Millman's theorem

Specifically, Millman's theorem is used to compute the voltage at the ends of a circuit made up of only branches in parallel.

It is named after Jacob Millman, who proved the theorem.

Then Millman states that the voltage at the ends of the circuit is given by:[2] That is, the sum of the short circuit currents in branch divided by the sum of the conductances in each branch.

[3] Then, according to Ohm and Kirchhoff, the voltage between the ends of the circuit is equal to the total current entering the supernode divided by the total equivalent conductance of the supernode.

A branch that is already a current source is simply not converted.

An ideal current source has zero conductance (infinite resistance) and so adds nothing to the denominator.

The theorem does not work with ideal voltage sources because such sources have zero resistance (infinite conductance) so the summation of both the numerator and denominator are infinite and the result is indeterminate.