14: Power in AC Circuits - Electrical Engineering

103 Pages·2015·2.2 MB·English

14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
•
IdealTransformer
•
TransformerApplications
•
Summary
14: Power in AC Circuits
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 1 / 11
Average Power
14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
•
IdealTransformer
•
TransformerApplications
•
Summary
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 2 / 11
Average Power
14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
• 2
IdealTransformer v (t)
Intantaneous Power dissipated in R: p(t) =
•
TransformerApplications R
•
Summary
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 2 / 11
Average Power
14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
• 2
IdealTransformer v (t)
Intantaneous Power dissipated in R: p(t) =
•
TransformerApplications R
•
Summary
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 2 / 11
Average Power
14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
• 2
IdealTransformer v (t)
Intantaneous Power dissipated in R: p(t) =
•
TransformerApplications R
•
Summary
Average Power dissipated in R:
T
P = 1 p(t)dt
T 0
R
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 2 / 11
Average Power
14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
• 2
IdealTransformer v (t)
Intantaneous Power dissipated in R: p(t) =
•
TransformerApplications R
•
Summary
Average Power dissipated in R:
T T
P = 1 p(t)dt = 1 1 v2(t)dt
T R0 R × T R0
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 2 / 11
Average Power
14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
• 2
IdealTransformer v (t)
Intantaneous Power dissipated in R: p(t) =
•
TransformerApplications R
•
Summary
Average Power dissipated in R:
2
T T v (t)
P = 1 p(t)dt = 1 1 v2(t)dt = h i
T R0 R × T R0 R
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 2 / 11
Average Power
14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
• 2
IdealTransformer v (t)
Intantaneous Power dissipated in R: p(t) =
•
TransformerApplications R
•
Summary
Average Power dissipated in R:
2
T T v (t)
P = 1 p(t)dt = 1 1 v2(t)dt = h i
T R0 R × T R0 R
v2(t) is the value of v2(t) averaged over time
(cid:10) (cid:11)
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 2 / 11
Average Power
14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
• 2
IdealTransformer v (t)
Intantaneous Power dissipated in R: p(t) =
•
TransformerApplications R
•
Summary
Average Power dissipated in R:
2
T T v (t)
P = 1 p(t)dt = 1 1 v2(t)dt = h i
T R0 R × T R0 R
v2(t) is the value of v2(t) averaged over time
(cid:10) (cid:11)
,
We define the RMS Voltage (Root Mean Square): V v2(t)
rms
ph i
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 2 / 11
Average Power
14:PowerinACCircuits
•
AveragePower
•
CosineWaveRMS
•
PowerFactor +
•
ComplexPower
•
PowerinR,L,C
•
Tellegen’sTheorem
•
PowerFactorCorrection
• 2
IdealTransformer v (t)
Intantaneous Power dissipated in R: p(t) =
•
TransformerApplications R
•
Summary
Average Power dissipated in R:
2
T T v (t)
P = 1 p(t)dt = 1 1 v2(t)dt = h i
T R0 R × T R0 R
v2(t) is the value of v2(t) averaged over time
(cid:10) (cid:11)
,
We define the RMS Voltage (Root Mean Square): V v2(t)
rms
ph i
The average power dissipated in R is P = hv2(t)i = (Vrms)2
R R
V is the DC voltage that would cause R to dissipate the same power.
rms
E1.1 Analysis of Circuits (2017-10213) AC Power: 14 – 2 / 11