Resistance of metal wire of length 1 m is 26 Ω at 20°C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature? Using Table 12.2, predict the material of the wire.

Example 12.5 Resistance of metal wire of length 1 m is 26 Ω at 20°C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature? Using Table 12.2, predict the material of the wire.
Resistance of wire = 26 Ω
Length of the wire = 1 m
Diameter of the wire = 0.3 mm
= 0.3/1000 m
= 3/10000 m
= 3 × 10−4 m
Radius of the wire = r = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2
= (3 × 〖10〗^(−4))/2 m
Area of cross-section = A = 𝜋 r2
= 22/7 × (3/2×〖10〗^(−4) )^2
= 22/7 × (3/2)^2× (10−4)2
= 22/7 × 9/4 × 10−8
= (11 × 9 )/(7 × 2) × 10−8
= 99/14 × 10−8 m2
We need to find resistivity (𝜌)
We know that
R =𝜌 𝑙/𝐴
R 𝐴/𝑙 =𝜌
𝜌 = R 𝐴/𝑙
𝜌 = 26 × 99/14 × 10−8 × 1/1
𝜌 = (13 × 99 × 〖10〗^(−8))/7
𝜌 = (1287 × 〖10〗^(−8))/7
𝜌 = 183.85 × 10−8
𝜌 = 1.8385 × 100 × 10−8 Ω m
𝜌 = 1.8385 × 10−6 Ω m
= 1.84 × 10−6 Ω m
Resistivity of metal is 1.84 × 10−6 Ω m
The metal is manganese.

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.