ELECTRICAL CIRCUITS 2
STUDY GUIDE
MODULE 1 - Introduction to AC Circuit Analysis
Time-Variant Voltage
Time-varying voltage that is commercially available in large quantities and is commonly
called the ac voltage.
Alternating waveform
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The term alternating indicates only that the waveform alternates between two
prescribed levels in a set time sequence
Sinusoidal Voltage
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A sketch of Vm sin ωt as a function of ωt.
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A sketch of Vm sin ωt as a function of t.
Periodic Function
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A periodic function is one that satisfies f(t) = f(t + nT), for all t and for all integers n.
Instantaneous value:
The magnitude of a waveform at any instant of time; denoted by lowercase letters
Peak amplitude:
The maximum value of a waveform as measured denoted by uppercase letters (such as
Em for sources of voltage and Vm for the voltage drop across a load).
Peak-to-peak value:
Denoted by Ep-p or Vp-p, the full voltage between positive and negative peaks of the
waveform, that is, the sum of the magnitude of the positive and negative peaks.
Period
The time interval between successive repetitions of a periodic waveform (the period T1 ,
T2 , and T3 ), as long as successive similar points of the periodic waveform are used in
determining T.
Frequency
The number of cycles that occur in 1 s
General Expression for the Sinusoid
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Where (ωt + Ф) is the argument and Ф is the phase. Both argument and phase can be in
radians or degrees.
Effective (rms) value of a sinusoid
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The equivalent dc value is called the effective value of the sinusoidal quantity.
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Root-mean-square (rms) value is the root-mean-square or effective value of a
waveform.
THE SINE WAVE
Degree. Radian
The unit of measurement for the horizontal axis is the degree.
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A second unit of measurement frequently used is the radian (rad).
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The radian is defined by a quadrant of a circle where the distance subtended on the
circumference equals the radius of the circle.
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The velocity with which the radius vector rotates about the center, called the angular
velocity, can be determined from the following equation:
Generating sinusoidal waveform
SUBTOPIC 1 – Phase Relations
Sine wave
Positive-going slope before 0°
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If the waveform passes through the horizontal axis with a positive going (increasing with
time) slope before 0°, as shown the expression is
Positive-going slope after 0°
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If the waveform passes through the horizontal axis with a positive-going slope after 0°,
as shown, the expression is
Cosine wave
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If the waveform crosses the horizontal axis with a positive-going slope 90° (π/2)
sooner, as shown, it is called a cosine wave; that is,
Lead and lag phase relationship
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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.
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If both waveforms cross the axis at the same point with the same slope, they are in
phase.
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SUBTOPIC 2 - Complex Phasors
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Sinusoids are easily expressed in terms of phasors, which are more convenient to work
with than sine and cosine functions.
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A phasor is a complex number that represents the amplitude and phase of a sinusoid.
Complex Numbers
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A complex number z can be written in rectangular form as
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where j = √−1; x is the real part of z; y is the imaginary part of z.
Complex Number Representation
BASIC OPERATIONS OF COMPLEX NUMBERS
Time-domain and Phasor-domain
Sinusoid-Phasor Transformation
TRIGONOMETRIC IDENTITIES
PHASOR RELATIONSHIPS FOR CIRCUIT ELEMENTS
Voltage-Current Relations for a Resistor
Voltage-Current Relations for an Inductor
Voltage-Current Relations for a Capacitor
Voltage-Current Relationships