# Joule effect

The effect Joule is the thermal demonstration of the electrical resistance. It occurs at the time of the passage of a Electric current in all conducting materials, except for the superconductive S which require particular conditions however.

# Nature

The Joule effect is a heating effect which occurs at the time of the passage of the electric current in a driver. It appears by an increase in the thermal energy of the driver and thus of its Température. The effect bears the name of the English physicist James Prescott Joule which studied it about 1860.

The energy dissipated in the form of heat between two moments T 1 and T 2 by a dipole of resistance R crossed by a current of intensity I is written:

$W = R \ int_ \left\{t_1\right\} ^ \left\{t_2\right\} i^2 dt \,$
The average power is thus worth:
$P = \ frac \left\{W\right\} \left\{t_2 - t_1\right\} = \ frac \left\{R\right\} \left\{t_2 - t_1\right\} \ int_ \left\{t_1\right\} ^ \left\{t_2\right\} i^2 dt$
• In periodic mode of current the expression of the power can be put in the form:

$P = R I_ \left\{EFF\right\} ^2 \,$ with $I_ \left\{EFF\right\} \,$, the effective Value of the intensity of the current.
• In mode of D.C. current the expression of the power becomes:

$P = R I^2 \,$

If this dipole checks the Loi of Ohm, one can write:

$P = U \ cdot I \,$
$P = \ frac \left\{U^2\right\} \left\{R\right\} \,$
with $U \,$, the effective value of the tension on its terminals.

Remark : The use of these formulas is not always simple, particularly when resistance depends on the temperature of the driver. The power dissipated by Joule effect modifies the temperature which modifies the resistance which modifies the power dissipated by Joule effect.

the Joule effect appears in any electric driver with more or less of importance. In certain cases, it is a question of a required effect to produce heat (electric radiator, water-heater, toaster) or light (incandescent lamp). Indeed, the rise in the temperature of the driver causes an energy exchange with outside in the form of heat transfer. If this temperature becomes very important, it also yields energy by visible radiation.

Sometimes, the Joule effect is responsible for losses of energy , i.e. of conversion undesirable, but inevitable, of part of electrical energy in thermal energy.

Example: on-line losses during the transport of the electric current which one seeks to limit by increasing the tension to decrease the intensity of the current.

# Applications

## Heating

The most common use of the Joule effect is the electric Chauffage: radiator, furnace, hotplate, hair drier, toaster. These apparatuses using an electrical resistance restore 100 % of electrical energy in heat by convection and radiation. The heat pumps, which use the laws of the Thermodynamique, are much more sparing.

## Lighting

The bulbs with incandescence also resort to the Joule effect: the tungsten filament, placed in an enclosure containing an inert gas, is brought up to an high temperature (more 2  200°C). At this temperature the matter emits radiations in the visible one (Loi of Planck). Nevertheless the apparent brightness of the incandescent lamps is rather low (5 times less than fluorescent lighting, 10 times less than the gas-discharge lamps).

## Protection of the circuits

The fusible are devices using the Joule effect to dissolve a gauged driver, in order to insulate a Electrical circuit in the event of overcurrent. The Disjoncteur S thermics use the same effect, but without destruction, they are réarmables.

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