The flow of electric charges is normally known as a
current. There are two types of charges. They are:
1) Positive Charges - protons
2) Negative Charges - electrons

Certain substances, known as concuctors, for instance, have free electrons in them, moving in random directions at slower speeds. If such a conductor is connected to a cell or battery, the electron absorbs energy from the cell / battery and become highly active. They, then, start moving at very high speed in a certain direction. We call it an electric current.

How do metals get free electrons?

The electrons of the atoms inside a metal are much more loosely attracted to the nuclei than those of non-metals. Therefore, when the electrons of a metal are provided with an extra dose of energy, they become highly active and break free from the atoms - and then come out of them. That's how metals get free electrons.
The electrons of insulators, on the other hand, are tightly bound to their corresponding neclei. Threfore, even if we provide them with substantial amount of energy, it is highly unlikely that they would break free from the atoms. It means, insulators do not have free electrons inside them. Therefore, they are not in a position to form electric currents, even if we connect them to batteries.

Semiconductors

In semiconductors, there are no free electrons either. However, if they are heated, the electrons in the outermost shell can come out and the substance get free electrons. Therefore, the semiconductor behaves as a conductor at high temperature; the higher the temperatue, the more free electrons it gets.

Electric charge is measured in a unit called, Coublomb(C).

Charge of an electron = 1.6 X 10^-19C

Electric Current(I)

The amount of charge that goes past a point in a circuit in a unit time is called the current.

I = Q / t

Units: I = Coulomb / seconds = Cs^-1 = Amp(A)

E.g.1

The current through a conductor is 2A. Find the charge that passes through it in an hour.

I = Q / t
2 = Q / 1*3600 => Q = 7200C.

E.g.2

The number of electrons that pass through a certain point in a metal is 20 X 10⁴ in 16 seconds. Find the current.

I = Q / t
Total charge = 20 X 10⁴ * 1.6 X 10^-19 = 3.2 X 10^-14C
So, I = 3.2 X 10^-14C / 16
I = 2.0 X 10^-15A.

Resistance of a wire

The resistance of a wire depends on two three factors. They are,
1) length
2) cross sectional area



The longer the wire, the greater the resistane.
The thicker the wire, the less the resistance.

R ∝ l
   ∝ 1/A
R = K l/A
K = ρ = resistivity

So, R = ρ l/A

Definition of Resistivity - ρ

The resistance of a wire with unit cross sectional area and unit length is called the resistivity of the subsance of the wire.

Units

ρ = RA/l = Ωm²/m = Ωm

The following table shows the resistivity of some metals.

Metal	Resistivity - Ωm
Silver	1.59x10-8
Nickel	6.99x10-7
Iron	1.0x10-7
Copper	1.68x10-8
Lead	2.2x10-7
Tungsten	5.69x10-8

E.g.

1) The copper wire that connects the lightning conductor to the ground, is a thick one. It reduces the resistance so that the massive electric current in the event of a thunder strike passes through to the ground quickly.
2) The heating element in a hair dryer is long and thin - an arrangement to increase the resistance which in turn increases the rate of heat generation.

E.g.1

The dimensions of a metal cuboid are 6cm, 4cm and 2cm respectively. Find its resistance, if the resistivity is 1.2 X 10^-8Ωm and the current enters throgh the smallest surface.
R = ρl/A
A = 8 x 10^-4m²
l= 6 x 10^-2m
R = 1.2 X 10^-8 x 6 x 10^-2 / 8 x 10^-4
R = 9 X 10^-5Ω

E.g.2

The radius of a wire is 2cm and the length is 8cm. If the resistivity is 3x10^-6

, find the resistance of the wire.

A = πr² = 3.142*2²*10^-4 = 12.562*10^-4
R = ρl/A = 3X10^-6*8*10^-2/12.562*10^-4 = 1.9x^-4Ω.

E.g.3

The resistance of a wire is 4Ω. It is folded up and then twisted in the middle. What is its new resistance?

When it is folded up and then twisted, the cross sectional area gets doubled and length gets halved.
So, 4 = ρl/A for the first wire
R = ρ(l/2)/2A for the second wire
4/R = 4
R = 1Ω.