An (often) easier way: Mesh Analysis

WOO E44 BACK ON LETS GO IT’S GONNA BE A GOOD DAY

This was the sentiment that surged into the forefront of my mind as professor Mason entered the room.  It subsided with almost equal haste as Mason began to wax on about the wonders of nodal analysis.

We did an long-af example problem.  Some BS:

Seen above: a tedious nodal analysis problem. Could've used mesh but why not use the hard way.


You can pretty much always use node analysis.  It’s a shitty way to approach a lot of problems.  A better way is Cramer’s rule, mesh analysis, and using Thevenin and Norton’s theorems.  We’ll probably talk about those after lab.

THE LAB: Nodal Analysis.  We calculated (and recalculated) values for voltages across a trio of resistors with trio of voltage sources.  We then set up the circuit on the breadboard, and measured for voltages.  We found a very good correlation! Less than 1% error. See picture below.
1. Schematic with nodes labeled and Voltages v1, v2 calculated.

2. Measured Resistance Values 

We measured -2.43+-.01V and -4.40+.01V for V1 and V2 respectively.  Our calculated values were -2.43 and -4.43 for V1 and V2.  

The circuit in action:

MESH ANALYSIS!

It only works with planar circuits.  But when it does? It’s great.  More good news: all circuits for this class will be planar.  

To do mesh analysis, 3 steps: (Note than there are equal numbers of meshes to loops)

1. Assign mesh currents to the n meshes
2. Appyl KVL to each of th en meshes.  Use Ohm’s law to express voltages in terms of currents.
3. Solve the n equations.

(To contrast w/ nodal: assign nodal voltages, Apply KCL, solve.)

BY CONVENTION, mesh currents are always clockwise.