The resistance of a wire is R ohm. If it is melted and stretched to n times its original length, its new resistance will be

Step-by-step solution

The resistance of a wire is given by R = l A , where is the resistivity, l is the length, and A is the cross-sectional area. When the wire is stretched to n times its original length, the new length becomes l' = nl . Since the volume of the wire remains constant during stretching, V = A l = A' l' . Substituting l' = nl , we get A l = A' nl , which implies A' = A n . The new resistance R' is given by R' = l' A' . Substituting the values of l' and A' , we get R' = nl A/n = n² l A . Since R = l A , it follows that R'