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Homework 04

# Homework 04 - EE 3410 Homework 04 Solution Problem I An...

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Unformatted text preview: EE 3410 Homework 04 Solution Problem I. An inductor has a magnetic core with relative permeability of u = 8000, cross-section A = 25 cm2 and the length of the magnetic path I = 50 cm. The inductor is to operate at the voltage RMS value U = 240 V. Calculate the number of the coil turns N on the condition that the magnetic ﬂux density is not higher than B = 1.2 [Wb/mz]. Calculate the inductanceL of the inductor and its current RMS value at U = 240 V. Since —N = 44 J5 4 NAme hence, the number of the coil turns is The core reluctance R0: I =-—+57-7=19.9'103A/Wb. ##oA 8000x47z'x10' x2510— The coil inductance l 2 1 2 . L=—N =—-———-—300 =5.52H. Re 199-103 The coil current RMS value U 240 1=—=——=0. 11A. 0L 377x5. 52 IIIIIIIII*IhhhkIII************************ Problem 2. Repeat the problem 1, assuming that the care has an air gap of the width A = 0.5mm. The air gap reluctanxe is A 0.510—3 3 R _____-_'______=1s91o A/Wb #oA 4nx10'7x25 10‘4 The coil inductance N2 = 1 3002 =O.50H. Rc+Ra 19.9-103+159.1o3 The coil current RMS value U 240 I=w—L= 377x050 “127A' Problem 3. Calculate the air gap width A that would reduce the inductor current RMS value by half as compared to its value calculated in Problem 2. To reduce the coil current by half, its inductance should have double value, i.e., L ' = 2 x L = 1.0 H. Thus, the core should have reluctance 1N2=_l_ 2_ . 3 f 1.0 300 .90.0 10 A/Wb, R' = R0 + R ', = thus, the reluctanc of the air gap should be R’a =R'—Rc =90.o-103—19.9-103 =70-103A/Wb The air gap has such reluctance when its length is A' =ttoAR'a = 4nx10‘7 x25-10‘4 x70.1-103 = 0.00022m= 0.22 mm Symbols U — coil voltage RMS value, N — coil number turns, A — core cross section area, I — core magnetic path length, Bm— maximum value of the magnetic ﬂux density, a) - voltage angular frequency, ,uo — magnetic permeability of free space, a - relative permeability of the core, Rc - core reluctance, L — core inductance, I — coil current RMS value, A - air gap length, R, - air-gap reluctance, (.)’ — symbols for the core with reduced air gap ...
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