Question

A 1 kg piece of copper is drawn into a wire 1mm thick and another piece into awire 2mm thick.compare the resistances of these wires

Answer 1

Hey just apply the equation and you will get the answer

Answer 2

Let r1 and r2 be the resistance of two wires.Let l1 and l2 be the lengthsand density be d.As mass of copper =1kg is same for both wires,mass of first wire=mass of second wire.volumexdensity of  first wire = volume x density of second wire.v1xd=v2xd2(πr1² l₁) x d = (π r2² l₂)xdl₁/l₂=(r₂/r₁)² ----- equation 1now ratio of resistances of two wiresR1/R2₂= (ρ l₁/A₁)/(ρ l₂/A₂)=(A₂/A₁) x l₁/l₂=(πr₂²/πr₁² )x (r₂/r₁) ² --------------[from equation 1]   =(r₂/r₁)⁴=(2/1)⁴=16: 1so, the ratio of new resistances of wires will be 16:1therefore, R1/R2=16/1R1=16R2