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    AC Fundamentals

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    19M647 - SRIRAM A
    Alternating currents and voltages change direction periodically. AC quantities can be defined by their waveform, frequency, time period, amplitude, instantaneous and peak values. Voltages and currents may be out of phase with each other. Average values are the areas under waveforms divided by their bases. Effective or RMS values represent equivalent DC values in terms of power. Sine waves have zero average but non-zero averages for half cycles. RMS values can be determined by equating average power of a waveform to that of an equivalent DC current or voltage. Form and peak factors relate RMS and peak values.

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    AC Fundamentals

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    19M647 - SRIRAM A
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    Alternating currents and voltages change direction periodically. AC quantities can be defined by their waveform, frequency, time period, amplitude, instantaneous and peak values. Voltages and currents may be out of phase with each other. Average values are the areas under waveforms divided by their bases. Effective or RMS values represent equivalent DC values in terms of power. Sine waves have zero average but non-zero averages for half cycles. RMS values can be determined by equating average power of a waveform to that of an equivalent DC current or voltage. Form and peak factors relate RMS and peak values.

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    Alternating currents and voltages change direction periodically. AC quantities can be defined by their waveform, frequency, time period, amplitude, instantaneous and peak values. Voltages and currents may be out of phase with each other. Average values are the areas under waveforms divided by their bases. Effective or RMS values represent equivalent DC values in terms of power. Sine waves have zero average but non-zero averages for half cycles. RMS values can be determined by equating average power of a waveform to that of an equivalent DC current or voltage. Form and peak factors relate RMS and peak values.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
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    20 views31 pages

    AC Fundamentals

    Uploaded by

    19M647 - SRIRAM A
    Alternating currents and voltages change direction periodically. AC quantities can be defined by their waveform, frequency, time period, amplitude, instantaneous and peak values. Voltages and currents may be out of phase with each other. Average values are the areas under waveforms divided by their bases. Effective or RMS values represent equivalent DC values in terms of power. Sine waves have zero average but non-zero averages for half cycles. RMS values can be determined by equating average power of a waveform to that of an equivalent DC current or voltage. Form and peak factors relate RMS and peak values.

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    of 31

    AC fundamentals

    • Alternating currents (ac) are currents that alternate in direction (usually many
    times per second). Such currents are produced by voltage sources whose
    polarities alternate between positive and negative. By convention, alternating
    currents are called ac currents and alternating voltages are called ac voltages.
    Definitions

    • Waveform: It is a graph showing the manner in which an alternating


    quantity changes with t
    • Frequency: The number of cycles per second of a waveform is defined as
    its frequency.
    1 Hz =1 cycle per second .
    Time period(T):
    Example
    Amplitude and Peak Value:
    Instantaneous value:
    • Instantaneous values are the values of the alternating quantities at any instant of time. They are
    represented by small letters, i, υ, e, etc
    Example:
    Voltages and Currents with Phase Shifts
    Phase difference:
    Phase relations:
    • The terms lead and lag are used to indicate the relationship between two sinusoidal waveforms
    of the same frequency plotted on the same set of axes. In Fig. 5.7, the cosine curve is said to
    lead the sine curve by 90°, and the sine curve is said to lag the cosine curve by 90°. The 90° is
    referred to as the phase angle between the two waveforms.
    Example
    Example
    Example:

    • The current in an a.c. circuit at any time t seconds is given by: i =120sin
    (100πt +0.36) amperes. Find: (a) The peak value, the periodic time, the
    frequency and phase angle relative to 120 sin100πt (b) The value of the
    current when t =0 (c) The value of the current when t =8ms (d) The time
    when the current first reaches 60A
    Average value

    • To find the average value of a waveform, divide the area under the waveform by the
    length of its base. Average values are also called dc values, because dc meters
    indicate average values rather than instantaneous values. In general, average value is
    given by:
    Example : Determine the average value of the waveforms of the figures
    shown below:
    • Sine Wave Averages Because a sine wave is symmetrical, its area below the
    horizontal axis is the same as its area above the axis; thus, over a full cycle its net
    area is zero, independent of frequency and phase angle. The average of half a sine
    wave, however, is not zero. Consider Figure 5–8. The area under the half-cycle may
    be found using calculus as:
    Effective value (or Root Mean Square –RMS)

    An effective value is an equivalent dc value:

    It tells you how many volts or amps of dc that a time-varying waveform is

    equal to in terms of its ability to produce average power. Effective values

    depend on the waveform.


    Effective Values for Sine Waves:
    • The effective value of a waveform can be determined using the circuits of Figure
    5–9.

    • Consider (a) sinusoidally varying current, i(t). By definition, the effective value of i
    is that value of dc current that produces the same average power.

    • Consider (b). Let the dc source be adjusted until its average power is the same as
    the average power in (a).

    • The resulting dc current is then the effective value of the current of (a). To
    determine this value, determine the average power for both cases, and then
    equate them.
    Example
    Example
    Example
    Form Factor
    Peak Factor(Crest Factor)

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