Tutorial Sheet IV 1. Two identical inductors 1 H each are connected in series as shown. Deduce the combined inductance. If a third and then a fourth are similarly connected in series with this combined inductor, with the dots all at the left ends what are the resulting inductances? What do you infer is the relation between number of turns and the inductance of a coil? Assume coefficient of coupling as1.0. (Ans: 4H; 9H; 16H). Fig. IV_1. 2. There are three air-gaps, 1 mm, 1 mm, 1.5 mm, in the magnetic circuit alongside. Assuming an infinite relative permeability of the magnetic material and neglecting fringing, calculate the self and mutual inductance of the coils. Area of cross section of the core is 200 mm 2, and μ 0 = 4π 10-7. (Ans: 150 Turns: 3.5 mh; 200 Turns: 6.3 mh; M = 2.8 mh). 3. An iron ring of mean length 30 cm has an air gap of 2 mm and a winding of 200 turns. The iron has a permeability of 300 and the coil carries 1 A current. What is the flux density in the core? (Ans: 83.77 mwb/m 2 ). 4. The magnetic core in Fig. IV_4 is made from transformer plates. A 400-turn coil is wound on limb AB. What will be the current in the coil to obtain a flux of 1.2 mwb in the air-gap? Refer Fig. 1 and Fig.2 of Parker Smith (Page 6). (Ans: 4.19 A). Fig. IV_2. Fig. IV_3. Fig. IV_4.
5. Fig. IV_5 shows a rectangular magnetic core with an air gap. Given N = 400 turns; the cross section of the core is 4 cm 4 cm; and µ r (iron) = 4000. Find the exciting current needed to establish a flux density of 1.2 T in the air gap: (i). Without considering the effect of fringing. (ii). Considering the effect of fringing (Area of cross section of the flux through the air gap is 1764 mm 2 ). (Ans: (i). 5.11 A; (ii). 5.14 A). Fig. IV_5. 6. The magnetic circuit of Fig. IV_6 has a cast steel core with dimensions as shown. It is required to establish a flux of 0.8 mwb in the air gap of the central limb. Determine the mmf of the exciting coil, if for the core material µ r =. Neglect fringing. (Ans: 1343.98 AT). Fig. IV_6. 7. The core of Fig. IV_7 has a relative permeability of 4000. The central limb is required to carry a flux of 0.01 Wb. Find the current needed for the exciting coil. The cross section of the core is 4cm 4cm. (Ans: 2.99 A). Fig. IV_7. 8. In the magnetic circuit of Fig. IV_8, the coil F 2 is supplying 500 AT in the direction indicated. Find the mmf (in magnitude and direction) that the coil F 1 must provide to produce a flux of 4 mwb in the air gap of the central limb from A to B. The relative permeability of the core is 4500 and the area of cross section of the core is 30 cm 2. (Ans: 1786.54 AT).
Fig. IV_8. 9. For the magnetic circuit shown in Fig. IV_9, the magnetization curve of the core is as follows: H (AT/m) 200 400 500 600 800 1000 1400 B (T) 0.46 0.87 0.98 1.08 1.23 1.33 1.48 Calculate the exciting current required to create a flux of 0.25 mwb in the air gap. What is the flux in the central limb? (Ans: 0.59 A; 0.94 mwb). Fig. IV_9.
10. In the magnetic circuit shown in Fig. IV_10, the area of cross section of the central limb is 12 cm 2 and that of each outer limb (A to B) is 6 cm 2. A coil current of 0.5 A produces 0.5 mwb in the air-gap. Find the relative permeability of the core material. (Ans: 7627.51) Fig. IV_10. 11. For the magnetic circuit shown in Fig. IV_11, find the self and mutual inductances between the two coils. The relative permeability of the core is 1600. (Ans: L 1 =0.73 H; L 2 =3.55 H; M=0.64 H). Fig. IV_11.
12. (a). Determine the force necessary to separate two surfaces with 100 cm 2 of contact area when the flux density normal to the surfaces is 1 Wb/m 2. (Ans: 3978.87 N). (b). Calculate the force of attraction on the armature of the cast steel electromagnet shown in Fig. IV_12, when the flux density is 1 Wb/m 2. Find the ampere turns required to produce this flux density. Refer Fig.1 and Fig.2 of Parker Smith (Page 6). (Ans: 1989.44 N; 2491.55 AT). Fig. IV_12. 13. The mean diameter of a steel ring is 50 cm and a flux density of 1 Wb/m 2 is produced by a field intensity of 40 AT/cm. If the area of cross section of the ring is 20 cm 2 and if a 500 turn coil is wound around the ring; (a). Find the inductance of the coil in Henry; (b). When an air gap of 1 cm is cut in the ring, find the exciting current required to maintain a flux density of 1 Wb/m 2 and also find the new inductance of the coil. Ignore the effects of leakage and fringing. (Ans: (a). 0.0796 H; (b). 28.4 A, 0.0352 H). 14. (a). The combined inductance of two coils connected in series is 0.6 H or 0.1 H depending on the relative directions of the currents in the coils. If one of the coils when isolated has a self inductance of 0.2 H, calculate (i). The mutual inductance and (ii). The coupling coefficient. (Ans: (i). 0.125 H; (ii). 0.72). (b). Two identical 1000 turn coils X and Y lie in parallel planes such that 60 % of the magnetic flux produced by one coil links the other. A current of 5 A in X produces in it a flux of 0.05 mwb. If the current in X changes from +6 A to 6 A in 0.01 sec, what will be the magnitude of the emf induced in coil Y. Calculate the self inductance of each coil and the mutual inductance. (Ans: 7.2 V; L X =L Y =0.01 H, M=0.006 H). 15. Two coils X of 12000 turns and Y of 15000 turns lie in parallel planes so that 45 % of the flux produced by coil X links coil Y. A current of 5 A in X produces in it a flux of 0.05 mwb, while the same current in Y produces in it a flux of 0.075 mwb. Calculate (a). The mutual inductance and (b). The coupling coefficient. (Ans: (a). 0.0675 H; (b). 0.41).