Resistance of a metal wire of length 1m is 26 ohm at room temperature. If diameter of wire is 0.3 mm, find the resistivity of the wire

By K Balaji|Updated : November 12th, 2022

If diameter of wire is 0.3 mm, the resistivity of the wire is 1.8356 × 10⁻⁶ Ωm at room temperature.

Step 1, It is given that resistance , R = 26Ω

Diameter of circular part of wire, d = 0.3 mm = 0.3 × 10⁻³m

Length of wire, L = 1 m

Step 2, now we have to determine the resistivity

Base area of wire, A = πr² = πd²/4 [ ∵d = 2r]

Substituting the values in above eqaution

Area = [3.14 x (0.3 x 10⁻³)2]/4

On simplifying we get

Area = 7.06 × 10⁻⁸ m²

Using the formula,

R = ρL/A

Here, R = resistance, ρ = resistivity, The wire's base area is A, and its length is L.

So, ρ = RA/L

Substituting the values in above equation

ρ = 26Ω x 7.06 × 10⁻⁸ m²/1

On simplifying we get

ρ = 26Ω x 7.06 × 10⁻⁸ m²

ρ = 1.8356 × 10⁻⁶ Ωm

Therefore, resistivity is 1.8356 × 10⁻⁶ Ωm at room temperature.

Summary:-

Resistance of a metal wire of length 1m is 26 ohm at room temperature. If diameter of wire is 0.3 mm, find the resistivity of the wire

Resistance of a metal wire of length 1m is 26 ohm at room temperature. If diameter of wire is 0.3 mm, the resistivity of the wire is 1.8356 × 10⁻⁶ Ωm at room temperature.

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