1. ELECTRIC CIRCUITS EIGHTH EDITION
JAMES W. NILSSON
&
SUSAN A. RIEDEL
ELECTRIC CIRCUITS EIGHTH EDITION

2. SINUSOIDAL STEADY – STATE POWER CALCULATIONS
CHAPTER 10
SINUSOIDAL STEADY – STATE POWER CALCULATIONS
© 2008 Pearson Education

3. Understand the following ac power concepts & how to calculate them in a circuit.
instanteneous power
Average(real) power
Reactive power
Complex power
Power factor
Understand the condition to deliver max. average power to
a load & then how to calculate the load impedance.
3. In ac circuits, Understand how to calculate ac power with
linear transformer and ideal transformer.

4. CONTENTS 10.1 Instantaneous Power 10.2 Average and Reactive Power
10.3 The rms Value and Power Calculations
10.4 Complex Power
10.5 Power Calculations
10.6 Maximum Power Transfer
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Generally,
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8. 10.1 Instantaneous Power
The positive sign is used when the reference direction for the current is from the positive to the negative reference polarity of the voltage.
The frequency of the instantaneous power is twice the frequency of the voltage (or current).
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9. 10.1 Instantaneous Power
Instantaneous power, voltage, and current versus ωt for steady-state sinusoidal operation
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10. 10.2 Average and Reactive Power
Average Power
Average power is the average value of the instantaneous power over one period.
It is the power converted from electric to non-electric form and vice versa.
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11. Note:

12. 10.2 Average and Reactive Power
This conversion is the reason that average power is also referred to as real power.
Average power, with the passive sign convention, is expressed as
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13. 10.2 Average and Reactive Power
Reactive power is the electric power exchanged between the magnetic field of an inductor and the source that drives it or between the electric field of a capacitor and the source that drives it.
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14. 10.2 Average and Reactive Power
Reactive power is never converted to nonelectric power. Reactive power, with the passive sign convention, is expressed as
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15. Note:

16. Note:

17. Note:

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20. 10.2 Average and Reactive Power
Power Factor
Power factor is the cosine of the phase angle between the voltage and the current:
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21. 10.2 Average and Reactive Power
The reactive factor is the sine of the phase angle between the voltage and the current:
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26. 10.3 The rms Value and Power Calculations
A sinusoidal voltage applied to the terminals of a resistor
Average power delivered to the resistor
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27. 10.3 The rms Value and Power Calculations
The average power delivered to R is simply the rms value of the voltage squared divided by R.
If the resistor is carrying a sinusoidal current, the average power delivered to the resistor is:
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28. rms value = effective value.

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33. a) max. amplitude 625 V vtg. Is applied to
50 Ω . Average power at this resistor?
b) Repeat (a) by 1st finding IR.
Sol.:
rms value of vtg. = 625/√2 ≈ V
P = V2rms/R
b) max. amplitude of ct. = 625/50 = 12.5 A
rms value of ct. = 12.5/ /√2 ≈ 8.84 A
Hence,

34. 10.4 Complex Power
Complex power is the complex sum of real power and reactive power.
| S | = apparent power
Q = reactive power θ
P = average power
A power triangle
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35. 10.4 Complex Power Quantity Units Complex power volt-amps
Average power
watts
Reactive power
var
Three power quantities and their units
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37. 10.4 Complex Power Apparent Power is the magnitude of complex power.
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38. Remind: > 0 Lagging pf: ct. lags vtg. Hence inductive load < 0
Leading pf: ct. leads vtg. Hence capacitive load

39. PF lagging → inductive → reactive power +

41. Electric facilities( that is, refrigerators, fans, air conditioners, fluorescent lighting fixtures, & washing machines) & most industrial loads operate at a lagging power factor.
Correction of power factor of these loads using capacitor.
This method is often used for large industrial load.

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44. See:

45. 10.5 Power Calculations(abbreviation.)
The phasor voltage and current associated with a pair of terminals
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48. Load impedance: 39 + j26
Line impedance: 1 + j4
Effective(or rms) value of S. : 250 V

50. load1: lead pf 0.8, 8 kW av. Power absorbed
load2: lag pf 0.6, 20 kVA absorbed
c) S. freq.: 60 Hz .
value of capacitor with pf = 1 if placed in
parallel with 2 loads?
c) S. freq.: 60 Hz

52. appearance power supplied to load, magnitude of current,
av. power :

53. Place capacitor with 10 KVAR in parallel with existing load
Place capacitor with 10 KVAR in parallel with existing load. Then pf = 1(그림10.15c)
So capacitive reactance is

55. a) Power supplied to each impedance?
b) Power of each source?
c) Delivered av. power = absorbed av.
power
Delivered reactive power = absorbed
reactive power

56. Reactive power delivered to (12 – j16)Ω

57. see: absorbed av. power:1950 W , delivered reactive power3900 VAR
b) Complex power of independent S.
see: absorbed av. power:1950 W ,
delivered reactive power3900 VAR
Complex power of dependent S.
주: 5850 W 평균전력 공급, 5070 VAR 무효전력 공급
see: delivered av. Power:5850 W ,
delivered reactive power 5070 VAR

59. 10.6 Maximum Power Transfer
A circuit describing maximum power transfer
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60. 10.6 Maximum Power Transfer
Condition for maximum average power transfer
The circuit with the network replaced by its Thévenin equivalent
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61. Proof:
Let
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65. a) ZL value to deliver max. power to ZL?
b) av. power at a)?
Sol.:
a) Thevenin eqvalent cit. seen to a, b terminal

66. b) in Fig.

67. a) ZL to be able to max. power & then max.
power(mW)
b) load: 0 ~ 4000 Ω
reactance: 0 ~ Ω
RL & XL to be able to transfer most av.
power to load & then max. av. power?
See:

68. See: P = I2eff RL
See: P(no restriction) > P(restriction)

69. ZL phase is o.
Magnitude of ZL changes until av. power becomes biggest under given restriction.
Specfy ZL in rectangular form.
Av. Power to delivered to ZL ?
a) In case magnitude of ZL be varied but
its phase not,
The greatest power is transferred to load when magnitude of ZL
is set equal to magnitude of ZTH ; that is,
Therefore,

70. See:
No restrictions on ZL

71. Previous knowledge
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72. Adjust RL until max. av. power is be delivered to RL.
a) RL?
b) max. av. power to be delivered to RL?
sol.:
a) Thevenin equivalent cit.
so V20
Note that Vth = - V2

73. Fig. is used to determine the short ckt current.
Using
Rearranging,
Therefore,
RTh = VTh/I2 =

74. Pmax = I2R =

75. 제출기일을 지키지않는 레포트는 사정에서 제외함
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Home work
Prob
제출기한:
다음 요일 수업시간 까지
제출기일을 지키지않는 레포트는 사정에서 제외함
제출기한:
다음 요일 수업시간 까지
제출기일을 지키지않는 레포트는 사정에서 제외함
Prob
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76. THE END
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