# Where did $P=VI$ come from?

Where did the basic physics law $P=VI$ come from? Here, $P$ is power, $V$ is voltage and $I$ is current. It doesn't have a name like Ohm's law, as far as I could find. So where did it originally come from, who invented it and when? Or what are early references for it?

• Could you hint what are $P$, $V$ and $I$? – Alexandre Eremenko Jul 18 '15 at 19:04

Joule discovered, in the 1840s, that the power in a circuit was proportional to the current squared times the resistance. He published a short paper entitled "On Production of Heat by Voltaic Electricity". Joule used the form $$P=I^2R$$ One version of Ohm's law, of course, is $$V=IR$$ Doing some substitution yields the form you give.
I suspect that it is impossible to determine who first wrote Joule's law by substituting in Ohm's law. It would be akin to asking, "Who was the first person to write Ohm's law as $R=\frac{V}{I}$?" This might be worth looking through, although I do not know if it is comprehensive.