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shutvik [7]
3 years ago
7

Calculate the reluctance of a 4-meter long toroidal coil made of low-carbon steel with an inner radius of 1.75 cm and an outer r

adius of 2.25 cm. The permeability of the steel is 2 x 10^-4 Wb/At - m.
A) 31.9 x 10^6 At/Wb
B) 1.96 x 10^-5 At/Wb
C) 4.03 x 10^5 AtWb
D) 2.29 x 10^6 At/Wb
Engineering
1 answer:
My name is Ann [436]3 years ago
8 0

Answer:

R = 31.9 x 10^(6) At/Wb

So option A is correct

Explanation:

Reluctance is obtained by dividing the length of the magnetic path L by the permeability times the cross-sectional area A

Thus; R = L/μA,

Now from the question,

L = 4m

r_1 = 1.75cm = 0.0175m

r_2 = 2.2cm = 0.022m

So Area will be A_2 - A_1

Thus = π(r_2)² - π(r_1)²

A = π(0.0225)² - π(0.0175)²

A = π[0.0002]

A = 6.28 x 10^(-4) m²

We are given that;

L = 4m

μ_steel = 2 x 10^(-4) Wb/At - m

Thus, reluctance is calculated as;

R = 4/(2 x 10^(-4) x 6.28x 10^(-4))

R = 0.319 x 10^(8) At/Wb

R = 31.9 x 10^(6) At/Wb

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Answer:

γ_{xy} =0.01, P=248 kN

Explanation:

Given Data:

displacement = 2mm ;

height = 200mm ;

l = 400mm ;

w = 100 ;

G = 620 MPa = 620 N//mm²;    1MPa = 1N//mm²

a. Average Shear Strain:

The average shear strain can be determined by dividing the total displacement of plate by height

γ_{xy} = displacement / total height

     = 2/200 = 0.01

b. Force P on upper plate:

Now, as we know that force per unit area equals to stress

τ = P/A

Also,  τ = Gγ_{xy}

By comapring both equations, we get

P/A = Gγ_{xy}   ------------ eq(1)

First we need to calculate total area,

A = l*w = 400 * 100= 4*10^4mm²

By putting the values in equation 1, we get

P/40000 = 620 * 0.01

P = 248000 N or 2.48 *10^5 N or 248 kN

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Does a thicker core make an electromagnet stronger?
mel-nik [20]

Answer:

Yes

Explanation:

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3 0
3 years ago
Three identical fatigue specimens (denoted A, B, and C) are fabricated from a nonferrous alloy. Each is subjected to one of the
Law Incorporation [45]

Answer:

B A and C

Explanation:

Given:

Specimen         σ_{max}                      σ_{min}

A                       +450                      -150

B                       +300                      -300

C                       +500                      -200

Solution:

Compute the mean stress

σ_{m} =  (σ_{max}  +  σ_{min})/2

σ_{mA} =  (450 + (-150)) / 2

       =  (450 - 150) / 2  

       = 300/2

σ_{mA} = 150 MPa

σ_{mB}  = (300 + (-300))/2

        = (300 - 300) / 2

        = 0/2  

σ_{mB}  = 0 MPa

 

σ_{mC}  = (500 + (-200))/2

        = (500 - 200) / 2

        = 300/2

σ_{mC}  = 150 MPa  

Compute stress amplitude:

σ_{a} =  (σ_{max}  -  σ_{min})/2    

σ_{aA} =  (450 - (-150)) / 2

       =  (450 + 150) / 2

       = 600/2

σ_{aA} = 300 MPa

σ_{aB} =  (300- (-300)) / 2

       =  (300 + 300) / 2

       = 600/2

σ_{aB}  = 300 MPa

σ_{aC}  = (500 - (-200))/2

        = (500 + 200) / 2

        = 700 / 2

σ_{aC}   = 350 MPa

From the above results it is concluded that the longest  fatigue lifetime is of specimen B because it has the minimum mean stress.

Next, the specimen A has the fatigue lifetime which is shorter than B but longer than specimen C.

In the last comes specimen C which has the shortest fatigue lifetime because it has the higher mean stress and highest stress amplitude.

7 0
3 years ago
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