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Unformatted text preview: California State Polytechnic University Pomona '
Department of Electrical and Computer Engineering ECE 209 Network Analysis l  Fall 2016 Solution for Homework 3
Magnetically coupled circuit and linear transformer Due: Thu, Nov ’17, 2016 in class Problem 1 rﬂﬂﬁr—ﬁﬂ i——— ' i
it i +
4H ; {gilt iF mam
i. .1 For the magnetically coupled circuit in the figure aboVe.
1) Find the coupling coefﬁcient.
2) Calculate vo(t)_ Solution: 1: = Mfi./L1L2 : mil4x2 = 0.3535 0.5(1—j) Cal Poly Pomona ECE 209 Network Analysis ll W5“! 12 Z (2 +_j16)11+j412 3:9..454g19ﬁngaga ‘ I
New: 0 = 68+05 40.5)13+31411 «1 'CMWZT 0.445%! A V0 = 12(05JC1—j) = 0.321745759Di/
07069 = 321.7cesl4t + 57.6°) mV Problem 2 An ideal transformer is rated at 11000/4600 V and the secondary current is rated at 30 A. Calculate:
t) the transformer turns ratio 2) the kVA rating
3) the primary current. Solution: V1 = 11*1000.; % primary voltage in V V2 2 4600; l2 = 30; % secondary rated current in A 1') nturn = V1/V2 = 2.3913
2) kVA = V2*l2 = V1 * l1 = 138 kVA
73) Primary current I1 = I2 / nturn = 12.5455 A Cal Poly Pomona ECE 209 Network Analysis ll Problem 3
Find V0 in the following circuit. Solution: Mall 2444""""l;2'+32»35)I 34 51,, 15> zaJ (22533141151; £0 MfﬂalJ Flow161;, +(jz, 32+34*Z+4)I2_ «522' sag)5; leImLéﬁQJIl c2)
1 J l
I; M 1» 2245145527” A Cal Poly Pomona ECE 209 Netwgrk Analysis. ll Problem 4 Find the impedance seen by the source in the circuit below. Cal Poly Pomona ECE 209 Network Analysis H Problem 5 The coupled circuit in the following ﬁgure has a coefﬁcient of coupling of1 (i.e., k = 1), L1 = 23.653 mH
and L2 = 10.61 mH. Determine the energy stored in the mutually coupled inductors at time t = 5 ms. Solution: Cal Poly Pomona ECE 209 Network Analysis ll ...
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 Fall '09
 Cal Poly Pomona, California State Polytechnic University, Pomona, Cal Poly Pomona ECE, Poly Pomona ECE

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