Question

if the length of conductor is increased three times then find the increase in resistance.



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Answer 1

Even though length of conductor increases by 3 times, volume of wire remains same.

i.e. V₁ = V₂

A₁L₁ = A₂L₂

L₂ = 3L₁

A₂ = A₁/3

$R_{1} = \frac{\rho l_{1}}{A_{1}} \\R_{2} = \frac{\rho l_{2}}{A_{2}} \\\\R_{2} = \frac{\rho 3l_{1}}{\frac{A_{1}}{3} }\\R_{2} = \frac{9\rho l_{1}}{A_{1}} \\\\R_{2} = 9 R_{1}$