Respuesta :
Explanation:
The given data is as follows.
Resistance (R) = 1200 ohm, Area (A) = [tex]20 \times 10^{-6}[/tex] m (as [tex]1 \mu m = 10^{-6} m[/tex])
Diameter (d) = 2.3 mm = [tex]2.3 \times 10^{-3}[/tex] m
First, we will calculate the length as follows.
R = [tex]\rho \frac{L}{A}[/tex]
Here, [tex]\rho[/tex] = resistivity of aluminium = [tex]2.65 \times 10^{-8}[/tex]
Putting the given values above and we will calculate the value of length as follows.
R = [tex]\rho \frac{L}{A}[/tex]
1200 = [tex]2.65 \times 10^{-8} \times \frac{L}{20 \times 10^{-6}}[/tex]
L = [tex]9.056 \times 10^{5}[/tex]
As the circumference of circular wire = [tex]2 \pi r[/tex]
or, = [tex]2 \times \pi \times \frac{d}{2}[/tex]
= [tex]\pi \times d[/tex]
And, number of turns will be calculated as follows.
No. of turns × Circumference = Length of wire
No. of turns × [tex]3.14 \times 2.3 \times 10^{-3} = 9.056 \times 10^{5}[/tex]
= [tex]1.25 \times 10^{8}[/tex]
Thus, we can conclude that [tex]1.25 \times 10^{8}[/tex] turns of wire are needed.
The number of turns of wire that should be required is 2506.
Calculation of the number of turns of wire:
Here we know that
The resistance of the wire should be
R = Resistivity of material * length / cross-sectional area
So,
Length = AR / P
= (20*10^-6)^2 * 1200 / 2.65 * 10^-8
= 18.1 m
Now the circumference of the circle should be
= 2πr
= 2π (2.3*10^-3)/2
= 7.22 *10^-3 m
Now the no of loop should be
= 18.1/7.22*10^-3
= 2506 turns
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