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

Let*T* be the temperature of the wire. Let *α* be the thermal coefficient of resistance. Let* e* be the charge on an electron. Let there be* n *electrons per unit volume of the conductor. Let *m* be mass of the wire. Let **M** be molar mass of the conductor. Let** d** be volume density of the conductor.

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

Let us say that there are* f *free electrons in each atom.

*I *= current flowing across the wire = number of charged particles * their charge crossing a particular cross section P' of wire in one second.

Suppose an electron travels (on an average)*x *meters in* t *seconds. Then average drift speed *v *of an electron is* x/t *meters/sec.

Let us take volume* x * A *to one side of* P'.* All the electrons in the volume *x * A *will cross P' in *t *seconds.

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 = ρ₀ (1+αT) t*aking into account the thermal

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) ] *

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