Sinusoidal Power

1
Sinusoidal Power

• Chapter 14

2
Average Power and Power Factor

• See Overhead slides.
• Instantaneous power is the product of the
  instantaneous current times instantaneous voltage.

3
Instantaneous Power Trigonometric Identity

• recall the trig identity

4
Instantaneous Power Equation
5
Instantaneous Power Substitute
6
Instantaneous Power Solved
Fixed (constant) Value
varies with time
7
Effective Values
8
Power Factor

• Define the power factor as
• Whether voltage leads or lags current will not
  affect power factor.

9
Power Factor lead, lag

• Because power factor itself does not indicate
  leading or lagging, fully expressing the power
  factor gives a value and leading or lagging.
• Example PF0.8 lagging.
• Lagging means inductive circuit current lags
  voltage.

10
BIG CONCLUSION Average Power

• Average power is constant part of instantaneous
  equation. Time varying portion is sinusoid with
  a zero average.

11
Resistor ac Power

• current and voltage are
• in phase.
• thus have same sign.
• thus product is always positive.
• instantaneous power absorbed by a resistor is
  always zero or greater

12
Resistor Average Power

• Phase angle difference is one.
• Cosine of zero is one. Power factor is one.

13
Reactive Power

• Current and voltage are 90 degrees out of phase
  for pure inductor or capacitor.
• Instantaneous power will be equally positive and
  negative.
• Positive power absorbed from source by magnetic
  or electric field.
• Negative power returned to source by magnetic
  or electric source.

14
Reactive Average Power

• The phase angle between current and voltage is
  /- 90 degrees.
• The cosine of /- 90 degrees is 0.
• The average power absorbed by a pure inductor or
  capacitor is zero.
• No power is consumed!

15
Real and Reactive Power

• Power consumed is considered real power.
• Power exchanged with source and magnetic or
  electric field is reactive power.
• Note that with reactive power a current still
  exists. It does not do any work.