Electrical resistance

in electricity, the resistance term indicates various things, which remain however dependant :
a physical property : the aptitude of a conducting material to slow down the passage of the electric current
an electric dipole which is used to reduce the intensity of the current or to produce heat
a mathematical model which respects the law of Ohm ideally, baptized conducting ohmic and which makes it possible to model the real dipoles
an electronics component designed to approach in a very satisfactory way the law of Ohm in a broad beach of use.
The physical property
It is the property of a material to slow down the passage of an electric current. It is often indicated by the letter R and its measuring unit is the ohm. It is related to the concepts of resistivity and electric conductivity. For a homogeneous thread-like driver, at a given temperature, there exists a relation making it possible to calculate its resistance according to the material which constitutes it and of its dimensions :
R = ρ * l ⁄ S = l ⁄ γ * S
ρ being resistivity out of ohmmeter (Ω·m)
l : the length in meters (m)
S : the section in square meter (m²)
γ conductivity in mho per meter (S ⁄ m)
Resistance is also responsible for a dissipation of energy in the form of heat. 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) but often inevitable.
One of the main issues for the engineers is that conductivity, and its reverse, the resistivity, strongly depend on the temperature. 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 : Power, in Watt, dissipated by Joule effect by a D.C. current
I : intensity of the current, in amps, crossing resistance
R : resistance, in ohms
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 8 (insulating perfect).
It is an electronics component which makes it possible to voluntarily increase the resistance 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 resistivity with the temperature of the dipole.
One distinguishes:
Resistances of power of which the goal is to produce heat
Fixed resistances of which the goal is to obtain, in an electronic assembly, perfectly given potentials or currents in certain places of the circuit. One then indicates by a code of color his value of resistance and the precision of this value. These resistances are the only ones with truly checking the law 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, potentiometer or transistor CMOS
The dipoles whose resistance varies with a physical size: the temperature, illumination, forces applied
The ohmic driver
Characteristic of an ideal resistance : Curve of I = f(U) = U ⁄ R
An ohmic driver is an electronics component called also resistance and which checks the law of Ohm :
U = R * I with
I : intensity of the current, in amps, crossing resistance
U : the tension, in volts, between its terminals
The curve representative of the characteristic of a resistance is a line passing by the origin of the reference mark.
The terms of pure resistance or ideal resistance are sometimes used. 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 the law of Ohm exactly. 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 = R0 (1 + aθ + bθ²) with R0 a hypothetical ohmic driver modelling the behavior of the driver perfectly thermostated at the temperature of 0 K and θ the temperature in K.
Laws of electrokinetic
Expression of the consumption
The consumption by an ohmic driver of resistance R can be calculated in two manners :
Either one knows U, the effective value of the tension actually applied at the boundaries of the dipole the latter can be different from the tension delivered by the generator
P = U² ⁄ R
Maybe, more rarely, one knows I, the effective value of the intensity of the current which crosses indeed the dipole
P = R * I²
Equivalent resistances
The laws known as of associations of resistances apply in any rigor only to ohmic drivers :
in series :
Req = R1 + R2
in parallel
1 ⁄ Req = 1 ⁄ R1 + 1 ⁄ R2

Register the values in the boxes and validate. The decimal symbol is the point!
Calculation of the total resistance of a grouping of resistances in parallel. R total = 1 ⁄ R = 1 ⁄ R1+1 ⁄ R2
Form two resistances in parallel.
 Resistance n°1 = Resistance n°2 = Ω Ω
 The resistance of the grouping is :Ω

Form three resistances in parallel.
 Resistance n°1 = Resistance n°2 = Resistance n°3 = Ω Ω Ω
 The resistance of the grouping is : Ω

Form four resistances in parallel.
 Resistance n°1 = Resistance n°2 = Resistance n°3 = Resistance n°4 = Ω Ω Ω Ω
 The resistance of the grouping is :Ω

Form five resistances in parallel.
 Resistance n°1 = Resistance n°2 = Resistance n°3 = Resistance n°4 = Resistance n°5 = Ω Ω Ω Ω Ω
 The resistance of the grouping is :Ω

Form six resistances in parallel.
 Resistance n°1 = Resistance n°2 = Resistance n°3 = Resistance n°4 = Resistance n°5 = Resistance n°6 = Ω Ω Ω Ω Ω Ω
 The resistance of the grouping is :Ω

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