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2) In particular, what about the motor-start capacitors
Forsooth, in any context whatsoever, the physics depends on ΔV, never
directly on V. The fancy name for this is /gauge invariance/. It is
a fundamental property of the EM field. It is built into the Maxwell
equations.
And (!!) your typical dimmer circuit draws current during some
small part of the circuit ...
This is a really big deal because many of their costs (including
dissipation in the distribution network) depend on ⟨I⟩² and/or ⟨ΔV⟩
Let [P] represent the algebraic average of P.
Since Ohm's law is linear (!) we can average both sides, so:
ΔV = I R
becomes:
⟨ΔV⟩ = ⟨I⟩⟨R⟩
This is a really big deal because many of their costs