## 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.

**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.

**Step 2:**
Identify nodes and label accordingly.

**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.

(*V*_{1} - 9)/5 + *V*_{1}/6 + (*V*_{1} + 9)/12 = 0
**Step 4:**
Solve the equation to obtain the value of the unknown.

**Solution:**
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.