A wire of given material having length l and area of cross-section Ahas a resistance of 4 โฆ. What would be the resistance of another wireof the same material having length l/2 and area of cross-section 2A?

Example 12.6 A wire of given material having length l and area of cross-section A has a resistance of 4 โฆ. What would be the resistance of another wire of the same material having length l/2 and area of cross-section 2A?
We know that
Resistance of a wire = ๐ ๐/๐ด
where
๐ = resistivity of the material
l = length of the wire
A = Area of cross-section of wire
It is given that R = 4 ฮฉ
โด ๐ ๐/๐ด = 4
Now,
For the second wire
Length of the wire = ๐2 = ๐/2
Area of cross โ section = A2 = 2A
Resistivity = ๐
Finding resistance,
R2 = ๐ ๐_2/๐ด_2
R2 = ๐ (๐/2) ร 1/2๐ด
(because the material is same)
R2 = ๐๐/๐ด (1/2ร1/2)
R2 = ๐๐/๐ด (1/4)
R2 = 4 ร 1/4
R2 = 1 ฮฉ
Resistance of second wire is 1 ฮฉ

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.