A motor with polar moment of inertia Jdevelops torque according to the relationshipT = aω + b. The motor drives a load defined by thetorque–speed relationship TL = cω2 + d. If the fourcoefficients are all positive constants, determine theequilibrium speeds of the motor-load pair, andwhether these speeds are stable.

A 480V synchronous generator. 200 kVA, 0.8 power factor lagging, 60 Hz, two poles. connected in Y. It has a synchronous reactance of 0.25Ω and an armature resistance of 0.04Ω at 60 Hz, its own friction losses and with the air are 6 kW and its core losses are 4 kW. The field circuit has a voltage of 200 V and the maximum Is is 10 A. The field resistance is adjustable in a range of 20 to 200 Ω. The generator occ is shown in the figure below.Assume that the field current of the generator from the problem in the previous task has been set to 4.5A.a) What will be the voltage at the terminals of the generator if it is connected to a load at A with an impedance of 5<30° Q?b) Draw the phasor diagram of this generator.c) What is the efficiency of the generator under these conditions?d) Suppose now that another charge at A, identical, is placed in parallel with the first one. What happens in the phasor diagram of the generator?e) What is the new terminal voltage after adding charge?…

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A 480V synchronous generator. 200 kVA, 0.8 power factor lagging, 60 Hz, two poles. connected in Y. It has a synchronous reactance of 0.25Ω and an armature resistance of 0.04Ω at 60 Hz, its own friction losses and with the air are 6 kW and its core losses are 4 kW. The field circuit has a voltage of 200 V and the maximum Is is 10 A. The field resistance is adjustable in a range of 20 to 200 Ω. The generator occ is shown in the following figure…Assume that the field current of the generatoradjusts to achieve nominal 480V voltage under full load conditionsfor each of the questions below.a) What is the efficiency of the generator at nominal load?b) What is the voltage regulation of the generator if it is loaded with nominal KVAwith charges with a FP of 0.8 behind?c) What is the voltage regulation of the generator if it is loaded with nominal KVAwith charges with a FP of 0.8 in advance?d) What is the voltage regulation of the generator if it is loaded with nominal KVA with loads with a…