Tutorial # 3 1. A ferromagnetic ring with a mean circumference of 36 cm and a cross-sectional area of 3 cm2 is

wound with 400 turns of wire. When the excitation current is 1.4 A, the flux is found to be

1.4 mWb. Determine the relative permeability of the iron. (The solution is 2387)

2. A cast steel ring has a mean length of 30 cm and an air gap of 2 mm length. Find the number of

ampere-turns required to produce a flux of 0.6 T in the air gap. (The solution is 1084 At)

3. Find the average value of permeability (B/H) of sheet steel for the flux densities of B1 = 0.4T,

B2 = 0.8 T, B3 = 1.2 T, and B4 = l.6 T. (The solution is 3.08x10-3 H/m; 2.16x10-3 H/m; 1.67x10-3 H/m; 0.604x10-3 H/m)

4. A cast iron pipe has a 100-turn coil wound on it, as illustrated in Figure 1. The dimensions (in

cm) are as indicated;

(a) For a coil current of 10 A, determine the flux set up in the material.

(b) If a cast steel pipe had been used, what coil current would he required to establish the

same flux as part in (a)?

Figure 1 (The solution is (a) 432 µWb; (b) 1.1 A)

5. Calculate the magnetization curve for:

(a) The circuit shown in Figure 2 and,

(b) The same circuit with an air gap introduced as indicated by the dotted lines.

The excitation coil has 200 turns, and the material is sheet steel. Plot the total flux as a function

of excitation current for flux values of 4 to 12 mWb, in steps of 2 mWb. The dimensions (in

cm) are as indicated;

18 0.1

8

18

10

10

10

Figure 2

(The solution is (a) 4 mWb, 0.65 A; 6 mWb, 1.12 A; 8 mWb, 1.26 A; 10 mWb, 2.70 A; 12 mWb, 6.00 A;

(b) 4 mWb, 2.64 A; 6 mWb, 4.10 A; 8 mWb, 5.73 A; 10 mWb, 7.68 A; 12 mWb, 11.95 A)

6. A 280-turn coil is wound on the center leg of the sheet steel core shown in Figure 3. A flux of 1

mWb is required in the air gap. The core is built up to a thickness of 3 cm. Determine the coil

current. The dimensions (in cm) are as indicated;

Figure 3 (The solution is 2.74 A)