Question

A wire of 10 ohm resistance is stretched to thrice ots original length . Calculate its new resistance and new resistivity.

Answer 1

Explanation:

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Let resistance of a conductor = ρL/AWhere ρ is the resistivity of the material, L is the length and A is the cross sectional area.Let's assume the wire is cylindrical.Volume of a cylinder = V = πr^2 x hWhere r is the radius and h is the height.Here, A = πr^2 and h = LSo, V = ALWhen you are stretching the volume will remain the same.So V = A'L' = A'x(1.1)L (stretching by 10%)Thus A' = V/(1.1L) = 0.909ASo new resistance = ρL'/A' = ρx1.1L/(0.909xA) = 1.21R = 12.1Ω

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Answer 2

resistivity will not change because it is independent of length and area of cross section of the wire.

R=10ohm

original length=l

new length=l' =3l

then area will also decrease by three times

so

R'=rho *l'/area'

=rho*3l/(area/3)

=rho*9l/area

=9 (rho*l/area)

= 9R

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