Resistivity Laws of Resistance and Unit of Resistivity

Resistivity or Coefficient of Resistance

Laws of Resistance

The resistance of any substance depends on the following factors,

1. Length of the substance.
2. Cross sectional area of the substance.
3. The nature of material of the substance.
4. 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

The resistance of a substance is directly proportional to the length of the substance. electrical resistance R of a substance is

Where L is the length of the substance.
If the length of a substance is increased, the path traveled by the electrons is also increased. If electrons travel long, they collide more and consequently the number of electrons passing through the substance becomes less; hence current through the substance is reduced. In other words, the resistance of the substance increases with increasing length of the substance. This relation is also linear.

Second Law of Resistivity

The resistance of a substance is inversely proportional to the cross-sectional area of the substance. Electrical resistance R of a substance is
Where A is the cross-sectional area of the substance.
The current through any substance depends on the numbers of electrons pass through a cross-section of substance per unit time. So, if the cross section of any substance 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 substance. For fixed voltage, more current means less electrical resistance and this relation is linear.

Resistivity

Combining these two laws we get,Where, ρ (rho) is the proportionality constant and known as resistivity or specific resistance of the material of the conductor or substance. 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 alternatively be defined as the electrical resistance between opposite faces of a cube of unit volume of that material.

Third Law of Resistivity

The resistance of a substance is directly proportional to the resistivity of the materials by which the substance is made. The resistivity of all materials is not the same. It depends on the 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 the resistivity of a 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

Temperature affects the resistance of a substance. In metals, heat causes more atomic vibrations, making it harder for electrons to move, thus increasing resistance. In nonmetals, higher temperatures break more covalent bonds, creating more free electrons and reducing resistance.

Therefore, it’s essential to specify the temperature when stating the resistance of any substance.

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.

List of Resistivity of Different Commonly Used Materials