We have resistance of one wire
\(R_1=\frac{pl}{A}=\frac{pl}{\pi\,r^2}=\frac{4\,pl}{\pi D^2}\)
Where l is length and D is diameter of the wire. The resistance of second wire of double the length and double the diameter is,
Heat produced per second
\(H=\frac{V^2}{R}\infty \,\frac{1}{R}\)
As second coil has resistance equal to half of first coil, therefore heat produced in second coil is double than that in first coil.
