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Q11. An elementary two-pole cylindrical rotating machine with a uniform air gap is shown in Figure Q11. The rotor is free to rotate about its axis and the position of the rotor at any instant is given as e = wmt + d, where @m is angular velocity of the rotor and d is the rotor position at t = 0. The mutual inductance between the rotor and the stator is given by = 7cos0 H An AC current source i =8cos 50t A is applied to the stator winding and another AC current source i, = 9sin 40f A is applied to the rotor winding. (i) Derive the instantaneous developed torque, T. (ii) Let 0= 45° at t=0, evaluate the average torque developed by the machine at @m = 10, 50 and 90 rad/s. (iii) If the rotor is locked at 0=45°, determine the average torque developed by the machine. Rotor axis 0 = Omt + 8 Stator axis

Q11. An elementary two-pole cylindrical rotating machine with a uniform air gap is shown in Figure Q11. The rotor is free to rotate about its axis and the position of the rotor at any instant is given as e = wmt + d, where @m is angular velocity of the rotor and d is the rotor position at t = 0. The mutual inductance between the rotor and the stator is given by = 7cos0 H An AC current source i =8cos 50t A is applied to the stator winding and another AC current source i, = 9sin 40f A is applied to the rotor winding. (i) Derive the instantaneous developed torque, T. (ii) Let 0= 45° at t=0, evaluate the average torque developed by the machine at @m = 10, 50 and 90 rad/s. (iii) If the rotor is locked at 0=45°, determine the average torque developed by the machine. Rotor axis 0 = Omt + 8 Stator axis

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Q11. An elementary two-pole cylindrical rotating machine with a uniform air gap is shown in Figure Q11. The rotor is free to rotate about its axis and the position of the rotor at any instant is given as 0 = wmt + 8, where @m is angular velocity of the rotor and d is the rotor position at t = 0. The mutual inductance between the rotor and the stator is given by L2 = 7cos0 H An AC current source i =8cos 50t A is applied to the stator winding and another AC current source i, = 9sin 401 A is applied to the rotor winding. (i) Derive the instantaneous developed torque, T. (ii) Let 0= 45° at t=0, evaluate the average torque developed by the machine at @m = 10, 50 and 90 rad/s. (iii) If the rotor is locked at 0=45°, determine the average torque developed by the machine. Rotor аxis 0 = Omt + 8 Stator аxis
Transcribed Image Text:Q11. An elementary two-pole cylindrical rotating machine with a uniform air gap is shown in Figure Q11. The rotor is free to rotate about its axis and the position of the rotor at any instant is given as 0 = wmt + 8, where @m is angular velocity of the rotor and d is the rotor position at t = 0. The mutual inductance between the rotor and the stator is given by L2 = 7cos0 H An AC current source i =8cos 50t A is applied to the stator winding and another AC current source i, = 9sin 401 A is applied to the rotor winding. (i) Derive the instantaneous developed torque, T. (ii) Let 0= 45° at t=0, evaluate the average torque developed by the machine at @m = 10, 50 and 90 rad/s. (iii) If the rotor is locked at 0=45°, determine the average torque developed by the machine. Rotor аxis 0 = Omt + 8 Stator аxis
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