**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 cross-section 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 = n e A v _{d}**

**Here A is cross-sectional area of cylinder and n e is charge density of charge carriers (e.g. electrons).**

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

**e = charge on electron.**

**v _{d} = drift velocity **

**Current density( J ^{→}):**

**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 = n e v _{d}**

**In vector form, I = J ^{→ }. A^{→ }**

__Electrical Resistance & Ohm’s Law__

__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 = R = 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**

**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) **

** , which has units of mho/m**

**Variation of resistance with temperature**

** ; Where alpha is temperature coefficient .**