Question

Resistance of a metal wire of length 0.5 m is 13 Ω at 20°C. If the diameter of the wire is 0.4 mm, resistivity of the metal at that temperature is
1 point
6.53x10*-8 ohm
6.53 x 10*-8 ohm m
6.53 x10*-6 ohm
6.53 x 10*-6 ohm m​

Answer 1

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Step-by-step explanation:

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Answer 2

Given : Resistance of a metal wire of length 0.5 m is 13 Ω at 20°C. diameter of the wire is 0.4 mm,

To Find : resistivity of the metal at that temperature

Solution:

R = ρ L /A

R = resistance  = 13 Ω

ρ = ?

L = 0.5 m

A  = π r²

r = radius =  Diameter/2 =  0.4/2 = 0.2 mm

= 0.2 * 10⁻³

= 2 x 10⁻⁴ m

A =  π  (2 x 10⁻⁴)²

=> A =  3.14 * 4 * 10⁻⁸  m²

=> A = 12.56 * 10⁻⁸  m²

R = ρ L /A

=> ρ = R A / L

=> ρ =  13 x  12.56 * 10⁻⁸   / 0.5

=> ρ =  326.56 * 10⁻⁸    

=> ρ =  3.26 * 10⁻⁶ ohm - m

   

Resistivity is   3.26 * 10⁻⁶ ohm - m  

None of the given option is correct

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