Question

The resistance of a metal wire of length 2 m is 400 at 20∘C. If the diameter of the wire is 1 mm, what will be the resistivity of the metal at that temperature?

Answer 1

Answer:

2.275 ×10⁻⁶ Ω-m

Explanation:

Resistance of a metal wire is given by:

where ρ is the resistivity, l is the length of the wire and A is the area of the cross-section.

It is given that, R = 35 Ω

length, l = 2 m

Diameter of area, d = 0.4 mm

Radius, r = 0.2 mm

Area of the wire, A = 0.13 ×10⁻⁶ m²

Thus, ρ = ( R × A)/ l = (35 Ω ×0.13 ×10⁻⁶ m²)÷2 m = 2.275 ×10⁻⁶ Ω-m

Answer 2

Answer:

1.412 × 10⁻⁶ Ωm

Explanation:

Resistance , R = 40Ω

Length of wire , L = 2m

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 = 40Ω × 7.06 × 10⁻⁸m²/2m

ρ = 1.412 × 10⁻⁶ Ωm

Hence, resistivity is 1.412× 10⁻⁶ Ωm.