= Joule heating
{c}
{title2=$P=VI=I^2R=V^2/R$}
{wiki}
= Ohmic heating
{c}
{synonym}
= Electrical dissipation
{synonym}
<Joule heating> is the dissipative conversion of electrical <work> into <internal energy> in an <electrical conductor>. In a metal, the <electric field> supplies <energy> to <charge carriers>, which transfer it to the material. This makes an immersed <resistor> a useful calibrated heater and makes <electrical resistance> a source of losses in wiring. Wind-driven <electric currents> are a proposed source of <heating of an inflated giant planet>.
For a stationary, purely resistive <Ohmic conductor>, use the <passive sign convention>: $V$ is the terminal <electric potential difference> from the entry to the exit of positive <electric current> $I$. The absorbed electrical <power> and <Ohm's law> give
$$
P=VI=I^2R=\frac{V^2}{R}\geq0,\qquad R>0.
$$
The last two expressions assume $V=IR$ at the relevant material <temperature>. For constant <electrical resistance> and <electric current> over a duration $\Delta t$, the dissipated <energy> is $E_{\rm diss}=I^2R\Delta t$; otherwise use $E_{\rm diss}=\int V(t)I(t)\,dt$. In <SI>, $\mathrm{V\,A}=\mathrm W=\mathrm{J/s}$.<University Physics Volume 2 by Samuel J. Ling and others>[§9.5, Power Dissipated by a Resistor and Summary of Relationships: combining terminal power with Ohm's law]{ref}
Absorbed electrical <power> $VI$ is more general than <Joule heating>: a <capacitor> can store <energy>, a <battery> can change its chemical <energy>, and an <electrical circuit> can deliver mechanical <work> or emit <light>. Even a heated <resistor> need not show an indefinitely rising <temperature>: in a thermal <steady state>, its dissipated <power> leaves by <heat transfer>. With the heater inside a <calorimeter> boundary, electrical input crosses as <work>; the subsequent <heat transfer> to the room is a different term in the <first law of thermodynamics>.
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