HOME WORK # 2 – SOLUTIONS

1. Draw an analog electric schematic for the parallel magnetic circuit of the following figure for both cases of μ = ∞ and μ ≠ ∞.

SOLUTION:As , reluctances of the ferromagnetic paths approach zero, giving the simple, decoupled equivalent circuit below.

If lumped parameter reluctance values are formed for each of the branches and if leakage is neglected, the magnetic equivalent circuit for is drawn below.

2. For the parallel magnetic circuit of the following figure, assume that the core material is infinitely permeable. Let = 3 mm and = 2 mm. The thickness of all core members is =50 mm. The core has a uniform depth into the page of 75 mm. = 2 = 100 turns. Neglect air gap fringing.

(a) If = 0 and = 15 mWb, find the value of .(b) If = 10 A and = 20 A, determine and .

SOLUTION:

Since the core material is infinitely permeable, the first figure of Problem 1 is applicable.

(a) Summation of mmf’s around the decoupled left-hand branch gives

(b) Since the two branches are decoupled,

- , or 2 = 2.36 mWb.

3. In the magnetic circuit shown below, the relative permeability of iron is. The length of the air-gap is g=3 mm and the total length of the iron is 0.4 m. For the magnet B510=rμr = 1.07 T, Hc=800 kA/m and the length of the magnet lm is 5 cm. Assuming the cross section is uniform, what is the flux density in the air gap?

SOLUTION:

Since the cross section is uniform, B is the same everywhere and there is no current:

Solving for B: