Resistivity

Resistivity Revealed: Navigating the Electrical Resistance Maze

Resistivity is a property of a material that quantifies its inherent resistance to the flow of electric current. It is denoted by the symbol ρ (rho).

Recall, from ohm’s law - V/I = R, where R is the resistance of a conductor. It is constant for a given conductor. The resistance depends on the following factors:

• Resistance(R) is directly proportional to the length (l) of the conductor- R ∝ L
• Resistance (R) is inversely proportional to the area (A) of the conductor - R ∝ 1/A

i.e. R ∝ l/A

R = ρ x l /A, Where ρ is a constant called electrical resistivity of the material of the conductor. SI unit is Ω m.

• Resistivity of conductors is very low whereas the insulators have a very high resistivity.
• Resistivity varies with Temperature.
• Alloys having higher resistivity than metals are used in electrical heating devices, like iron and toasters, tungsten is used in filament of electric bulbs and copper and aluminum are used for electrical transmission lines.
• Resistivity of Conductors < Resistivity of Alloys < Resistivity of Insulators.
• Resistivity of materials varies with temperature.

Numerical on Resistivity:

1. What will be the resistivity of a metal wire of 2 m length and 0.6 mm in diameter, if the resistance of the wire is 50 Ω.
   

   Given:

   Resistance (R) = 50 Ω, Length (l) = 2 m
   
   Diameter = 0.6 mm = 0.6 x 10⁻³ m = 6 x 10⁻⁴ m {∵ 1 mm = 10⁻³ m}
   
   Radius = 0.3 mm = 3 ×10⁻⁴ m
   
   To find Resistivity (ρ) =?
   
   Now, area of cross section of wire A = πr²
   
   = 3.14 × (3×10⁻⁴)²
   
   = 28.26 ×10⁻⁸ m²
   
   = 2.826 ×10⁻⁹ m²
   
   We know that ρ = R x A / l
   
   = 50 Ω × 2.826 × 10⁻⁹ m² / 2 m
   
   = 7.065 × 10⁻⁸ Ω m

2. The area of cross section of wire becomes half when its length is stretched to double. How the resistance of wire is affected in new condition?

       Given: The area of cross section of wire becomes half when its length is stretched to double.

       Let the area of cross section of wire = A

       Let length of wire before stretching = L

       Let Resistance of wire = R1

       After stretching of wire,

       Area of cross section = A / 2

       Length = 2 x L

       Let new Resistance = R2

       We know, R = ρ x l /A

       Thus, ratio of resistance before stretching to resistance after stretching can be given as follows:

        R1: R2 = ρ L A: ρ 2L A/2

        R1: R2 = ρ L A/ 4 ρ L A

                   = 1 : 4

Test yourself on Resistivity: