Question

# 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

Solution

## 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

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