Question

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.

Answer 1

Answer:

The resistance is $2.98$Ω

Explanation:

Data

diameter:  $d=1.3mm$, $d=1.3*10^{-3} m$

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

Resistivity constant:   $p=1.65*10^{-8}$Ω$m$

To find Area:

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

To find circumference:

$l=260*(2\pi (0.15))\\l=245.04m$

Now we can apply the Resistivity formula:

$R=p\frac{l}{A}$

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

$R=2.98$Ω