Two wires have equal area of cross section. One is copper and other is Aluminium have the same resistance. Find Which one is longer.

Two wires have equal area of cross section. One is copper and other is

1.	Two wires have equal area of cross section. One is copper and other is Aluminium have the same resistance. Find Which one is longer.
Answer» Solution :Suppose the resistance of COPPER and aluminium wires are `R_(1)andR_(2).` Suppose their AREA of cross section is A, length of copper wire `=l_(1),` length of the Al wire `=l_(2)` The resistivity of copper `(rho_(1))=1.68xx10^(-8)` The resistivity of aluminium `(rho_(2))=2.82xx10^(-8)` Given that `R_(1)=R_(2)` `rho_(1)(l_(1))/(A)=rho_(2)(l_(2))/(A)` `(l_(1))/(l_(2))=(rho_(2))/(rho_(1))=(2.82xx10^(-8))/(1.68xx10^(-8))=1.678` `l_(1)=1.678l_(2)` `therefore` Length of copper wire 1.678 times more than length of aluminium wire.