Resistance of a metal wire of length 1m is 26 ohm at temperature 20 degree celcius, if diameter of wire is 0.3mm, what will be the restivity of the metal at the temperature
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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 × 10⁻⁸m²/1mρ = 1.8356 × 10⁻⁶ Ωm
Hence, resistivity is 1.8356 × 10⁻⁶ Ωm at 20°C
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 × 10⁻⁸m²/1mρ = 1.8356 × 10⁻⁶ Ωm
Hence, resistivity is 1.8356 × 10⁻⁶ Ωm at 20°C
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