TABLE OF CONTENTS Anyone who has studied geometry should be familiar with the concept of a theorem: a relatively simple rule used tosolve aproblem, derived from a more intensive analysis using fundamental rules of mathematics. Atleast hypothetically, any problemin mathematics can be solved just by using the simple rules of arithmetic (in fact, this is how modern digital computers carry out the most complex mathematical calculations: by repeating many cycles of addition and subtraction!), but human beings aren't as consistent or as fast as a digital computer. We need "shortcut" methods in order to avoid procedural errors.
In electric network analysis, the fundamental rules are Ohm's Law and Kirchhoff's Laws. While these humble laws may be applied to analyze just about any circuit configuration (even if we have to resort to complex algebra to handle multiple unknowns), there are some "shortcut" methods of analysis to make the mathematics easier for the average human.
As with any theorem of geometry or algebra, these network theorems are derived from fundamental rules. In this chapter, weare not goingtodelve into the formal proofs of any of these theorems. If you doubt their validity, you can always empirically test them by setting up example circuits and calculating values using the "old" (simultaneous equation) methods versus the "new" theorems, to see if the answers coincide. They always should!
In Millman's Theorem, the circuit is redrawn as a parallel network of branches, each branch containing a resistor or series battery/resistor combination.
