Please solve.

Problem 1.1 KPWS Problem 3.1 Problem 1.2 Figure 1.1 shows a circuit model for the utility (represented here as an ac voltage source) supplying one phase of an ac induction motor. The motor system parameters are Rs = 0.08 Q, Lis = 1 mH, Lm = 40 mH, Li = 1 mH, Rs = 0.1 , and Rx= 33 Q. (Rs and R,; represent parasitic resistances in the motor, while the energy delivered to R, represents energy converted to mechanical form by the motor.) a. If the utility voltage 1s 170cos(377t), what is the current into the motor? b. At what power factor does the motor operate? c. It is desired to improve the power factor of the motor system at the utility interface. It is proposed to do this by placing a capacitor across the ac line in parallel with the motor. What value of capacitor would be necessary such that the utility would see a power factor of 1? Figure 1.1 A Circuit model for one phase of an induction motor being driven by the utility