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The rate of Joule heat is given by P =V ...

The rate of Joule heat is given by `P =V xx I` where V is the potential difference across the ends of a conductor and I is the current flowing through it. Does this relation hold for a condutor that does not obey Ohm's law?

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Yes, because rate of Joule heat is equal to work done in maintaing the current through a conductor in a unit time [i.e., `P = VI`] which is independent, whether `V prop I` or not. It means the rate of Joule heat will also be applicable to the devices which may not obey Ohm's law.
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