Question

Aluminum wire has radius 0.25mm and length 15m .If resistance of wire is 10ohm ,find the resistivity of the wire

Answer 1

Answer:

1.306 × 10⁻⁷ Ω m

Explanation:

Given :

Radius r = 0.25 mm = 0.25 × 10⁻³ m

= > Area of cross section = 0.25² × 10⁻⁶ π m²

Length L = 15 m

Resistance R = 10 Ω

We are asked to find resistivity  ρ :

We know :

R = ρ L / A

= > ρ = R A / L

= > ρ = ( 10 × 0.25² × 10⁻⁶ π ) / 15 Ω m

= > ρ = ( 10 × 0.0625 × 10⁻⁶ π ) / 15 Ω m

= > ρ = (  0.625 × 10⁻⁶ π ) / 15 Ω m

= > ρ = (  0.0416 × 10⁻⁶ π ) Ω m

= > ρ = 0.1306 × 10⁻⁶  Ω m

= >  ρ =  1.306 × 10⁻⁷ Ω m

Therefore , the resistivity of the wire is 1.306 × 10⁻⁷ Ω m.