EE 4501UMDSPRING, 2017

Name: ______

EXAM I: 100 Points – Show work for partial credit

  1. (25 Pts) The following sinusoidal waveform, v(t), is applied to a load. The load draws the current, i(t):

v(t) = 282.8 cos (377t) volts i(t) = 14.14 sin (377t + /4) amps

  1. Sketch v(t) and i(t) on the axis below:

t
  1. Calculate the RMS values of the voltage and current waveforms:

Vrms = ______volts Irms = ______amps

  1. Choose one of the waveforms as reference, convert both waveforms to phasors (including phase angles) and plot them on the axis below:

Phasors: V = ______volts I = ______amps

180° / 90°
270° / 0°
  1. What is power factor of the load? ______
  1. What is the complex impedance, Z, for the load? ______ohms

  1. (25 pts) A 10 HP, 240 volt single-phase motor is 86.3% efficient and operates at 60% power factor, lagging. It spins at N = 1720 RPM at full load.

a)Calculate Pe, the electric power into the motor at full load in watts. (1HP=746 W)

b)Calculate the Line Current at full load

c)Using 10HP and 240 volts as base, what is the line current from a) in per-unit?

d)Using 10HP and 1720 RPM as base, what is the base Torque of the machine in newton-meters? (=P/) (=2N/60)

  1. (25 pts) For the following single-phase AC circuit, the line current, I, is 10 amps, rms. Shown are the impedance of the Line (5 + j0.5 ohms) and the impedance of the Load (10 + j7.5 ohms).

a)What is the power factor of the load (10+j7.5 ohms)?

b)Find the magnitude of VLin the circuit

c)Find the magnitude and angle of Vs using the current phasor, I, as the reference

d)Calculate the average power, P, in the load

e)Calculate the reactive power, Q, in the load

  1. (25 Pts) A 600 volt three-phase system feeds a three-phase load with apparent power of 500 kVA at 0.6 pf, lagging.

a)Calculate the Line Current drawn by the load

b)If the load is WYE connected, what is the impedance per each phase?

c)If the load is DELTA connected, what is the impedance per phase?

d)Calculate the amount of shunt capacitance, in kVARs, necessary to correct the power factor to 0.90, lagging

Scott NorrPage 19/26/2018