Something's bugging me. Suppose we take kvl around a loop in a circuit, we have:(adsbygoogle = window.adsbygoogle || []).push({});

v1(t)+v2(t)+....=0

Suppose v1, v2, v3(t) are all sinusoidal (they can be written as Acos(wt+s)).

So we have

A1cost(wt+s1)+A2cost(wt+s2)+....=0

Suppose we replace all of them by their phasors, this should also equal zero but why? I'll write it out here (without suppressing e^jwt, but just adding the imaginary parts)

(A1cos(wt+s1)+A2cos(wt+s2)+....) + j(A1sin(wt+s1) + A2sin(wt+s2)+....)

If I know the group of real terms add to zero, does that necessary imply that the group of imaginary terms add to zero? Is there a proof of this?

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# Kirchoff laws for phasors

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