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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.

Cheers

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    $\begingroup$ Current does not have 2 dimensions. Where did you get that idea? Do you even know what a 'dimension' is? $\endgroup$ May 20 '16 at 11:20
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    $\begingroup$ No, if you take $a\cdot y$, you have the product of $a$ and $y$. If you have a square of sides $a$ and $y$, then this product is equal to the area of your square. But a multiplication of two values is not necessarily the area of a square. $\endgroup$
    – Wasabi
    May 20 '16 at 12:07
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    $\begingroup$ Kris, welcome to Engineering SE. I've done my best to clean up your question in light of what you've expressed in comments and your acceptance of Jodes' answer. Please check to make sure I haven't misrepresented what you're trying to understand and if necessary edit to correct. Keep in mind for the future that the more time and effort you put into clearly communicating your question - and researching the topic in advance, and discussing the fruits of that research - the more likely your question is to be well received and attract good answers. $\endgroup$
    – Air
    May 20 '16 at 17:48
  • $\begingroup$ Kris, I'll repeat: you have no idea what a "dimension" is. Polynomial power is not the number of dimensions, or even degrees of freedom. $\endgroup$ May 22 '16 at 9:39
  • $\begingroup$ @Kris my 15 Physics teachers (undergrad and grad) would beg to disagree. Stop making things up. $\endgroup$ May 22 '16 at 15:43
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Firstly, by temporal I think you mean spatial. Secondly if you consider acceleration, the units are m/s^2. Seconds-squared are not spatial, but they are temporal. But they needn't be either. Consider E=mc^2. c is the speed of light.

Your formula comes from these two formulas:

P = I V

In other words, the power consumed by a device is equal to the voltage across it multiplied by the current flowing through it.

V = I R

Which means the voltage across a resistive element is equal to the current flowing through it multiplied by its resistance.

If you substitute the second into the first, you get:

P = I V = I ( I R ) = I^2 R

If you look at the equivalent SI units for power, volts, current and resistance, you will find the above to be consistent.

If this doesn't answer your question, you really need to be clearer!

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