Re: [Phys-l] Thermal heating in a resistor?

[John Denker <jsd@av8n.com>]

On 05/15/2010 08:12 AM, Tony wrote:
> Why is the formula P=I^2V used to describe thermal power loss in resistor

It isn't.  I assume that's a typo.

> instead of P=IV or P=V^2/R? Is this just the textbook author's choice of
> formula?

Well, the facts are these:

   P = I V    always         [1]

Homework:  Derive equation [1].  This is a one-liner, i.e. 
an immediate corollary of the definition of current, the 
definition of voltage, and the definition of power.

If we define R to be the large-signal resistance 
   R := V / I                [2]
then we obtain both
   P = I^2 R                 [3]
and
   P = V^2 / R               [4]

which are also one-liners.  

Note that we do not require the "resistor" to be Ohmic; all 
we require is for R to be defined according to equation [2].

Note that this is not the only definition of resistance.  It
is conventional and reasonable to also define the small-signal
resistance
   r := dV / dI

in which case equation [1] continues to hold, as it must, 
but there are no equations resembling equation [3] or
equation [4] involving r.

> instead of P=IV or P=V^2/R? Is this just the textbook author's choice of
> formula?

There is no "instead of".  The idea of using any subset 
of these equations to the exclusion of the others would 
be amazingly silly.

There is no "choice".  All of these equations are true,
and there is nothing a textbook author (or anybody else)
can do to change that.