Answer :
Answer:
[tex]P=42.075W[/tex]
Explanation:
The power provided by a resistor (wire in this case) is given by:
[tex]P=\frac{V^2}{R}[/tex].
The resistance of a wire is given by:
[tex]R=\frac{\rho L}{A}[/tex]
Where for the resistivity the one of the copper should be used: [tex]\rho=1.68\times10^{-8}\Omega m[/tex].
The area A is that of a circle, which written in terms of its diameter is:
[tex]A=\pi r^2=\pi (d/2)^2=\frac{\pi d^2}{4}[/tex]
Putting all together:
[tex]P=\frac{AV^2}{\rho L}=\frac{\pi d^2V^2}{4\rho L}[/tex]
Which for our values is:
[tex]P=\frac{\pi (0.00025m)^2(12V)^2}{4(1.68\times10^{-8}\Omega m)(10m)}=42.075W[/tex]