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The following is my solution. see picture enclosed.

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

A = cross section of a conductor wire of length L.

ρ = resistivity of material of wire.

I = current flow

V = voltage difference across the conductor.

R = resistance of wire.

T = temperature of the wire.

α = Linear thermal coefficient of resistance.

e = charge on an electron.

n = number of electrons per unit volume of the conductor.

m = mass of the wire.

M = molar mass of the conductor.

d = volume density of the conductor.

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

f = number of free electrons in each atom.

Then,

I = current flowing across the wire

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

Let

Let us take volume (vt * A) on one side of P'. All the electrons in the volume (vt * A) will cross P' to the other side in t seconds.

So the charge crossing P' in one second is = current = vt * A * n * e / t

I = n A e v or v = I / (n A e)

Resistivity of a conductor = ρ = ρ₀ (1+αT)

taking 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 f / (M/d) = N f d / M

So

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

A = cross section of a conductor wire of length L.

ρ = resistivity of material of wire.

I = current flow

V = voltage difference across the conductor.

R = resistance of wire.

T = temperature of the wire.

α = Linear thermal coefficient of resistance.

e = charge on an electron.

n = number of electrons per unit volume of the conductor.

m = mass of the wire.

M = molar mass of the conductor.

d = volume density of the conductor.

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

f = number of free electrons in each atom.

Then,

I = current flowing across the wire

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

Let

**v = Average drift speed is v meters/sec**. An electron travels (on an average) vt meters in t seconds.Let us take volume (vt * A) on one side of P'. All the electrons in the volume (vt * A) will cross P' to the other side in t seconds.

So the charge crossing P' in one second is = current = vt * A * n * e / t

I = n A e v or v = I / (n A e)

Resistivity of a conductor = ρ = ρ₀ (1+αT)

taking 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)]

**= electron density = N atoms * f free electrons per atom / molar volume***n*= N f / (M/d) = N f d / M

So

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