Resistance of a conductor ∝ I (length of the conductor)
R∝I/A (area of cross - section)
Thus = pI/A (where p is resistivity)
Resistances are of three types holmic, non holmic and negative. Ohmic resistances follow ohm's law V = IR(that is V ∝I). In nonohimc resistance V is not linearly related to I. vacuum tubes and semiconductor are examples of non holmic resistances. We find dynamic resistance for a non-ohmic device. In a negative resistance device I∝ I/V.
Examples of negative resistances are tunnel diode, tutored and thruster.
Resistivity or specific resistance:- (p) is the resistance of a unit cube of a material.
P = 2m/ne2τh
Its unit is ohm-m
Conductivity:- (σ) is reciprocal of resistivity, that is, σ = 1/p its unit is (ohm-m)
Resistance depends upon:- (a) collision between electrons and electrons (b) collision between electron and core (C) interaction between electrons and lattice vibration (d) trap centers.
Alloys have higher resistance due to more trap centers. Material used to make standard resistances is margin in as it has high specific resistance and it varies negligibly with temperature.
Alloy used in making rheostats is constantan
Alloy used in heaters (press, geyser, room heaters and so on) Nichrome.
Specific resistance: - depends upon the nature of the substance. It varies directly with temperature p (T) = p0 (1 + a/T) where a is called thermal coefficient of resistivity. Resistivity varies inversely with pressure. It does not depend upon length and area of cross - section of the material.
Deliver is the best conductor followed by copper and then aluminum. Hence copper is commonly used followed by aluminum.
Conductance: - G = 1/R its unit is ohm-1 or mho or sidemen (S), superconductors have zero resistance.
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