ELECTRICITY

ELECTRIC CURRENT

Electric current is defined as the rate at which charge flows through a surface (the cross section of a wire, for example).

Mathematically,

Charge = current × time

Q = I × t

Therefore, current = charge/time

I = Q/t

THE COULOMB

The coulomb is that charge passing a point in a circuit when there is a current of one ampere for one seconds.

QUANTIZATION OF A CHARGE

Quantization of charge is a statement that the smallest practical amount of charge one can perceive is the charge of an electron. Hence any practical charge present must be the integral multiple of charge of electron.

Hence, 

Q = ne

MEAN DRIFT VELOCITY

Charged particles do not travel in a straight line through a conductor, because they collide with other particles in the material. We therefore use the average speed the particle travels at along the conductor. This is called the drift velocity.

Drift velocity is defined as the average velocity with which a free electron (in addition to its random motion) gets drifted under the influence of an external electric field applied to the conductor.

To deduce an expression for the current flowing through the conductor above,

the number of charge carriers in a length x of the of the conductor = nAx

the amount of charge that leaves this volume in time, t = nAxq

the time interval, t = x/v

recall that the current I = charge/time

therefore,

I = nAxq/x/v

I = nAvq

Where:

I = current (amps, A)

v = drift velocity (m/s)

A = cross-sectional area of the conductor (m²)

n = charge density (m-3) This is the number of charge carriers that can move per m³

q = charge on each charge carrier (coulombs, c)

Example

1.    The average drift speed in a metal wire is 6.5 × 10^-4 m s^-1 when the current is 0.80 A. The diameter of the wire is 0.50 mm. Calculate the number of free electrons per unit volume in the wire.