How does the resistance of wire change when (a) its length is increased by 20 % (b) its diameter is increased by 20 %
Resistance = §L/A
a) Increasing length by 20% means the total resistance increases by 20%, because as per the formula they are directly proportional.
b) Resistance is inversely proportional to area.
If the diameter is increased by 20%, so is the radius. And as per the formula for area of a circle, if the radius increases by 20%,the area increases by 44% ( 1.2 x 1.2 = 1.44)
If the area increases by 44%, the resistance decreases by 44%.