In the electric power equation $P=RI^2$, $P$ represents the product of $RII$.
I'm trying to understand the fundamental anatomy of the $RII$ term. More precisely, why does the current, $I$ appear twice as a factor? Does this represent two different dimensions of $I$, in the sense of a measurable, albeit temporal or spatial quantity?
For example, is one factor "speed" and the other one "direction?"
Update:. This link about angular velocity seems to support my question regarding direction, speed, and dimensions.