## PHYS345 Electricity and Electronics

Example with Mixed Sources - Nodal Analysis

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

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

Solution:
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.

"http://www.physics.udel.edu/~watson/phys345/examples/mixed-source-nodal.html"
Last updated Sept. 14, 1999.
Copyright George Watson, Univ. of Delaware, 1999.