Respuesta :
To calculate the length of the wire, we use formulas,
[tex]R = \frac{V}{I}[/tex] (A)
[tex]R= \rho \frac{l}{A}[/tex] (B)
Here, R is the resistance of the wire, I is the current flows through wire and V is potential difference. A is cross sectional area of wire and [tex]\rho[/tex] is the density of copper wire and is value,[tex]\rho = 1.7\times 10^{-8} \Omega m[/tex].
Given [tex]I = 0.86 A,V=15 V and r = \frac{0.47 mm}{2} =2.35 \times 10^{-4} m, V= 15 V.[/tex]
Substituting the values of I and V in equation (A ) we get,
[tex]R=\frac{15V}{0.86A} = 17.44 \Omega[/tex]
Now from equation (B),
[tex]l=\frac{R A}{\rho }[/tex]
Therefore,
[tex]l= \frac{17.44\times\pi \times r^2 }{1.7\times 10^{8} \Omega m} \\\\ l= \frac{17.44\times 3.14 \times(2.35\times10^{-4}m)^2 }{1.7\times 10^{-8} \Omega m} = 177.9 m[/tex]
Thus the length of the copper wire is 177.9 m.
