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You don't need vector calculus. My demonstration of the power factor is a children's swing: if you push against your friend as they travel out you do work on them: if you make contact with your friend aas they're coming back, they do work on you.

Kids have a pretty good mechanical model of swing sets.

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Do kids actually learn about power factor?

That point aside, while an intuitive understanding is nice, power factor is really a mathematical construct arising from the multiplication of two out-of-phase sinusoids (i.e. voltage and current).

I think to really understand active / reactive power and pf, you need to look at the maths. It's really not that difficult. And you certainly don't need to know vector calculus, merely high school trig.

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