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E E 2315. Lecture 15 Phasor Circuit Analysis, Effective Value and Complex Power: Watts, VAR’s and Volt-Amperes. Effective Value of a Sinusoid (1/2). Average Power:. Effective Value of a Sinusoid (2/2). In our example:. Also:. The effective value is also called the Root Mean

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E e 2315 l.jpg

E E 2315

Lecture 15

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



Effective value of a sinusoid 2 2 l.jpg
Effective Value of a Sinusoid (2/2)

In our example:

Also:

The effective value is also called the Root Mean

Square value or rms value.


R c circuit example 1 6 l.jpg
R-C Circuit Example (1/6)

Capacitive Reactance


R c circuit example 2 6 l.jpg
R-C Circuit Example (2/6)

Using rms phasor for voltage source.


R c circuit example 3 6 l.jpg
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 l.jpg
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 l.jpg
R-C Circuit Example (5/6)

Phasor Diagram of Voltage and Current

Current leads voltage.


R c circuit example 6 6 l.jpg
R-C Circuit Example (6/6)

The Power Triangle showing leading

power factor.



Calculating complex power 2 2 l.jpg
Calculating Complex Power (2/2)

From now on, we use the above method

to calculate complex power.



Lagging power factor example 2 4 l.jpg
Lagging Power Factor Example (2/4)

Calculate complex power directly:


Lagging power factor example 3 4 l.jpg
Lagging Power Factor Example (3/4)

Power Factor:

Power Factor is Lagging

Phasor Diagram of Voltage and Current


Lagging power factor example 4 4 l.jpg
Lagging Power Factor Example (4/4)

Power Triangle for lagging Power Factor




Phasor power example 3 4 l.jpg
Phasor Power Example (3/4)

Capacitor VAR’s: