Question

resistance of a metal wire of length one metre is 25 ohms if the radius of the wire is 0.15 mm calculate the resistivity of the material​

Answer 1

Step-by-step explanation:

recall resistivity ρ = π r2 R / L

Data :

r = 0.15 mm = 1.5 * 10-4 m

R = 25 ohm

L = 1 m

Plug this for ρ and you get

ρ = 3.14 * (1.5 * 10-4)2 * 25 / 1 = 176.625 * 10-8 = 1.77 * 10-6 ohm m

Answer 2

Hello friend

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

Hope helps

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