Stretching of Wire

If a conducting wire stretches, its length increases, area of cross section decreases. So resistance increases but volume remains constant.

Suppose for a conducting wire before stretching (Fig. 11) its length = l1, area of cross section = A1, radius = r1, diameter = d1, and resistance .

Fig. 11

After stretching length = l2, area of cross section = A2, radius = r2, diameter = d2, and resistance .

Ratio of resistances before and after stretching

⇒ If length is given then
⇒ If radius is given then

Notes:
• After stretching if length increases by n times, then resistance will increase by n2 times, i.e., R2 = n2R1. Similarly, if radius be reduced to 1/n times, then area of cross section decreases 1/n2 times. So the resistance becomes n4 times, i.e., R2 = n4R1.
• After stretching, if length of a conductor increases by x%, then resistance will increases by 2x% (valid only if x < 10%).