What is the value of flux?

Question

two questions only!use the others for information.

http://s3.supload.com/free/Picture_249-20080728113336.jpg/view/

1. what is the reluctance R234 presented to flux Ф3?

ans: 5.10 X 10^3 1/H

2. what is the reluctance R24 presented to flux Ф2?

ans: 0.743 X 10^3 1/H

3. what is the equivalent reluctance of the core as seen by the applied mmf?

ans: 5.75 X 10^3 1/H

4. if the value of current flowing in the coil is 6 mA, what is the value of Ф1?

ans: 2.09 X 10^-3 Wb

5. refer to question 4. what is the value of Ф2?

1) 0.970 X 10^-3 Wb

2) 1.18 X 10^-3

3) 1.83 X 10^-3 Wb

6. what is the value of Ф3?

1) 0.583 X 10^-4 Wb

2) 0.993 X 10^-4 Wb

3) 0.267 X 10^-3 Wb

Answer 1

5.

You can solve this problem following the same concept as for electrical circuits.

At a node the sum magnetic fluxes flowing to it equals the magnetic fluxes flowing away. So at point 2 and 4:

Ф₁ = Ф₂ + Ф₃

Moreover you've got the same magneto-motive force between point 2 and 4 irrespective of the path. Hence:

MMF₂₄ = R₂₄ ∙Ф₂

MMF₂₄ = R₂₃₄ ∙Ф₃

=>

Ф₃ = (R₂₄/R₂₃₄) ∙Ф₂

Insert to magnetic flux euqation and solve for Ф₂:

Ф₁ = Ф₂ + (R₂₄/R₂₃₄) ∙Ф₂

=>

Ф₂ = Ф₁/(1 + (R₂₄/R₂₃₄))

= 2.09×10⁻³Wb / (1 + (7.43×10²H⁻¹ / 5.10×10³H⁻¹) )

= 1.82×10⁻³Wb

=>

3) is the correct answer

6.

Ф₃ = (R₂₄/R₂₃₄)∙Ф₂

= (7.43×10²H⁻¹ / 5.10×10³H⁻¹) ∙ 1.82×10⁻³Wb

= 0.266×10⁻³Wb

3) is the correct answer