ONLINE ELECTRICAL ENGINEERING STUDY SITE

# Resistivity and Laws of Resistance

## Resistivity or Coefficient of Resistance

Resistivity or Coefficient of Resistance is a property of substance, due to which the substance offers opposition to the flow of current through it. Resistivity or Coefficient of Resistance of any substance can easily be calculated from the formula called Laws of Resistance.

## Laws of Resistance

The resistance of any substance depends on the following factors,
1. The resistance of a substance depends on its length.
2. The resistance of a substance depends on its cross sectional area.
3. The resistance of a substance depends on the nature of material of the substance.
4. The resistance of a substance depends on the temperature of the substance.

There are mainly four (4) laws of resistance from which the resistivity or specific resistance of any substance can easily be determined.

#### First Law of Resistivity

If the length of the conductor is increased, the path traveled by the electrons is also increased. If electrons travel long, they collide more and consequently the numbers of electrons passing through the conductor become less; hence current through the conductor is reduced. In other word, resistance of the conductor increases with increasing length of the conductor. This relation is also linear. Electrical resistance R of a conductor or wire is Where, L is the length of the conductor.

#### Second Law of Resistivity

The current through any conductor depends on the numbers of electrons pass through a cross-section of conductor per unit time. So, if cross section of any conductor is larger then more electrons can cross the cross section. Passing of more electrons through a cross-section per unit time causes more current through the conductor. For fixed voltage, more current means less electrical resistance and this relation is linear. So it can be concluded like that, resistance of any conductor is inversely proportional to its cross-sectional area. Electrical resistance R of a conductor or wire is Where, A is the cross-sectional area of the conductor.
Combining these two laws we get,
Electrical resistance R of a conductor or wire is Where, ρ (rho) is the proportionality constant and known as resistivity or specific resistance of the material of the conductor or wire. Now if we put, l = 1 and a = 1 in the equation, We get, R = ρ. That means resistance of a material of unit length having unit cross - sectional area is equal to its resistivity or specific resistance.
Resistivity of a material can be alliteratively defined as the electrical resistance between opposite faces of a unit cube of that material.

#### Third Law of Resistivity

The resistivity of materials are not same. It depends on number of free electrons, and size of the atoms of the materials, types of bonding in the materials and many other factors of the material structures. If resistivity of material is high, the resistance offered by the substance made by this material is high and vice versa. This relation is also linear.

#### Fourth Law of Resistivity

The temperature of the substance also affects the resistance offered by the substance. This is because, the heat energy causes more inter-atomic vibration in the metal, and hence electrons get more obstruction during drifting from lower potential end to higher potential end. Hence, in metallic substance, resistance increases with increasing temperature. If the substance in non metallic, with increasing temperature, the more covalent bonds are broken, these cause more free electrons in the material. Hence, resistance is decreased with increase in temperature.
That is why, mentioning resistance of any substance without its mentioning its temperature is meaning less.

### Unit of Resistivity

The unit of resistivity can be easily determined form its equation The unit of resistivity is Ω-m in MKS system and Ω-cm in CGS system and
1 Ω-m = 100 Ω-cm.

### Temperature Coefficient of Resistance and Inferred Zero Resistance Temperature

 Materials Resistivity in μ Ω-cm at 20oC Temperature Coefficient of Resistance in Ω per oC at 20oC Inferred Zerro Resistance Temperature in oC Aluminium 2.82 0.0039 - 236 Brass 6 to 8 0.0020 - 480 Carbon 3k to 7k 0.00005 Constantan 49 0.000008 -125000 Copper 1.72 0.00393 - 234.5 Gold 2.44 0.0034 - 274 Iron 12.0 0.005 - 180 Lead 22.0 0.0039 - 236 Manganin 42 to 74 0.00003 - 236 Mercury 96 0.00089 - 1100 Nickel 7.8 0.006 - 147 Silver 1.6 0.0038 - 310 Tungsten 5.51 0.0045 - 200 Zinc 6.3 0.004 - 230