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

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

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.

Effective Value of a Sinusoid (3/3)

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

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

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:

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.

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

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

Calculating Complex Power (1/2)

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

Lagging Power Factor Example (1/4)

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

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

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

Phasor Power Example (1/4)

Phasor Power Example (2/4)

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

Phasor Power Example (4/4)

Impedance and Admittance Conductance Susceptance