Question

The resistance of wire of length 31.4 and diameter 1mm is 20 ohms find the resistivity of the material of the wire

Answer 1

Given

Resistance of the wire R = 20 Ω

Length of the wire L= 31.4 m

Diameter of the wire d = 1 mm

Radius of wire r = 0.5 ×10⁻³ m

Now we know

Resistance R = ρ(L/A)

ρ=RA/L = (20×π×0.5²)/31.4

ρ = 0.5

Answer 2

Solution 5 : Data : l = 31.4 m, d = 1mm = 1× 10 - 3 m

∴ r = d/2 = (1× 10-3m)/2 = 5× 10-4 m , R = 20 Ω , ρ = ?

R = ρ (l/A) = ρ (l/π r2)

∴ ρ = (Rπr2)/l

∴ ρ = 20Ω × 3.14 × (5× 10-4 m)2 / 31.4m

∴ ρ = 5× 10-7Ω .m

The resistivity of the material of the wire = 5 × 10-7 Ω m.