1. E E 2415
Lecture 9
Phasor Circuit Analysis, Effective Value and Complex Power: Watts, VAR’s and Volt-Amperes

2. Effective Value of a Sinusoid (1/3)
Average Power:

3. Effective Value of a Sinusoid (2/3)
In our example:
Also:
The effective value is also called the Root Mean
Square value or rms value.

4. Effective Value of a Sinusoid (3/3)

5. R-C Circuit Example (1/6)
Capacitive Reactance

6. R-C Circuit Example (2/6)
Using rms phasor for voltage source.

7. R-C Circuit Example (3/6)
Calculate Real Power:
And Reactive Power:
Apparent power is the product of voltage and
current of the source.
Also:

8. R-C Circuit Example (4/6)
Power Factor is the ratio of real power to
apparent power:
Power Factor is also the Cosine of the angle
between the load voltage and the load current:
If the load current leads the load voltage, the
power factor is leading; if it lags the load voltage,
the power factor is lagging.

9. R-C Circuit Example (5/6)
Phasor Diagram of Voltage and Current
Current leads voltage.

10. R-C Circuit Example (6/6)
The Power Triangle showing leading
power factor.

11. Calculating Complex Power (1/2)

12. Calculating Complex Power (2/2)
From now on, we use the above method
to calculate complex power.

13. Lagging Power Factor Example (1/4)

14. Lagging Power Factor Example (2/4)
Calculate complex power directly:

15. Lagging Power Factor Example (3/4)
Power Factor is Lagging
Phasor Diagram of Voltage and Current

16. Lagging Power Factor Example (4/4)
Power Triangle for lagging Power Factor

17. Phasor Power Example (1/4)

18. Phasor Power Example (2/4)

19. Phasor Power Example (3/4)
Capacitor VAR’s:

20. Phasor Power Example (4/4)

21. Impedance and Admittance
Conductance
Susceptance