Question

Resistance of a metal wire of length 1 m is 26 ohm at 20degree C. if the diameter of the wire is 0.3mm what will be the resistivity of the metal at that temperature?

Answer 1

Resistance , R = 26Ω
Length of wire , L = 1m
diameter of circular part of wire ,d = 0.3mm = 0.3 × 10⁻³m
so, base area of wire , A = πr² = πd²/4 [ ∵d = 2r]
= 3.14 × (0.3 × 10⁻³)²/4m²
= 3.14 × 9 × 10⁻⁸/4 m²
= 28.26/4 × 10⁻⁸ m² = 7.06 × 10⁻⁸ m²

Now, use formula,
R = ρL/A
Here, R is the resistance, ρ is the resistivity , L is the length of wire and A is the base area of it .
So , ρ = RA/L = 26Ω × 7.06 × 10⁻⁸m²/1m
ρ = 1.8356 × 10⁻⁶ Ωm

Hence, resistivity is 1.8356 × 10⁻⁶ Ωm at 20°C

Answer 2

Resistance , R = 26Ω Length of wire , L = 1m diameter of circular part of wire ,d = 0.3mm = 0.3 × 10⁻³m

so, base area of wire , A = πr² = πd²/4

[ ∵d = 2r] = 3.14 × (0.3 × 10⁻³)²/4m²= 3.14 × 9 × 10⁻⁸/4 m² = 28.26/4 × 10⁻⁸ m² = 7.06 × 10⁻⁸ m²

Now, use formula,

R = ρL/A Here, R is the resistance, ρ is the resistivity , L is the length of wire and A is the base area of it .

So , ρ = RA/L = 26Ω × 7.06 × 10⁻⁸m²/1mρ = 1.8356 × 10⁻⁶ Ωm Hence, resistivity is 1.8356 × 10⁻⁶ Ωm at 20°C