Question

Show that the units $1 \textrm{ V}^2 \textrm{/}\Omega = 1\textrm{ W}$, as implied by the equation $P = \dfrac{V^2}{R}$.

Final Answer

see video solution for derivation.

Solution Video

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This is College Physics Answers with Shaun Dychko.
We’re going to show that the units of Ampere squared multiplied by Ohms is a Watt, so we’re verifying this formula basically. So a Watt in more base units is a Joule per second, this is energy per time. So we can replace this

*P*with units of Joule per second, and then a current is a Coulomb per second and since this formula squares, that way we have Coulombs squared per second squared, and resistance has unit of Ohms, now we need to breakdown the Ohms into more basic units now. So from Ohms Law we know that resistance is voltage divided by current, so a Volt is a Joule per Coulomb, and a Ampere is Coulombs per second, I suppose I should write a*A*here for the units Ampere. So an Ampere substituted with Coulombs per second, so one of this Coulombs per second cancels with one of this Coulombs per second, leaving us with just Coulombs per second there times Joules per Coulomb, the Coulombs cancel, leaving us with Joules per second. And Joules per second is a Watt, so we have verified that Ampere squared Ohms are units of Watt.