Resistance (electricity)

The physical property

It is the property of a material to be opposed to the passage of an electric current. It is often indicated by the letter R and its Measuring unit is the Ohm (symbol Ω ). It is related to the concepts of Résistivité and electric conductivity:

For a homogeneous thread-like driver, with a Temperature given, there exists a relation making it possible to calculate its resistance according to the material which constitutes it and of its dimensions:

R= \ rho \ frac L s= \ frac {L} {\ gamma.s} \,

$\ rho \,$ being the Resistivity in Ω.m,
$l \,$ the length in Meter S,
$s \,$ the section in m²,
$\ gamma \,$ the conductivity in (Ω.m) ^-1.

Resistance is also responsible for a dissipation of energy in the form of Chaleur. This property bears the name of Joule effect. This production of heat is sometimes a desired effect (resistances of heating), sometimes a harmful effect (Joule losses).

One of the main issues for the Engineer S is that conductivity, and its reverse, the resistivity, strongly depend on the Température. When a dipole is crossed by an electric current, its resistance causes a heating which modifies its temperature, which modifies its resistance. The resistance of a dipole thus depends strongly on the conditions of use.

The power dissipated by Joule effect is $P = U \ cdot I \,$

$I \,$ being intensity of the current, in amp S, crossing resistance and
$U \,$ the tension, in Volt S, between its terminals.

Resistance has this of private individual that it is one of the rare physical characteristics whose beach of values practically goes from 0 (superconductors) to the ∞ (insulating).

The dipole

To distinguish the dipole from its physical property, it would have in theory to be invited " résisteur" (the English word resistor or the Anglicism resistor is sometimes employed wrongly). By abuse language the dipole was thus made call him also " résistance" by the practice. This use is allowed by the dictionaries.

It is an electronics component which makes it possible to voluntarily increase the resistance (physical property) of a circuit. It is characterized by the proportionality between the intensity of the current which crosses it and the tension between its terminals. In practice this property is checked only roughly because of the variation of Résistivité with the Température.

One distinguishes:

resistances of power of which the goal is to produce heat, example: electric heating. Generally a plate indicates the nominal voltage of use and the value of the produced power.
fixed resistances of which the goal is to obtain, in an electronic assembly, perfectly given potentials or currents in certain places of the circuits. One then indicates by a code his value of resistance and the precision of this value. The maximum power which it can dissipate guesses (sometimes) by its size. These resistances are the only ones with truly checking the Loi of Ohm in a great field of application (but they were conceived after its death)
the variable resistors which make it possible a user to adjust a current (rheostat) or a tension (potentiometer).
the dipoles whose resistance varies with a physical size:

the temperature: CTN (resistance to negative temperature coefficient) and CTP (with positive temperature coefficient)
illumination: photoresistances
forces applied: strain gauges…

The ohmic driver

An ohmic driver is a Electronics component called also resistance and which checks the Loi of Ohm:

U = R \ cdot I \,

, with

$I \,$ being intensity of the current, in amp S, crossing resistance and
$U \,$ the tension, in Volt S, between its terminals.

Knowing this relation, one can then notice that the curve representative of the characteristic of a resistance is a line passing by the origin of the reference mark.

One uses sometimes the terms of pure resistance or ideal resistance . The term of resistor had been introduced a certain time into the programs of French State education, it was withdrawn from it thereafter.

In any rigor no dipole applies exactly the law of Ohm. The ohmic driver is thus more a model making it possible to describe the real dipoles. For example, the resistance of a metal driver to a given temperature is well approached by the relation:

R = R_0 (1 + \ theta + B {\ theta} ^2 has) \,

with

R_0 \,

a hypothetical ohmic driver modelling the behavior of the driver thermostated perfectly at the temperature of 0°K and

\ theta \,

the temperature in K.

Laws of electrokinetic

Expression of the power

The consumption by an ohmic driver of resistance $R \,$ can be written

P = {R \ cdot I^2} = \ frac {U^2} {R}

with:

$I \,$ the current which crosses indeed the dipole
$U \,$ the tension indeed at the boundaries of the dipole, the latter can be different from the tension delivered by the generator.

$P \,$ is expressed in Watt.

Equivalent resistances

The laws known as of associations of resistance apply in any rigor only to ohmic drivers

in series:

\ R_ {eq} = R_1 + R_2 \,

in derivation:

\ frac {1} {R_ {\ rm eq}} = \ frac {1} {R_1} + \ frac {1} {R_2} \ Leftrightarrow R_ {\ rm eq} = \ frac {R_1. R_2} {R_1 + R_2} \,

See too

Internal bonds

Resistance (component)
electric Conductivity
electric Conduction in crystalline oxides
Impedance
Semiconductor
Law of Ohm
Effect of skin
Thermister = resistances depending on the temperature.

; Simple assemblies with resistances:

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