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**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.**

*Drift speed*Let

**be cross section of a conductor wire of length**

*A**Let its resistivity be*

**L.****Let a current I flow through it. Let**

*ρ.***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***lectrons per unit volume of the conductor. Let m be mass of the wire. Let*

**n e***be molar mass of the conductor. Letd be volume density of the conductor.*

**M****Avogadro number (number of atoms in a mole of the conductor).**

*N =*Let us say that there are

*ree electrons in each atom.*

**f f****= current flowing across the wire = number of charged particles * their charge crossing a particular cross section**

*I**of wire in one second.*

**P'**Suppose an electron travels (on an average) x meters in

*seconds. Then average drift speed v of an electron is x/t meters/sec.*

**t**Let us take volume

*to one side of*

**x * A***All the electrons in the volume*

**P'.***will cross*

**x * A****econds.**

*P' in t s*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 =

**ρ = ρ***taking into account the thermal*

**₀ (1+αT)**increase of resistance.

Resistance of a conductor = R = ρL / A =

**ρ**

**₀ (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 [ρ*

*₀*

*L (1+αT) ]*