homework from ECE

ECE 2054 Homework 8 Submit your work as a pdf to Canvas. Filename should be HW8_yourPID.pdf. Make sure your work is neat and legible; if I can’t read it or understand it, it will be marked wrong. Please box all your answers. Problem #1 For the circuit below, if Vs = 339.4cos(1000t), find the following:

a. The equivalent impedance of the circuit in phasor form b. The current supplied by the source c. The power factor d. The magnitude of the total power supplied by the source e. The real power absorbed by the load f. The reactive power in the load

Problem #2 You have a 1000 W electric motor connected to a 200 Vrms, 60 Hz source, and the resulting power factor is 0.8 lagging. (Hint: Based on the units, is power rating of the motor real power or apparent power?)

a. What is the voltage in terms of a phasor? b. By how many degrees does the current lag the voltage? c. What is the RMS current drawn by the motor? d. What is the current in terms of a phasor? e. What is the reactive power associated with the motor? f. What capacitor value put in parallel with the motor would result in a power factor of 0.95? g. What is the current in the parallel capacitor? h. What is the total current supplied by the source to the motor and capacitor parallel

combination, expressed as a phasor? i. What is the percentage decrease in the magnitude of the current drawn by the circuit with the

addition of the parallel capacitor? Problem #3 Suppose you have two power delivery setups, shown in Figure (a) and (b). For each case, determine

a. The power delivered by the source b. The power dissipated by the line resistance

c. The power delivered to the load d. The efficiency of the system (Pload/Ps)x100%

Hint: For Figure (b), reflect RL across the step-down transformer, then reflect R’L and the Rline together across the step-up transformer to find the total load seen by Vs.

Problem #4 For the 3-phase circuit shown, if the line voltage is 250 V (rms) and the total power absorbed is in all three loads is 600W with a leading power factor angle of 30o, find the following:

a. What is the per phase voltage? b. What is the RMS value of the current in each load? c. What is the impedance of each load in phasor form?