A copper wire of initial length L and radius r is drawn (without any loss of material) into a thinner wire of radius 3r. The temperature of the wire remains constant during the process.
a. (i) Show that the new length of the wire becomes 9L.
b. (ii) Express the new resistance R2 of the drawn wire in terms of the original resistance R1.
c. (iii) By what factor does the resistance change? Comment briefly on the practical significance of this result for the design of electrical conductors.