Respuesta :
Answer:
5.099 ohm
Explanation:
Let number of the turn of wire be
N = L/D
Where L is the length of the solenoid and d is the diameter 75 cm = 0.75m , 0.100 = 0.001m
N = 0.75/0.100
N = 750
Hence the number of turns of copper wire is 750
The expression for the length of the wire
L = N ( πD )
Where D is the diameter of the solenoid. And take 750 for N and 10.0cm for the diameter.
Hence, L = 750 ( π × 10/100 )
L = 750 ×3.142× 0.1
L = 235.65m
The resistance of the wire is given as : R = p 4l/πd×d
Where p is the resistivity of the wire
l is the length of the wire and
d is the diameter of the wire
Let l = 235.65m , p = 1.7×10~ -8
0.100cm = 0.001m for the diameter
R = 1.7×10~-8 { 4× 235.65 } / π × ( 0.001m* 0.001 m)
R = 0.000016024/ 3.142 × 0.000001
R = 0.000016024/0.000003142
R = 5.099 ohms
Answer:
Power = 2.22W
Explanation:
We are given;
Length of Solenoid; L = 75cm = 0.75m
Diameter of copper wire; d = 0.1 cm = 0.001m
B = 8 mT = 0.008T
From Ampere's law formula,
B = μo•I•N/L
Where;
B is magnetic field
I is current
N is number of turns
L is length of Solenoid
μo is vacuum permeability amd it has a constant value of 4π x 10^(-7) H/m
Now, let's find N.
N is given by; N = L/d
N = 0.75/0.001 = 750 turns
From earlier, B = μo•I•N/L
Thus, let's make I the subject;
I = B•L/(μo•N)
I = (0.008 x 0.75)/(4π x 10^(-7) x 750)
I = 0.006/(0.0009424778) = 6.367 A
Now, let's find the resistance; R.
The resistance; R is given by the formula;
R = ρ•N•π•d/A
Where;
ρ is resistivity of copper wire and has a value of 1.68 x 10^(-8) Ω.m
A is the area
Now area is given as; A = πd²/4
Putting this in the resistance equation gives;
R = ρ•N•π•d/(πd²/4)
This gives;
R = (4ρ•N•π•d)/(πd²)
This leads to; R = (4ρ•N)/(d)
Plugging in the relevant values, we have;
R = (4 x 1.68 x 10^(-8) x 750)/0.001
R = 0.0504 Ω
Now, we know that the formula for Power is;
P = I²R
where I is current and R is resistance.
Thus, Power = 6.637² x 0.0504 = 2.22 W
