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Class 10 > Learn Science > A wire is 1m long, 0.2mm in diameter and has resistance...
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A wire is 1m long, 0.2mm in diameter and has resistance of 10?. Calculate its resistivity.

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Given: - Length = 1m, Diameter = 0.2 mm and Resistance =10 Ohm Thus by formula R = ρ*L/A we get 3.4*10^-7 Ohm
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Length= 1m Diameter= 0.2 mm =0.2×10^-3m Radius =0.1×10^-3m Resistance= 10ohm R=¶1/A ¶=R×A/1 =10×3.14×(0.1×10^-3)2 =3.14×10^-6 ohm m
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Resistivity = (resistance x area of wire )/ length of wire Resistivity = ( 10 x pi x 0.01)/ 1000 in ohm mm = 3.142 × (10^-4) ohm mm
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R = (rho x l)/ A, where rho is resistivity, R= resistance, l= length of wire and A= cross sectional area. This gives us rho = RA/l, l= 1m, R= 10 ohm Since diameter= 0.2 mm = 2x 10^(-4) m, radius = 1x 10^(-4) m Hence, area= pi*10^(-8) On substituting, rho= 10pi*10^(-8) = pi x 10^(-7) Ohm m.
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R = (rho x l)/ A, where rho is resistivity, R= resistance, l= length of wire and A= cross sectional area.

This gives us rho = RA/l, l= 1m, R= 10 ohm

Since diameter= 0.2 mm = 2x 10^(-4) m, radius = 1x 10^(-4) m

Hence, area= pi*10^(-8)

On substituting, rho= 10pi*10^(-8) = pi x 10^(-7) Ohm m.

 

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