Question

A copper wire of resistivetly (rho) is stretched to make 5% longer.find the % in its resistance ?

Answer 1

where l = length of conductor, A = Area of cross section of conductor and ρ = Resistivity.  

In the above equation ρ = constant but when you change l, A will also change. So you need to modify the equation to have only one variable in the equation.  

R = ρlxl/Axl  

R = ρl^2/V  

where V = volume of the conductor and it will remain constant.  

Therefore;  

R ∝l^2  

Suppose initially length was l = 100%.  

But you increased it by 5%, therefore, it became l'=105%  

Now % change in resistance is related to % change in length as follows:  

ΔR/R = [l'^2 - l^2 / l^2 x 100]%  

ΔR/R = [(105)^2 - (100)2 / (100)^2 x 100]%  

ΔR/R = 10.25%