Q: How can you calculate the Resistivity of the material of a wire?
Ans: Resistance’s value is different for different wires.
1. The resistance R of the wire is directly proportional to the length of the wire i.e.,
R ∝ L ....... (i)
It means if we double the length of the wire, its resistance will also be doubled, and if its length is halved, its resistance would become one half.
2. The resistance R of the wire is inversely proportional to the area of cross section A of the wire i.e,
R ∝ 1/A ....... (ii)
It means that a thick wire would have smaller resistance than a thin wire.
After combining the two equations, we get
R ∝ L/A
R = ρ L/A........ (iii)
If we we know the
Specific resistance ‘ρ’ ,
Length of wire ‘L’
Area of cross section ‘A’
then we can calculate resistance of wire
Area of cross section ‘A’ can be calculated by using Micrometer screwguage or Digital Vernier Calliper.
where ‘ρ’ is the constant of proportionality, known as specific resistance. Its value depends upon the nature of conductor i.e., copper, iron, tin, and silver would each have a different values of ‘ρ’.
If we put L = 1 m, and A = 1 m2 in Eq. (14.5), then R = ρ, i.e., the resistance of one metre cube of a substance is equal to its specific resistance. The unit of ‘ρ’ is ohm-metre (Ω m).
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