Answer:
[tex]\frac{D}{d} = 4.12[/tex]
Explanation:
As we know that resistance of one copper wire is given as
[tex]r = \rho \frac{L}{a}[/tex]
here we know that
[tex]a = \pi (\frac{d}{2})^2[/tex]
now we have
[tex]r = \rho \frac{L}{\pi (\frac{d^2}{4})}[/tex]
[tex]r = \rho \frac{4L}{\pi d^2}[/tex]
now we know that such 17 resistors are connected in parallel so we have
[tex]R = \frac{r}{17}[/tex]
[tex]R = \rho \frac{4L}{17 \pi d^2}[/tex]
Now if a single copper wire has same resistance then its diameter is D and it is given as
[tex]R = \rho \frac{4L}{\pi D^2}[/tex]
now from above two equations we have
[tex]\rho \frac{4L}{\pi D^2} = \rho \frac{4L}{17 \pi d^2}[/tex]
[tex]D^2 = 17 d^2[/tex]
now we have
[tex]\frac{D}{d} = 4.12[/tex]
