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Why does $P=i^2R$ apply only to transfer of electrical potential energy to thermal energy in a device with resistance while $P=iV$ apply to electrical energy transfers of all kinds?

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2 Answers 2

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Why does P=i^2R apply only to transfer of electrical potential energy to thermal energy in a device with resistance

How would you expect a formula involving a term "R" to apply to something that doesn't have any characteristic called "R"?

while $P=iV$ apply to electrical energy transfers of all kinds?

This formula applies to all electrical devices (or more correctly, to any branch in a lumped circuit).

The alternate formula involving $R$ is derived from this one, based on Ohm's Law

$$V=iR.$$

If you substitute this into the power formula $P=iV$ you can get either

$$P=i(iR)$$

or

$$P = \left(\frac{V}{R}\right)V$$

Both of which simplify to well-known formulas for the power consumption of a linear resistor ($P=i^2R$ or $P=V^2/R$).

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  • $\begingroup$ If we connect the two terminals of a cell with an ideal conducting wire, to where is the the energy transferred to ( since according to $P=iV$ there is energy transfer) ? $\endgroup$
    – Lordinkavu
    Jul 23, 2017 at 5:15
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    $\begingroup$ @GauthamShankar, 1. There is no such thing as a perfect conducting wire, so some power will be converted to heat in the wire. 2. There is no such thing as a perfect voltage source, so some power will be converted to heat in the cell itself. Practically speaking, the majority of the heat will typically be generated in the cell. $\endgroup$
    – The Photon
    Jul 23, 2017 at 5:55
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    $\begingroup$ If you had a perfect voltage source, and want to think about what happens if you get close to an ideal wire, use the form $P=V^2/R$ and take the limit as $R\to 0$. $\endgroup$
    – The Photon
    Jul 23, 2017 at 5:57
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Remember the definition of voltage as energy change upon moving a charge. So you know the energy changes by QV for every charge that moves across. That gives a rate IV. It didn't have to be an Ohms law resistor in this derivation.

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