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Drift speed of electrons is the average speed of electrons over the length of a conductor when a potential difference is applied to the ends of the conductor. The electrons move under the influence of electric and magnetic effects of atoms and particles inside conductor.

Let

Let

Let us say that there are

Suppose an electron travels (on an average)

Let us take volume

So the charge crossing P' in one second is

Resistivity of a conductor =

increase of resistance.

Resistance of a conductor =

current

n = electron density = N atoms * f free electrons per atom / molar volume

So

Let

**be cross section of a conductor wire of length***A**. Let its resistivity be***L****Let a current***ρ.***flow through it. Let***I**be voltage difference across the conductor.***V***be the resistance of wire.***R**Let

**be the temperature of the wire. Let***T***be the thermal coefficient of resistance. Let***α***be the charge on an electron. Let there be***e***electrons per unit volume of the conductor. Let***n***be mass of the wire. Let***m**be molar mass of the conductor. Let***M***be volume density of the conductor.***d****= Avogadro number (number of atoms in a mole of the conductor).***N*Let us say that there are

**free electrons in each atom.***f***= current flowing across the wire = number of charged particles * their charge crossing a particular cross section P' of wire in one second.***I*Suppose an electron travels (on an average)

**meters in***x***seconds. Then average drift speed***t***of an electron is***v***meters/sec.***x/t*Let us take volume

**to one side of***x * A***All the electrons in the volume***P'.***will cross P' in***x * A***seconds.***t*So the charge crossing P' in one second is

*= I = x*A*n * e / t**I = n A e v or v = I / (n A e)*Resistivity of a conductor =

**aking into account the thermal***ρ = ρ₀ (1+αT) t*increase of resistance.

Resistance of a conductor =

*R = ρL / A = ρ₀ (1+α T) L / A*current

*= I = V/R = V / [ ρ₀ L (1+α T) L / A ] = V A / [ ρ₀ L (1+α T)]*n = electron density = N atoms * f free electrons per atom / molar volume

*= N f / (M/d) = N f d / M*So

**=**__drift velocity__*v = I / n A e = {V A / [ρ₀ L (1+αT) ] } / (N f d /M) (A) e**v = V M / N f d e [ρ₀ L (1+αT) ]*