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# H_5 - Winding 2 is placed at and angle α relative to...

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Homework Set #5 (ECE743) Problem 1: Express the force of attraction between the iron faces of the air gap in Fig. 1. Assume N = 1000 turns, g = 10 -3 m and the switch “S” closes on the reactor when the input voltage V, is at its maximum value with the amplitude of 120 volts (f = 60 Hz). Neglect the reluctance of the iron. Assume r l = 1 and L l = 0.01 H. Fig. 1. 1

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Problem 2: In the Fig. 2, θ r and ϖ r are positive in the clockwise direction. The peak amplitude of the mutual inductance is L sr . Express (a) the mutual inductance L ab and (b) the electromagnetic torque T e . Fig. 2. A 2-winding device with clockwise rotation. 2
Problem 3: Consider the electromechanical system shown in Fig. 3. Assume the peak amplitude of the mutual inductance is L sr . (a) Express the mutual inductance. (b) Show the location of the north and south poles of the stator (N and S) and of the rotor (N and S) for positive i 1 and negative i 2 . (c) Express the electromagnetic torque T e . Fig. 3 3

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Problem 4: The device shown in Fig. 4 has two stator windings. Winding 1 is fixed in the position shown.
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Unformatted text preview: Winding 2 is placed at and angle α relative to winding 1. (a) Express the mutual inductance between winding 1 and 2 as a function of α . Let the peak amplitude be M. (b) Use the concept of virtual displacement to express the torque between the windings. Fig. 4 4 Problem 5: Consider the reluctance motor given Fig. 5. (a) Derive an expression for force (f em ) acting on the rotor as a function of flux, φ which is produced by the winding. (b) Show that if the current is switched on and off as shown in Fig.2, an average electromagnetic torque is exerted on the rotor. Give the waveform of this torque. (c) Assume the reluctance of the magnetic circuit varies with the rotor position as R = R + R 2 cos2 θ . Compute the instantaneous electromagnetic torque and the average electromagnetic torque. For part (c), assume t v ϖ sin V 2 = and neglect the resistance of the coil (R ≈ 0). Fig. 4 5...
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H_5 - Winding 2 is placed at and angle α relative to...

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