Question

1 kg piece of copper is drawn into a wire 1mm thick and another piece into a wire 2mm thick compare the resistance of these wire.

Answer 1

Given :

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 1

now ratio of resistances of two wires

R1/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: 1

so, the ratio of new resistances of wires will be 16:1

therefore, R1/R2=16/1

R1=16R2