Ask Your Teacher A coil is formed by winding 260 turns of insulated 16 gauge copper wire (diameter = 1.3 mm) in a single layer on a cylindrical form of radius 15 cm. What is the resistance of the coil? Neglect the thickness of the insulation.

Respuesta :

Answer:

The resistance is [tex]2.98[/tex]Ω

Explanation:

Data

diameter:  [tex]d=1.3mm[/tex], [tex]d=1.3*10^{-3} m[/tex]

Radius:    [tex]r=\frac{d}{2} ,r=\frac{1.3*10^{-3} }{2} ,r=6.5*10^{-4} m[/tex]

Resistivity constant:   [tex]p=1.65*10^{-8}[/tex]Ω[tex]m[/tex]

To find Area:

[tex]A=\pi r^{2} \\A=\frac{22}{7} *(6.5*10^{-4} )\\A=1.33*10^{-6} m^{2}[/tex]

To find circumference:

[tex]l=260*(2\pi (0.15))\\l=245.04m[/tex]

Now we can apply the Resistivity formula:

[tex]R=p\frac{l}{A}[/tex]

[tex]R=(1.65*10^{-8} )[/tex]Ω[tex]m*\frac{240.04m}{1.33*10^{-6}m^{2} }[/tex]

[tex]R=2.98[/tex]Ω