Verified answer

When a quantity of charge, Q, is transferred over a potential difference V, the change in energy is U = Q V.

If that is done in a time t, the power needed is

P = U/t

= (Q V) / t

= (Q/t) V

But the amount of charge transferred per unit of time (which is the same as the amount of charge passing a cross section of a wire say per unit time) is the current (by definition!). So Q/t = I and therefore

P = I V

1 Volt is defined as 1 Joule per coulomb of charge

1 Amp is defined as 1 coulomb of charge per second

If we were to multiply these units together, you get:

J*(1/C)*C*(1/t)

=J/t

As a result, I*V is equivalent to the power in such a circuit