1.17 An inductor is to be designed using a magnetic core of the form of that...

  

Transcribed Image Text:

1.17 An inductor is to be designed using a magnetic core of the form of that of Fig. 1.29. The core is of uniform cross-sectional area A, = 5.0 cm? and of mean length le = 25 cm. a. Calculate the air-gap length g and the number of turns N such that the inductance is 14 mH and so that the inductor can operate at peak currents of 6 A without saturating. Assume that saturation occurs when the peak flux density in the core exceeds 1.7 T and that, below saturation, the core has permeability u = 3200µg. b. For an inductor current of 6 A, calculate (i) the magnetic stored energy in the air gap and (ii) the magnetic stored energy in the core. What is the total magnetic stored energy? Core: mean length area A permeability a N-turn coil Figure 1.29 Inductor for Problem 1.17. 1.28 The coils of the magnetic circuit shown in Fig 1.36 are connected in series so that the mmf's of paths A and B both tend to set up flux in the center leg C in the same direction. The coils are wound with equal turns. N = N = 100. The dimensions are: Cross-section urea of A und B legs 6.58 cm Cros-section area of C legs = 13.16 cm Length of A path = I17 cm Length of B path- 17 cm Length of C path 5.5 cm Air gap 04 cm The material is M-S graude, 0.012-in steel, with a stacking factor of 0.94. Neglect fringing and leakage a How many amperes are required to produce a flux density of 1.2Tin the sir gap? b Under the condition of part (a), how many joules of energy are stored in the magnetic field in the air gap? e Calculate the inductance, Figure 1.36 Magnete cecut for Problem 1.28. 24 22 20 16 14 12 ON 06 04 02 10 14 100 1000 10.000 000 H, Aumm De magnetization curve for MS grain oriented electrical stool 0012 in tick 1.17 An inductor is to be designed using a magnetic core of the form of that of Fig. 1.29. The core is of uniform cross-sectional area A, = 5.0 cm? and of mean length le = 25 cm. a. Calculate the air-gap length g and the number of turns N such that the inductance is 14 mH and so that the inductor can operate at peak currents of 6 A without saturating. Assume that saturation occurs when the peak flux density in the core exceeds 1.7 T and that, below saturation, the core has permeability u = 3200µg. b. For an inductor current of 6 A, calculate (i) the magnetic stored energy in the air gap and (ii) the magnetic stored energy in the core. What is the total magnetic stored energy? Core: mean length area A permeability a N-turn coil Figure 1.29 Inductor for Problem 1.17. 1.28 The coils of the magnetic circuit shown in Fig 1.36 are connected in series so that the mmf's of paths A and B both tend to set up flux in the center leg C in the same direction. The coils are wound with equal turns. N = N = 100. The dimensions are: Cross-section urea of A und B legs 6.58 cm Cros-section area of C legs = 13.16 cm Length of A path = I17 cm Length of B path- 17 cm Length of C path 5.5 cm Air gap 04 cm The material is M-S graude, 0.012-in steel, with a stacking factor of 0.94. Neglect fringing and leakage a How many amperes are required to produce a flux density of 1.2Tin the sir gap? b Under the condition of part (a), how many joules of energy are stored in the magnetic field in the air gap? e Calculate the inductance, Figure 1.36 Magnete cecut for Problem 1.28. 24 22 20 16 14 12 ON 06 04 02 10 14 100 1000 10.000 000 H, Aumm De magnetization curve for MS grain oriented electrical stool 0012 in tick