Question

A wire has a resistance of 16ohm it is melted and drawn into a wire of half its length calculate the resistance of the new wire what is the percentage change in its resistance

Answer 1

Let length of the wire be l and cross sectional area be A
New length= l/2
New cross sectional area= 4A ( radius is doubled)
Original resistance = p×l/A
16=p×l/A ......(1)
New resistance= p×l/2×4A
= p×l/8A
= 1/8(p×l/A)
=1/8× 16 ( from 1)
= 2

Therefore new Resistance will be 2 ohm