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1 CHAPTER 22 ALTERNATING CURRENT Alternating Currents Phasors Reactance Impedance Power in AC Circuits R-L-C Circuits Resonance

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  • 1

    CHAPTER 22

    ALTERNATING CURRENT

    Alternating Currents

    Phasors

    Reactance

    Impedance

    Power in AC Circuits

    R-L-C Circuits

    Resonance

  • 2

    For Resistor

    Consider voltage that is sinusoidal.

    =

    Note that V is the maximum value of voltage and v varies from 0

    to a maximum of V.

    Also, a current that is sinusoidal.

    =

    Note that is the maximum value of voltage and varies from 0 to a maximum of .

  • 3

    Fig 22.1

    Can represent using phasors. Phasors are just tools to help

    visualize.

  • 4

    The

    phasor, the vector from the origin to the curved line, has the

    length equal to the magnitude of the current or voltage or

    whatever the phasor represents.

    The projection on the horizontal axis represents the

    instantaneous value of the quantity.

  • 5

    AVERAGE VALUES

    Values for the ac quantities used to make calculations of averages

    are called root-mean-square values.

    They can be obtained from the max values, the amplitude, by:

    = 2

    = 2

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    Resistor in ac circuit with current

    =

    Instantaneous voltage across resistor is

    = =

    =

    cos

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    Inductor in ac Circuit with current =

    =

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    =

    Current changes rapidly - Voltage large

    Current doesnt change - Voltage Zero

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    It can be shown that

    (Calculus by differentiating, ! " )

    = = ( + &)

    Where & is the phase angle. For inductor that is 900.

    Inductive Reactance,

    Defined as ( =

    By analogy voltage for inductor = (

    Now Capacitor in ac Circuit with current =

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    )* = +* Therefore

    )*t = 1. qt = 1. = 1.

    Thus a sinusoidal curve as seen in Fig. 22.8.

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    Thus the voltage curve lags the current curve by 900.

    And we have (can be derived by calculus)

    0 = 1.

    Or

    0 = 1. cos( 903)

    Or 0 = 0cos( 903)

    Capacitive reactance

    (0 = 1.

    And 0 = (0

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    IMPEDANCE

    Impedance of a circuit is the sum of the resistance and reactance

    in the circuit. The symbol for impedance is Z.

    4 = 56 + (6

    4 = 56 + (( (0)6

    4 = 76 + 8 1.96

  • 19

    Consider

    (Across Resistor)

    What is reactance of the capacitor?

    (0 = 1. = 1:2500 ([email protected]) = 80

    What is the current in the circuit?

    = = 1.2 :2500 300

    = [email protected] :2500

  • 20

    What is the impedance?

    4 = 76 +8 1.96

    4 = 76 8 1.96

    4 = 5(300)6 (80)6 = 290

  • 21

    Power in ac circuits

    Remember this about power for pure resistance

    IJKL = 12 = 12 12 = 12 12 =

    But with capacitors or inductors

    MN)O = PQRSTUVW = RQ SQTUVW = SXYVRXYVTUVW

    cosW is called The Power Factor

    Also IZ[