KCL at the top node. Since the 8 ohm resistor has 12 V across it; 1.5 A flows through it toward the node. The top 4 ohm resistor has 14 V across it; thus 3.5  flows through it toward the node. Accounting for the 2 A source, application of KCL yields 3 A flowing away from the node through the 12 V source.

Last updated Sept. 14, 1999.
Copyright George Watson, Univ. of Delaware, 1999.