PHYS345 Electricity and Electronics

Detailed Nodal Analysis Example

The same elements are used as the Detailed Simple Circuit Example, with the addition of one 9 V battery as shown.

Circuit schematic involving 5 resistors and 2 emfs

Step 1: Replace any combination of resistors in series or parallel with their equivalent resistance. Here I simply use the result from the previous example.

Symmetrized schematic

Step 2: Identify nodes and label accordingly.

Node voltage specified

Step 3: Write the node equation. Here I suppress the "k" for each resistor; there is no problem as long as all resistances are written in the same units.

(V1 - 9)/5 + V1/6 + (V1 + 9)/12 = 0

Step 4: Solve the equation to obtain the value of the unknown.

Solution:
V1 :  7/3 V   2.33 V

This result may be used to find any of the quantities of interest. The current through each of the three resistors may now be calculated since the voltage difference across each has now been determined.

"http://www.physics.udel.edu/~watson/phys345/examples/nodal-analysis.html"
Last updated Sept. 7, 1999.
Copyright George Watson, Univ. of Delaware, 1999.