## 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.

- *V*_{1}/2 - *V*_{2}/4 - *V*_{3}/4 = 0

2*V*_{1} +*V*_{2} + *V*_{3} = 0
The next two equations may be written quickly by inspection of the voltage sources connecting pairs of nodes.

*V*_{1} - *V*_{3} = 10

*V*_{3} - *V*_{2} = 12
**Solve the equations to obtain the value of the unknowns.**

*V*_{1} = 8 V

*V*_{2} = -14 V

*V*_{3} = -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.