Joule heating

[큰나무]

Joule heating, also known as ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor releases heat.

Joule's first law, also known as the Joule–Lenz law, states that the power of heating generated by an electrical conductor is proportional to the product of its resistance and the square of the current:

${\displaystyle P\propto I^{2}\cdot R}$

Joule heating affects the whole electric conductor, unlike the Peltier effect which transfers heat from one electrical junction to another.

A coiled heating element from an electric toaster, showing red to yellow incandescence

Direct current

The most general and fundamental formula for Joule heating is:

${\displaystyle P=(V_{A}-V_{B})I}$

where

• P is the power (energy per unit time) converted from electrical energy to thermal energy,
• I is the current traveling through the resistor or other element,
• ${\displaystyle V_{A}-V_{B}}$ is the voltage drop across the element.

The explanation of this formula (P=VI) is:^[3]

(Energy dissipated per unit time) = (Energy dissipated per charge passing through resistor) × (Charge passing through resistor per unit time)

When Ohm's law is also applicable, the formula can be written in other equivalent forms:

${\displaystyle P=IV=I^{2}R=V^{2}/R}$

where R is the resistance.

Alternating current

Main article: AC power

When current varies, as it does in AC circuits,

${\displaystyle P(t)=I(t)V(t)}$

where t is time and P is the instantaneous power being converted from electrical energy to heat. Far more often, the average power is of more interest than the instantaneous power:

${\displaystyle P_{avg}=I_{rms}V_{rms}=I_{rms}^{2}R=V_{rms}^{2}/R}$

where "avg" denotes average (mean) over one or more cycles, and "rms" denotes root mean square.

These formulas are valid for an ideal resistor, with zero reactance. If the reactance is nonzero, the formulas are modified:

${\displaystyle P_{avg}=I_{rms}V_{rms}\cos \phi =I_{rms}^{2}\operatorname {Re} (Z)=V_{rms}^{2}\operatorname {Re} (Y^{*})}$

where ${\displaystyle \phi }$ is the phase difference between current and voltage, ${\displaystyle \operatorname {Re} }$ means real part, Z is the complex impedance, and Y* is the complex conjugate of the admittance (equal to 1/Z*).

For more details in the reactive case, see AC power∆0}

https://en.wikipedia.org/wiki/Joule_heating