**Electric Current :**

Electric current is the rate of flow of electric charge across any cross-section of a conductor. current flowing I = dQ/dt

where dQ is the quantity of electric charge flowing through S in time dt.

Mechanism of current flow in metallic conductors

**When an external potential difference is applied across a metallic conductor then an electric field is set up within the conductor.**

Applied electric field → Force on electrons → drift of electrons

Due to the externally applied electric field electrons drift with an average velocity called drift velocity.

This causes an electric current total charge crossing a cross-section in one second is equal to

**I = neAv _{d}**

Here Av_{d} is the volume of a cylinder of cross-section A length v_{d} and ne is charge density of charge carriers (e.g. electrons).

**Note:** n = no. of electrons per unit volume

e = charge on electron.

**Current density:**

Current density at a point, within a conductor, is the current through a unit area of the conductor, around that point, provided the area is perpendicular to the direction of flow of current at that point.

**J = I / A = nev _{d}**

In vector form, I = J

^{→ }. A

^{→ }

__Electrical Resistance & Ohm’s Law__

“The potential difference across a conductor is directly proportional to the current flowing through it at constant temperature”.

This fact is known as **Ohm’s** law. It is established by experiment.

Mathematically,

V ∝ I

V / I = Constant.

Obviously, this constant is what we call resistance.

If l be the length and A be the cross-sectional area of a wire the resistance ‘R’ is given by

**R = ρ(l/A) ;**

Where ρ is a constant which depends upon the material of the wire , it is called the resistivity of the material and has the unit ohm-meter.

The inverse of resistivity is known as conductivity.

σ = 1/ρ, which has units of mho/m