Resistance - From Basics to Higher

What is resistance?

Electrical Resistance
Resistance is defined as ‘‘The property of the electric circuit which opposes the flow of current’’.
Resistance is measured in ohms, symbolized by the Greek letter omega (Ω). Ohms are named after George Simon Ohm (1784-1854), a German physicist who studied the relationship between voltage, current and resistance. He is credited for formulating Ohm's Law.

Some materials have an abundance of free electrons, which require a low pressure to move them from atom to atom, and establish a high current. Such materials are known as good conductors. Eg silver, copper, gold and aluminum.

Other materials have few free electrons. In these the same electric pressure can move only a few electrons from atom to atom, establishing a low current. These are considered poor conductors. Examples: Rubber, paper, glass, wood and plastic.

 The progressive motion of free electrons is hindered in all materials, because they collide with atoms of the substance used. The opposition to flow of electrons (due to bonds between protons and electrons,  as well as to collisions) is called electrical resistance (R).

The practical unit of electric resistance is ohm (Ω). It (ohm) is defined as the resistance in which a constant current of 1 ampere generates heat at the rate of 1 watt. One volt applied across 1 ohm will produce 1 ampere.
1 Mega-ohm (M Ω) = 106 Ω
1 kilo-ohm (k Ω) = 103 Ω
1 milli-ohm (m Ω) = 10–3 Ω
1 micro-ohm (μ Ω) = 10–6 Ω 

Laws of Resistance

The resistance of a conductor, such as a wire, of uniform cross-section depends on the following
factors :
(i) Length (L)......Varies directly as its length, L.
(ii) Cross-section (A)......Varies inversely as the cross-section, A of the conductor.
(iii) Nature of the material.
(iv) Temperature of the conductor.
Neglecting the last factor (iv) for the time being, we can say that
R ∝ L/A
or R = ρL/A      ...(1)

where, L = Length of the conductor,
           A = Area of cross-section of the conductor, and
           ρ = Constant depending on the nature of the material of the conductor and is known as
its specific resistance or resistivity.

If in eqn. (1), L = 1 metre, A = 1 metre, then
R = ρ.
Hence specific resistance or resistivity of a
material may be defined as ‘‘the resistance between
the opposite faces of a metre cube of that material ’’

Unit of resistivity. From eqn. (1), we have
ρ =RA/L
In S.I. system of units
ρ = R ohm Am^2/Lm
        RA/L ohm-m
Hence the unit of resistivity is ohm-metre (Ω-m).

Conductance and Conductivity

Conductance (G) is reciprocal of resistance. Whereas resistance of a conductor measures the
opposition which it offers to the flow of current, the conductance measures the inducement which it offers to its flow.
 R =ρL/A
or G=1/ρ* A/L = σA/L
where σ is called the conductivity or specific conductance of a conductor. The unit of conductance
is siemens (S). Earlier, this unit was called mho.
It is seen from the above equation that the conductivity of a material is given by
σ=GL/A =G siemens*L metre/A metre^2 = GL/A  siemens/metre
Hence, the unit of conductivity is siemens/metre (S/m).

Effect of Temperature on Resistance

The effect of rise in temperature is :
(i) to increase the resistance of pure metals. The increase is large and fairly regular for normal
ranges of temperature. The temperature/resistance graph is a straight line. As
would be presently clarified, metals have a positive temperature co-efficient of resistance.
(ii) to increase the resistance of alloys, though in their case, the increase is relatively small and
irregular. For some high-resistance alloys like Eureka (60% Cu and 40% Ni) and manganin,
the increase in resistance is (or can be made) negligible over a considerable range of
temperature.
(iii) to decrease the resistance of electrolytes, insulators (such as paper, rubber, glass, mica etc.)
and partial conductors such as carbon. Hence, insulators are said to possess a negative
temperature-coefficient of resistance.

 Ohm's Law (click here)