Question

Resistance of a metal wire of length 1 m is 26 ω at 20°c. if the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature? using table 12.2, predict the material of the wire.

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

Answer:

We are given the resistance R of the wire = 26 Ω, the diameter d = 0.3 mm = 3 × 10-4 m, and the length l of the wire = 1 m.  

Therefore the resistivity of the given metallic wire is

= (RA/l) = (Rπd2/4l)

Substitution of values in this gives ρ = 1.84 × 10–6 Ω m The resistivity of the metal at 20°C is 1.84 × 10–6 Ω m.

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