circuits question

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hello, I need help with these circuit questions

Clear handwriting please.

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1. An electric motor (Zmotor = 18 + j24 Ohms) has been connected to a voltage source: Vs = 141.4 cos (377t). a) Determine the power factor for the motor (indicate if it's leading or lagging) b) Determine the average (real) and reactive power used by the motor. -Be sure to include THE PROPER UNITS to receive full credit 2. Draw the power triangle for the motor of problem 1, labeling each side of the triangle with numerical values. a. A shunt capacitor has been added to the motor to increase its power factor to 0.9 i. Draw the power triangle for the compensated circuit, labeling all sides ii. Calculate the capacitor value 3. In the circuit shown below, Vs = 40cos(100t) V. a) Determine the load impedance so that maximum power is transferred to it. b) Draw the load circuit and indicate the components used (type and value) to make the load impedance. 6Ω 100mH Vs -402 + 4. A balanced Y-source with positive phase sequence (V1 = 200 ej45° Vrms) is connected to a balanced Y-load with Za = (25 + j5)12. a. Sketch the circuit, labeling all values. b. Find the three line currents and line voltages
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