Question

A uniform wire of 10cm length and resistance 3ohm is stretched such that its radius become 1/3 times the initial
value. New resistance of the wire in ohm is :​

Answer 1

Given :  a uniform wire of 10cm length and resistance 3 ohm is stretched such that its radius become 1/3 times the initial value.

To Find :  New Resistance of Wire

Solution:

R₁ = 3 Ω

L₁  =  10 cm

A₁  =  πr₁²  cm²

ρ₁  = ρ

R₁   = ρ₁ L₁/A₁

= 3 =  ρ * 10 /A₁

R₂ =  ρ₂ L₂/A₂

A₂  =  π(r₁/3)²  = πr₁² /9  = A₁/9  cm²

Volume is constant

Hence L₁ A₁ = L₂A₂

=> 10 . A₁ = L₂A₁/9

=>  L₂ = 90 cm

ρ₂  = ρ

R₂ =  ρ  90 /A₁/9

=> R₂ =  ρ  (810) /A₁

=>  R₂ =  81 * ρ  * 10 / A₁

=> R₂ =  81 * R₁

=>  R₂ =  81 * 3

=> R₂ =  243 Ω

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