Answer:
The ratio of the diameter of iron to Cu is;
[tex]\frac{d{Fe} }{ d{Cu} } =\sqrt{\frac{p_{Fe} }{ p_{Cu} }}[/tex]
Explanation:
R=(ρL)/A
from the question the two materials have the same resistance per unit length.
[tex]\frac{R}{L}= \frac{p}{A}[/tex]
[tex]\frac{R}{L}[/tex] for iron = [tex]\frac{R}{L}[/tex] for copper
This means we can equate ρ/A for both materials.
[tex]\frac{p_{Fe} }{A_{Fe} } =\frac{p_{Cu} }{A_{Cu} }[/tex]
re-arranging the equation we have,
[tex]\frac{A_{Fe}}{A_{Cu} } =\frac{p_{Fe} }{ p_{Cu} }[/tex]
[tex]A=\pi \frac{d^{2} }{4}[/tex]
[tex]\frac{A_{Fe}}{A_{Cu} } =\frac{d^{2}{Fe} }{ d^{2}{Cu} }[/tex]
[tex]\frac{d^{2}{Fe} }{ d^{2}{Cu} } =\frac{p_{Fe} }{ p_{Cu} }[/tex]
[tex]\frac{d{Fe} }{ d{Cu} } =\sqrt{\frac{p_{Fe} }{ p_{Cu} }}[/tex]
