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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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