Does phi (from cos phi electricity) have anything to do with phi of the golden ratio?

Answer

Dear Jeff,

The answer is short and simple: not to my knowledge, no.

Mathematicians, scientists, and engineers eagerly use the Greek alphabet to use symbols to represent certain concepts in formulas.
When the latter is exhausted, they’ll start with the Hebrew alphabet … 😉

Mathematicians generally use Greek characters to represent angle arguments.
Physicists and engineers have adopted that habit. The well-known Phi, with Cos(Phi) associated with it, arises from this. In this case, Phi then represents the phase shift between current and voltage that can cause problems with inductive loads.
The phi is therefore a function of the load and can take on various values.

The situation is different with the Golden Ratio: this is an important mathematical constant.
Greek symbols are also usually assigned to mathematical constants, such as indeed Phi for the Golden Ratio (see link), or Gamma for the Euler constant, or by far the best-known of all constants: Pi.