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Could you please explain me the equation of drift velocity in Electric current???

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Thanks in advance

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where is the current density, is charge density (in units C/m3), and is the drift velocity, and where is the electron mobility (in units (m^2)/V.s) and is the electric field (in units V/m)...

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We find the expression for calculating the drift speed of electrons along the length of a conductor, across the ends of which, a potential difference is applied. The expression involves constants related to the material of the conductor.

See the 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 applied 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.

ρ = Resistivity of the conductor

Then,

I = current flowing across the wire in unit time

= (number of electrons crossing any cross section P' of wire in 1 sec.)

* (charge of an electron)

Let*v = Average drift speed.* So an electron travels v t meters in t seconds.

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

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

=> I = n A e v

=>*v = I / (n A e)* --- (1)

Resistance of a conductor = R = ρ L / A

Current = I = V / R = V / [ ρ L / A ] =*V A / [ ρ L ] * -- (2)

Molar volume = Molar mass / density = M kg/mole / d = M / d m^3/mole

n = electron density = number of electrons in a mole / volume of a mole

= (f free electrons per atom * N atoms/mole) / molar volume

=>*n = N f / (M / d) = N f d / M* --- (3)

So drift velocity = v = I / n A e = [V A / (ρ L) ] / [ (N f d / M) A e ]

* v = V M / [ N f d e ρ L ] * ---- (4)

Resistivity of a conductor = ρ = ρ₀ (1+αT) taking into account the thermal increase of resistance.

=>*v = V M / [ N f d e ρ₀ L (1+αT) ] * -- (5)

See the 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 applied 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.

ρ = Resistivity of the conductor

Then,

I = current flowing across the wire in unit time

= (number of electrons crossing any cross section P' of wire in 1 sec.)

* (charge of an electron)

Let

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

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

=> I = n A e v

=>

Resistance of a conductor = R = ρ L / A

Current = I = V / R = V / [ ρ L / A ] =

Molar volume = Molar mass / density = M kg/mole / d = M / d m^3/mole

n = electron density = number of electrons in a mole / volume of a mole

= (f free electrons per atom * N atoms/mole) / molar volume

=>

So drift velocity = v = I / n A e = [V A / (ρ L) ] / [ (N f d / M) A e ]

Resistivity of a conductor = ρ = ρ₀ (1+αT) taking into account the thermal increase of resistance.

=>