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 vd
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.
vd = 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 vd
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.
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 .