Current Electricity

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.

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

\displaystyle R = \rho \frac{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)

\displaystyle \sigma = \frac{1}{\rho} , which has units of mho/m

Variation of resistance with temperature

\displaystyle R_T = R_0 [1 + \alpha (T - T_0 )] ; Where alpha is temperature coefficient .

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