ENGR 12 Assignment 12 Due: next wed

Part I. Drills -- 1 point each

1) A sinusoid having a peak amplitude of 500V is applied to the terminals of a 75 Ohm resistor. Find the average power delivered to the resistor by a) finding the RMS voltage and using Vrms^2/R, b) finding the RMS current and using Vrms*Irms.

2)

3) Find the power factor angle and the power factor for the four sets of values in problem 2, and indicate "lagging" power factor (current phase lags or is smaller than voltage phase, i.e. positive pfa) or "leading" power factor (current leads voltage, i.e. negative pfa).

4)

5) An electrical load operates at 120 Vrms. The load absorbs an average power of 3 kW at a leading power factor of 0.5. Calculate a) the power factor angle, b) the apparent power, |S|, c) the reactive power |Q| of the load. d) the impedance of the load (use S = Vrms Irms*, or Irms = (S/Vrms)*, then find Z = Veff/Ieff )

Part II. Assisted Problem Solving – 2 pts

6) a) Find the capacitance C needed to improve the power factor to 0.95 lagging in the circuit shown, if the effective voltage of 120V has a frequency of 60 hertz.b) how much in percent has the apparent power been reduced by the pf correction ?

1) Plan: find S = P + jQ for the 20<30 load and then add enough –Qcap to lower power factor to .95 (that would be a pfa of arccos(.95))

2) First find Sload = Veff Ieff* (where Veff = Vrms)(realizing Ieff into load = Veff/(20<30), and then take the complex conjugate and multiply by Veff)

3) You should find the pfa = 30 degrees4) Find Qload = |Sload|sin(30)5) Power absorbed by added capacitor will be purely

imaginary: Scap =0 + j Vrms(Vrms/-jXc)* = -j V2rms/Xc, or Qcap = - V2rms/Xc

6) The total real power of the combined load does not change. The total reactive power Qt of the combined load will then be Qload + Qcap. This needs to be set to give the desired pfa.

7) Once you find Qcap you can then find Xc and from there find C using Xc = 1/(wC).

8) For b), find Stotal for the combined loads. The % reduction in apparent power will be 100*(1 -|Stotal|/|Sload| )

7) The load impedance ZL is adjusted for maximum average power delivered to ZL. Find the maximum average power to ZL.

PLAN1) Find the Thevenin equivalent circuit to the left of ZL2) Set up an equation for I and solve3) Use your answer to 2 and voltage divider to find Voc4) Find Isc = 5 I / 15) Find Zth = Voc/Isc6) Apply ZL = Zth* to the thevenin simplified circuit7) The reactance elements cancel and we have simply a

resistive voltage divider for finding VL and hence Pmax

Part III. Unassisted Problem Solving – 3 points

8) Find the complex power S delivered to the load, and the power factor angle of S, if ig = 125cos500t mA.