A 1 m long wire is broken into two unequal parts X and Y . The X part of the wire is stretched into another wire W . Length of W is twice the length of X and the resistance of W is twice that of Y . Find the ratio of length of X and Y .

Step-by-step solution

​​​​​​​ Resistance of a wire is given by R = ρ L A , where, ρ is conductivity, L is length of wire and A is cross-sectional area of wire. For a single wire, A and ρ are constant. Thus, for parts X and Y , resistance, R X R Y = l X l Y . When wire is stretched to double of its length, then resistance becomes four times, thus, R W = 4 R X = 2 R Y . Hence, the ratio is R X R Y = 1 2 . So, l X l Y = 1 2