A uniform metallic wire of original resistance R0, length L0 and cross-sectional area A0 is stretched gently and uniformly so that its length becomes kL0 (k>1). The temperature is kept constant and no material is lost during stretching.
(i) Write the mathematical relation connecting the resistance of a conductor with its geometrical dimensions and resistivity.
(ii) Using the condition of conservation of volume, obtain an expression for the cross-sectional area of the stretched wire in terms of A0 and k.
(iii) Hence derive an expression for the new resistance R of the stretched wire in terms of R0 and k, and show explicitly that R∝L2 for such a process.
(iv) Calculate the percentage change in resistance when k=2.