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the wire is actually stretched to increase in length. This means change in length casuses a change in cross section as well.
Given:Let the initial length of wire=l1Final length of wire after stretching l2 = l1 +(100/100)l1=2l1
l2/l1 = 2;
Area of initial wire=A1Area of final wire = A2Volume of wire remains constant.l1A1=l2A2A2=l1A1/l2As we know that R = ρ l/AR1/ R2 =( l1/A1 )/(l2/A2),= l1A2/l2A1.= l1 (l1A1/l2)/l2A1,R1/R2 = (l1/l2)^2= 0.25; (since l2/l1 = 2)R2 = 4R1;(ΔR/R)×100=(R2-R1/R1)×100= 300%The percentage increase in resistance is 300%.
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