Question

a wire of uniform thickness with a resistance 9 ohm is cut into 3 equal parts. what is the resistance of each part ?

Answer 1

Let initially the length of resistor be l and let the area of cross section be A and resistivity be P. Therefore 9=Pl/A
when the wire is cut into three parts length of each resistor is l/3 whereas the cross section area and resistivity remain same
R(resistance of each resistor)=Pl/3A
=1/3 Pl/A=1/39=3
Hence resistance of each part will be 3 ohm