Resistance and Resistivity

Resistance and Resistivity

Resistance and Resistivity, ab, abultimateguides
Resistance and Resistivity

The measure of opposition to flow of electric charge through a conductor due to continuous collisions with ionic cores (neighboring atoms) is called resistance 'R' of a conductor is the ratio between the potential difference applied across the ends of the conductor to the amount of current passing through it, provided the physical conditions of the conductor (for example temperature) do not change. Thus

Resistance = R = V / I = Volts / Ampere

To answer the queries why electric current if starts to flow after the application of potential difference consider a conductor whose ends are maintained at a constant potential difference 'V'.

An electric field (Ē) will be developed inside the conductor as given by the relation

V = E.d
This electric field € will generate an electric force Fₑ (= qE) which pushes the charge careers (electrons) through the conductor thus constituting a current I. In electrostatic equilibrium, the electric field must be zero inside the conductor but when a conductor carries a current, it is no longer in electrostatic equilibrium and free charges drift down the conductor driven by the applied electric field.

SI unit of Resistance is the ohm (Ω).

1 ohm = 1 volt / 1 ampere

R = V / I
When one-volt potential difference across a conductor causes the one-ampere current through it, the resistance of the conductor will be one ohm.

Ohm symbol is Ω.

The reciprocal of resistance is called conductance (G) of the conductor such that

G = 1 / R ⟹ G = 1 / 1ohm
G = 1 / Ω ⟹  G = Ω⁻¹
The resistivity of a conductor is the resistance per unit length per unit area of the conductor. If a conductor has length 'L' and its cross-sectional area 'A' then the resistance of the conductor will depend on its length and cross-sectional area as given by the following relation.

R ∝ L

R ∝ 1 / A


R ∝ L / A


R = ρL / A ➜ 1
In the above equation, ‘q’ is the resistivity of the conductor such that

ρ = R x A / L
In the above equation

R = V / I   Coulumb's law

Putting this value in equation 1 we have

ρ = V / I x A / L ➜ 2

ρ = V / J.L ➜ 3

In the above equation

V = E.L

E = V / L
ρ = E / J

The above equation gives the relation between resistivity and current density.

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