1. site.iugaza.edu.ps/ajasser
Assad Abu-Jasser, PhD Electric Power Engineering The Islamic University of Gaza
site.iugaza.edu.ps/ajasser

2. Review of AC Circuits

3. The Sinusoidal Waveform

4. Example 1
A sinusoidal current has a maximum amplitude of 20 A. The current passes through one complete cycle in 1 ms. The magnitude of the current at zero time is 10 A.
What is the frequency of the current in hertz?
What is the frequency in radians per second?
Write the expression for i(t) using the cosine function. Express Φ in degrees.
What is the rms value of the current?

5. Example 2
A sinusoidal voltage is given by the expression υ=300cos(120πt+30).
What is the period of the voltage in ms?
What is the frequency in hertz?
Write the magnitude of the voltage at t=2.778 ms?
What is the rms value of the voltage?

6. Passive Circuit Elements in f-Domain V-I Relationship for a Resistor

7. Passive Circuit Elements in f-Domain V-I Relationship for an Inductor

8. Passive Circuit Elements in f-Domain V-I Relationship for a Capacitor

9. Impedance and Reactance

10. Example 3
A 90Ω resistor, a 32 mH inductor, and a 5 μF capacitor are connected in series across the terminals of a sinusoidal voltage source. The steady-state expression for the source voltage υs is 750 cos(5000t+30o) V.
Construct the frequency-domain equivalent circuit
Calculate the steady-state current i by the phasor method

11. The Instantaneous Power

12. Active and Reactive Power

13. Power for Purely Resistive Circuit

14. Power for Purely Inductive Circuit

15. Power for Purely Capacitive Circuit

16. The Power Factor

17. The rms Value & Power Calculation

18. Example 4
A sinusoidal voltage having a maximum amplitude of 625 V is applied to the terminals of a 50 Ω resistor. Find the average power delivered to the resistor.
Repeat (a) by first finding the current in the resistor

19. Complex Power

20. Example 5
An electric load operates at 240 V rms. The load absorbs an average power of 8 kW at 0.8 lagging power factor.
Calculate the complex power of the load
Calculate the impedance of the load

21. Balanced Three-Phase Voltages

22. Three-Phase Voltage Sources
Source Load
Y Y
Y ∆
∆ Y
∆ ∆

23. Analysis of the Wye-Wye Circuit
Va’n = Vb’n= Vc’n
Zga=Zgb=Zgc
Z1a=Z1b=Z1c
ZA=ZB=ZC
Va’n = Vb’n= Vc’n
Zga=Zgb=Zgc
Z1a=Z1b=Z1c
ZA=ZB=ZC

24. Example 6
A balanced three-phase Y-connected generator with positive sequence has an impedance of 0.2+j0.5 Ω/Φ and an internal voltage of 120 V/Φ. The generator feeds a balanced three-phase Y-connected load having an impedance of 39+j28 Ω/Φ. The impedance of the line connecting the generator to the load is 0.8+j1.5 Ω/Φ. The a-phase internal voltage of the generator is specified as the reference phasor.
Construct the a-phase equivalent circuit of the system
Calculate the three line currents IaA, IbB, and IcC
Calculate the three phase voltages at the load, VAN, VBN, and VCN
Calculate the line voltages , VAB, VBC, and VCA at the terminals of the load
Calculate the phase voltages at the generator terminals, Van, Vbn, and Vcn
Calculate the line voltages at the generator terminals, Vab, Vbc, and Vca

25. End