Magnetic Circuit Theory and Examples: Understanding Toroidal Cores and Gap Effects
Explore magnetic circuit concepts like toroidal cores, gap effects, series circuits, and parallel circuits through examples and problems. Learn how to calculate current, flux, reluctances, and more in practical scenarios.
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Lecture 07 Magnetic Circuit Toroidal core. Effect of gapping toroidal core. Series Circuit. Parallel Circuit. 1
Example 01: For the magnetic circuit shown next, find: 1. The value of current I required to develop 4 10 4??. 2. Determine and r under the previous condition. Take H = 170 At/m Solution 1- to find the value of the current, flux density must be calculated. 4 10 4 2 10 3= 0.2 ????? ? =? ?= ? ? = ? 400 ? = 170 0.16 ? = 68 ?? 2- To find the permeability ? =? ?= 1.176 10 3 2
Example 02 Following the previous question, what will be the value of the flux if the core gapped by 0.1mm? ? = 68 ?? Air gap Solution: ? ? = ?( ????+ ???) = ????? 3
Magnetic Circuit Problems Q1:The magnetic circuit shown in Fig. 1 has dimensions??= ??=9 cm2, ? = 0.050 cm, lc = 30 cm, and N = 500 turns. Assume the value?? = 70,000 for core material. (a) Find the reluctances ?and ?. For the condition that the magnetic circuit is operating with Bc = 1.0 T, find (b) the flux ? and (c) the current i. Ex 03 Air gap length Area Figure (1) 4
Solution: a.The reluctances can be found from: ?? ?????? 70.000(4? 10 7)(9 10 4)= 3.79 103A.Turns 0.3 A T Wb 1 ?= = Wb 5 10 4 ? (4? 10 7)(9 10 4)= 4.42 105A.Turns A T Wb 1 ?= = ???? Wb Note: =4.42 105 3.79 103= 116.623 ? ? b.From ? = ????= 1.0(9 10 4)= 9 10 4Wb c.? =??? =?? =9 10 4(4.46 105) 500 =? ?+ ? ? =? = 0.08 A ? ? 5
Repeat the previous example Ex03 assume no air-gap Discuss the obtained results 6
Example 04 Determine the current value of the secondary inductor N2, in the figure shown next, to produce flux of 1.5 10 5?? ? Take H=20 A.turn/m Solution: ?1?1 ?2?2= ? ???? 60 2 = 30 ? = 20 0.16 ? = 3.89 ? 7
Example 05: Determine the current I required to establish a flux of =1.5x10-4 wb in the section of the core indicated in Figure? Take =0.006. Solution: Applying Amp re s circuital law around loop 2 in 8
