H_3 - L m1 = 263.9 mH L l1 = 13.5 mH r 2 ′ = 5 Ω L l2...

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Homework Set #3 (ECE743) 1. Problem 1: An iron-core transformer which has two windings is shown below. N 1 = 50 turns, N 2 = 100 turns, and μ r = 4000. a) Calculate L 12 , L m1 , and L m2 . b) Indicate the polarity of coupled coils with appropriate dots. 1
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2. Problem 2: Two coupled coils have the following parameters: r 1 = 10 , L l1 = 0.1 L 11 , r 2 = 2.5 , L l2 = 0.1 L 22 , L 11 = 100 mH, N 1 = 100 turns, L 22 = 25 mH, N 2 = 50 turns. Develop an equivalent “T” circuit with a) Winding 1 as the reference winding. b) Winding 2 as the reference winding. 2
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3. Problem 3: Two coupled coils have the following parameters: r 1 = 10 , L l1 = 0.1 L 11 , r 2 = 2.5 , L l2 = 0.1 L 22 , L 11 = 100 mH, N 1 = 100 turns, L 22 = 25 mH, N 2 = 50 turns. Develop a coupled coil equivalent circuit and compared with its “T” equivalent circuit. 3
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4. Problem 4: Consider a two-winding transformer with a “T” equivalent circuit model given below. Assume r 1 = 6
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Unformatted text preview: , L m1 = 263.9 mH, L l1 = 13.5 mH, r 2 ′ = 5 Ω , L l2 ′ = 13.5 mH. Compute the transient response of the transformer winding “1” current i 1 (t), assuming the windings are initially unexcited and winding “2” is open-circuited. a) When the switch is closed, the sinusoidal input voltage is at its maximum value. b) When the switch is closed, the input voltage is at its zero crossing point ( ϖ e = 377 rad/sec and V max = √ 2 ⋅ 110 volts). 4 5. Problem 5: Consider the elementary electromagnet shown below. Assume that the cross-sectional area of the stationary and movable member is the same and A i = A g = 4 cm 2 . Assume l i = 20 cm, N = 500 turns, and μ ri = 1000. a) Derive an expression for the magnetizing inductance L m (x). b) Compute the value of the magnetizing inductance when x = 1mm. 5...
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