Question

the length of a conducting wire is 50 cm and its and its radius is 0.5 mm if it's resistance is 30 ohm what is the resistivity of its material?
give me a very detailed explanation

Answer 1

R = ρL / A

ρ = RA / L
= (30 × π × (0.5 × 10^-3)^2) / (50 × 10^-2)
= 4.712 × 10^-5 Ω.m

Resistivity of its material is 4.712 × 10^-5 Ω.m

Answer 2

Given :

Length = 50 cm or 0.5 m .

Resistance = 30 Ω

Radius = 0.5 mm or 0.5 × 10⁻³ m

To find: We have to find the resistivity of material in the given question.

We would first find the area of wire,

                      ∴ Area = π r²

Area of wire  = 3.14 × 0.5 × 10⁻³ × 0.5 × 10⁻³ m²

                      = 0.785 × 10⁻⁶ m²

It is given that, Length of conducting wire is 0.5 Ωm

Now, putting the values in the formula of resistivity:

Resistivity = Resistance  ×  Area  / Length

                    ρ = R × A / L

ρ = 30 ×  0.785 × 10⁻⁶ / 0.5 Ω m

ρ  = 47.1  × 10⁻⁶  Ω m

ρ  = 4.71  × 10⁻⁵  Ω m

Therefore, resistivity of wire is 4.71 × 10⁻⁵ Ω m.