Thermal Energy Dissipated in a Resistor in AC vs DC

[Oijl]

Homework Statement

What direct current will produce the same amount of thermal energy, in a particular resistor, as an alternating current that has a maximum value of 2.60 A?

Homework Equations

The Attempt at a Solution

A DC would dissipate a constant amount of thermal energy in a resistor. An AC would dissipate a varying amount, but oscillating, so there would be an average. Couldn't I just say that since I know that current in an AC circuit oscillates as a sine wave, that the "average current" would just be half the amplitude, and so that over a period of time that is a multiple of the period of oscillation, a DC of half of the maximum value of current for the AC would have dissipated the same amount of thermal energy as the AC?

 

[Delphi51]

Not half the amplitude.
If you know calculus, you can find the answer yourself by integrating V*I*dt over a cycle. Or check out this article: http://en.wikipedia.org/wiki/Root_mean_square