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Re: electrical power



Michael Edmiston wrote:
...
If the device is a motor, or a light bulb, or some device
that is "emitting power" other than via thermal energy, then P=IV is the
total power consumption, and the joule heating would be some number less
than this.

Yes.

Another example: A battery. P=IV is the power going
in, but it might well all be going into charging
the battery, with no Joule heating at all.

There is not, and cannot be, any general formula
P = some_function_of (I, V)
for the Joule heating in something that is not
100% dissipative. You would need to know another
variable or another functional relationship to
tell you what fraction is being dissipated and
what fraction is not.

Maybe (!) in some circumstances the additional variable
might (!) be a resistance. For instance, the battery
might be modelled as a 100% ideal capacitor with an
ideal resistor in series. In that idealized case you
could write the power as I^2R. But the very next day
you might see a battery with an ideal resistor in
_parallel_ instead, in which case the dissipation would
be V^2/R and not I^R (where we are treating the lossy
battery as a two-terminal device and measuring I and
V at the terminals).

Summary:
- P=IV is power, for sure.
- The power dissipated in a resistive element is called
Joule heating, even if the resistor is non-ohmic.
- I^2R and/or V^2/R apply to ohmic systems, in which
case they are obvious corollaries of the P=IV law.