Question

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

Answer 1

Let r1 and r2 be the resistance of two wires.
Let l1 and l2 be the lengths and density be d.

As mass of copper =1 kg is same for both wires,
mass of first wire=mass of second wire.
volume x density of first wire = volume x density of second wire.

v1 x d=v2 x d2(πr1^2 l1) x d 
= (π r2^2 l2) x dl1/l2=(r2/r1)^2 ----- equation 1

Now, ratio of resistances of two wires:
R1/R2= (ρ l1/A1)/(ρ l2/A2)
=(A2/A1) x l1/l2
=(πr2^2/πr1^2 )x (r2/r1)^2 --------------[from equation 1] 
=(r2/r1)^2
=(2/1)^4
=16 : 1

so, the ratio of new resistances of wires will be 16:1
therefore, R1/R2=16/1
R1=16R2