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. It was first studied by James Prescott Joule in 1841. Joule immersed a length of wire in a fixed mass of water and measured the temperature rise due to a known current flowing through the wire for a 30 minute period. By varying the current and the length of the wire he deduced that the heat produced was proportional to the square of the current multiplied by the electrical resistance of the wire.
 Q \propto I^2 \cdot R
This relationship is known as Joule's First Law. The SI unit of energy was subsequently named the joule and given the symbol J. The commonly known unit of power, the watt, is equivalent to one joule per second.
It is now known that Joule heating is caused by interactions between the moving particles that form the current (usually, but not always, electrons) and the atomic ions that make up the body of the conductor. Charged particles in an electric circuit are accelerated by an electric field but give up some of their kinetic energy each time they collide with an ion. The increase in the kinetic or vibrational energy of the ions manifests itself as heat and a rise in the temperature of the conductor. Hence energy is transferred from the electrical power supply to the conductor and any materials with which it is in thermal contact.
Joule heating is referred to as ohmic heating or resistive heating because of its relationship to Ohm's Law. It forms the basis for the myriad of practical applications involving electric heating. However, in applications where heating is an unwanted byproduct of current use (e.g., load losses in electrical transformers) the diversion of energy is often referred to as resistive loss. The use of high voltages in electric power transmission systems is specifically designed to reduce such losses in cabling by operating with commensurately lower currents. The ring circuits, or ring mains, used in homes are another example, where power is delivered to outlets at lower currents, thus reducing Joule heating in the wires. Joule heating can be defeated using superconducting materials.
Resistors create electrical noise, called Johnson Nyquist noise. There is an intimate relationship between Johnson Nyquist noise and Joule heating, explained by the fluctuationdissipation theorem.
Formulas and proof
Direct current
The most general and fundamental formula for Joule heating is:
 P=VI
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,

V is the voltage drop across the element.
The explanation of this formula (P=VI) is:^{[1]}
 (Energy dissipated per unit time) = (Energy dissipated per charge passing through resistor) (Charge passing through resistor per unit time)
When Ohm's law is applicable, the formula can be written in other equivalent forms:
 P=IV=I^2R=V^2/R
where R is the resistance.
Alternating current
When current varies, as it does in AC circuits,
 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:
 P_{avg}=I_{rms}V_{rms}=I_{rms}^2R=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:
 P_{avg} = I_{rms}V_{rms}\cos\phi = I_{rms}^2 \operatorname{Re}(Z) = V_{rms}^2 \operatorname{Re}(Y^*)
where \phi is the phase difference between current and voltage, \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.
Reason for highvoltage transmission of electricity
In electric power transmission, high voltage is used to reduce Joule heating of the overhead power lines. The valuable electric energy is intended to be used by consumers, not for pointlessly heating the power lines. Therefore this Joule heating is referred to as a type of transmission loss.
The power station wants to transfer a certain amount of electrical power P_{load} through power lines. (P_{load} represents the power used by all the elevators, televisions, etc. served by the station.) Since P_{load}=I_{rms}V_{rms} (ignoring phase difference, see AC power), it is possible to deliver the same power using a higher current at a lower voltage, or a lower current at a higher voltage. Transformers can switch between one and the other method of power transmission.
Since P=I^2R, using very low current at a very high voltage is the best way to reduce the transmission loss associated with Joule heating of the power lines. This explains the use of high voltage in the electrical grid.
The formula P=V^2/R seems to suggest, incorrectly, that high voltage increases transmission losses. However, it is important to use the correct V: V is the slight reduction in voltage between the two sides of the power line, also called "line drop"; V is not the "line voltage" relative to ground.^{[1]} The line drop decreases when the line voltage increases (for a fixed power transmission).
Applications
An incandescent light bulb glows when the filament is heated by Joule heating, so hot that it glows white with thermal radiation (also called blackbody radiation).
Electric stoves and other electric heaters usually work by Joule heating.
Soldering irons and cartridge heaters are very often heated by Joule heating.
Selfheating thermistors
Thermistors and resistance thermometers are resistors whose resistance changes when the temperature changes. These are sometimes used in conjunction with Joule heating (also called selfheating in this context): If a large current is running through the resistor, the resistor's temperature rises and therefore its resistance changes. Therefore, these components can be used in a circuitprotection role similar to fuses, or for feedback in circuits, or for many other purposes. In general, selfheating can turn a resistor into a nonlinear and hysteretic circuit element. For more details see Thermistor.
Heating efficiency
As a heating technology, joule heating has a coefficient of performance of 1.0, meaning that every 1 watt of electrical power is converted to 1 watt of heat. However, a heat pump can have a coefficient of more than 1.0 since it also obtains heating energy from the environment. The definition of the efficiency of a heating process requires defining the boundaries of the system to be considered. When heating a building, the overall efficiency changes when considering heating effect per unit of electric energy delivered on the customer's side of the meter, compared to the efficiency considering the losses in the power plant.
References
See also
cs:Jouleovo teplo de:Heizwiderstand ja: sk:Joulovo teplo
