Laws Of Resistance

The resistance of a material depends upon the fallowing four factors, which are called laws of resistance.

1st law of resistance

The resistance of conductor is directly proportional to the length of the conductor. Greater is the length of conductor greater will be the resistance, similarly smaller is the length, and smaller will be the resistance of the conductor.

2nd law of resistance

The resistance of the conductor is inversely proportional to the cross sectional area of the conductor. Greater is the cross sectional area smaller will be the resistance and when smaller is cross sectional area greater will be the resistance

3rd law of resistance

The resistance of the conductor depends upon the nature of the conductor. Two wire having the same gauges, but different material will have different resistance.

4th law of resistance

The resistance of the conductor depends upon the temperature of it. Resistance of metallic conductor increase with increase in temperature of the conductor.

Taking in to consideration 1st three laws and neglecting 4th law for movement, we have

R ∝ L ...........(eq. 1)

R ∝ l / A ...........(eq. 2)

From equation 1 and 2 we get

Laws of Resistance Formula 1

Laws of Resistance Formula 2

Where ρ is called rho .it is a constant and is known as resistivity or specific resistance of a material.

Laws of Resistance Formula 3

Its unit is Ωm.

SPECIFIC RESISTANCE

It is the resistance of opposite faces of a unit cube of a material.

RESISTIVITY

The resistivity of a material is based on the resistance of define volume of that material the letter symbol for resistivity is ϱ (the Greek letter Rho).

Resistivity may also be called specific resistance. Table list the resistivity in ohm-centimetre (Ω.cm). It also lists values in uints of circular mil-ohms per foot (cmil-Ω/ft) for the conducotr group.

Resistivity of Selected Electrical Materials
Material ϱ (resistivity) at 20o C
Ω.cm cmil Ω/ft
Conductors
Silver 1.65 X 10-6 9.9
Copper 1.72 X 10-6 10.37
Gold 2.44 X 10-6 14.7
Aluminum 2.83 X 10-6 17
Tungsten 5.49 X 10-6 33
Nickel 7.81 X 10-6 47
Iron 1.23 X 10-5 74
Constantan 4.90 X 10-5 295
Nichrome 9.97 X 10-5 600
Semiconductors
Carbon 3.49 X 10-3  
Germanium 4.70 X 101  
Silicon 6.40 X 104  
Insulators
Polyvinylchloride >1010  
Mica >1012  
Teflon >1015  
Quartz > 1017  

Specific resistance can be derived from the following relations of the resistance dependence factors.

1. LENGTH

Resistacne is directly proportional to the length of conductor.

R ∝ L ---------1

2. AREA

Resistance is inversily proportional to the area of conductor.

R ∝ 1/A ----------2

by combining 1 and 2

R ∝ L/A

R = ϱ L/A

Where ϱ (Rho) is constant for the material called its specific resistance or resistivity.

"The Specific resistance of a material is the resistance of a piece of unit length and uint cross-sectional area."

OR

"It is the resistance between opposite faces of uint cube of the material."

Specific resistance is measured in Ohm-inch or Ohm-cm or Microohm-inch or Microohm-cm.