Resistivity and Laws of Resistance and Unit of Resistivity

Hi friends, this post is about the laws of resistance and resistivity.

Laws of Resistance

A conductor is anything that can conduct electricity. Every conductor offers certain resistance to the electric current through it. This resistance depends on four factors. These are the length,  cross-section, material, and temperature of the substance.

  1. The resistance (R) of a conductor is directly proportional to the length (L) of the conductor.
  2. R is inversely proportional to the cross-section (A) of the conductor.
  3. It depends on the material of the conductor.
  4. Also, the resistance also depends on the temperature of the conductor.  

Resistivity

From the above statements, we can write  

Where ρ is the constant of proportionality and we know it as resistivity.

Now if we put 1 meter at the place of the length (L) and 1 meter2 at the place of cross-sectional area (A), we get,

Hence ρ is the resistance of a conductor of unit length and unit cross-section.

The shape of a conductor of unit length and unit cross-section may be either cylindrical or cubical.  

If it is cylindrical then we can say the resistivity is the resistance between two plane faces. 

If it is cubical, then the resistivity is the resistance between two opposite faces of the cube.  

Resistivity

The resistance of the conductor of unit length and the unit cross-section is not the same for all conductors. It varies with the material of the conductor. In other words, it depends on the material of the conductor.  More precisely the resistivity is a property of material rather than the property of the conductor itself.

Effects of Temperature on Resistivity

Two factors affect the resistance of a substance. 

  1. The number of free electrons present in the substance.  
  2. Mean free paths through which these free electrons travel.  

Both of these factors depend on the temperature of the substance. Hence the resistance of the substance depends on the temperature. Similarly, the resistance of two opposite faces of a cube of unit volume also depends on the temperature. So we can say the resistivity depends on the temperature. In the metal, the resistance increases with an increase in the temperature. Due to the increased interatomic vibrations at a higher temperature, the effective free mean paths reduce. Hence, the resistivity increases. But is a semiconductor, the number of free electrons increases with the increasing temperature. Hence the resistivity of semiconductors decreases with increasing temperature. So, we have to mention the temperature when we talk about the resistivity of any substance.

Unit of Resistivity

As per laws of resistance, we can write the expression of resistivity as

Now, if we put a unit of length, a unit of cross-sectional area and the unit of resistance in that expression, we get the unit of resistivity.  

Hence the unit of resistivity is ohm-meter or Ω – m (in MKS System).  

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