Respuesta :
Explanation:
The given data is as follows.
number of turns = n = 190 turns
radius = r = 9.2 cm = 0.092 m
diameter of copper wire = d = 1.9 mm
radius of copper wire = [tex]r_{c}[/tex] = [tex]\frac{d}{2}[/tex]
= [tex]\frac{1.9}{2}[/tex]
= [tex]0.95 \times 10^{-3}[/tex] m
where, A = cross sectional area of the wire
As, length of each turn of wire is 2pr where r is radius of the coil.
L = 190(2pr)
= [tex]190 \times 6.28 \times 0.092 m[/tex]
= 109.77 m
The cross sectional area of the wire is as follows.
A = [tex]\pi r^{2}_{c}[/tex]
= [tex]3.14 (0.95 \times 10^{-3} m)^{2}[/tex]
= [tex]2.83 \times 10^{-6} m^{2}[/tex]
It is given that resistivity of copper wire is [tex]1.69 \times 10^{-8} \ohm[/tex]
R = [tex]\rho \frac{L}{A}[/tex]
= [tex]1.69 \times 10^{-8} \ohm \times \frac{109.77}{2.83 \times 10^{-6} m^{2}}[/tex]
= [tex]65.53 \times 10^{-2} \ohm[/tex]
Thus, we can conclude that resistance of the coil is [tex]65.53 \times 10^{-2} \ohm[/tex].
Answer:
The resistance of the coil is 0.655 Ω
Explanation:
Given that,
Number of turns = 190 turns
Diameter of coil= 1.9 mm = 0.95 mm
Radius of single layer = 9.2 cm
Pressure = 16 gauge
We need to calculate the length of the wire
Using formula of length
[tex]L=n2\pi r[/tex]
Where, n = number of turns
r = radius of cylinder
Put the value into the formula
[tex]L=190\times2\pi\times9.2\times10^{-2}[/tex]
[tex]L=109.8\ m[/tex]
We need to calculate the area of cross section
Using formula of area
[tex]A=\pi\times r^2[/tex]
Put the value into the formula
[tex]A=\pi\times(0.95\times10^{-3})^2[/tex]
[tex]A=0.000002835\ m^2[/tex]
[tex]A=2.83\times10^{-6}\ m^2[/tex]
We need to calculate the resistance of the coil
Using formula of resistivity
[tex]R=\dfrac{\rho\times l}{A}[/tex]
Put the value into the formula
[tex]R=\dfrac{1.69\times10^{-8}\times109.8}{2.83\times10^{-6}}[/tex]
[tex]R=0.655\ \Omega[/tex]
Hence, The resistance of the coil is 0.655 Ω
