Alternating Current
March 20, 2015
c Grob’s Basic Electronics, 11th Edition, Mitchel Schultz, 2010
The Direction of Current
The following may be considered when determining the direction of
current:
1. the flow of electrons, this is indicated in the circuit a
dashed arrow, or
2. the motion of positive charges in the opposite direction, this is
indicated in the circuit a solid arrow.
1. The direction of flow of electrons is from the negative
terminal through the load to the positive terminal.
2. The direction of flow of convectional current is from the
positive terminal through the load to the negative terminal.
Direct Current (DC) and Alternating Current (AC)
Direct Current (DC)
I In direct current (dc) electrons flow in only one direction.
I A dc voltage source can change the amount of its output
voltage, but with the same polarity.
I The dc voltage that changes the amount of its output voltage
is called a fluctuating or pulsating dc voltage.
I The dc voltage source that does not change the amount of
its output voltage is called a steady dc voltage source.
I A steady dc voltage source e.g. a battery has fixed
polarity and steady output voltage.
Alternating Current (AC)
An alternating voltage source periodically alternates in polarity.
Thus results in an alternating current (ac).
When polarity alternates, the direction of current also
reverses.
Waveform details and alternating polarities of an ac power-line
voltage with frequency of 60 Hz. Two cycles are shown.
Figure: Symbol for an ac voltage source.
Suppose the graph above shows V at terminal 2 with respect to
terminal 1 in the oscilloscope, then;
I the voltage at terminal 1 corresponds to the zero axis in the
graph as the reference level,
I at terminal 2, the output voltage has +ive amplitude
variations from zero up to the peak value and down to zero.
In the 2nd half-cycle, the voltage at terminal 2 becomes −ive:
All these voltage values are with respect to terminal 1.
When a sine wave of alternating voltage is connected across a load
resistance, the current that flows in the circuit is also a sine wave.
During the +ive half-cycle of v, terminal 1 is +ive with respect to
terminal 2. Electrons flows in the direction indicated by arrow A.
The voltage begins at 0v, increases to 100v then reduces to 0v.
During the −ive half-cycle of v, terminal 1 is −ive with respect to
terminal 2. Electrons flows in the direction indicated by arrow B.
The voltage begins at 0v, decreases to -100v then increases to 0v.
At each instant of the ac voltage, the alternating current is equal
to the value of the instantaneous alternating voltage divided
by Resistance (100Ω)
Voltage and Current Values for a Sine Wave
Since an alternating voltage or current has many instantaneous
values through the cycle, it is convenient to define specific
magnitudes as follows;
Peak Value
This is the maximum value VM or IM . The peak value applies to
either the positive or the negative peak.
Peak-to-peak Value
The peak-to-peak value is double the peak value. It is the
vertical value from the highest peak to the lowest peak.
Average Value
This is the arithmetic average of all values in a sine wave for
one half-cycle.
2
Average value = × peak value
π
Average value = 0.637 × peak value
Root-Mean-Square, or Effective, Value
This is the dc voltage and current that will produce the same
heating effect. It is abbreviated rms. The formula is;
1
rms value = √ × peak value
2
rms value = 0.707 × peak value
or
Vrms = 0.707Vmax
and
Irms = 0.707Imax
(It is necessary to be able convert from rms to peak value and
from peak to rms.)
1
Peak = × rms = 1.414 × rms
0.707
or
Vmax = 1.414Vrms
and
Imax = 1.414Irms
Thus:
Peak to peak value = 2.828 × rms value
Frequency
Frequency is the number of cycles per second. The symbol f .
Figure: ( a ) f = 1 Hz. ( b ) f = 4 Hz.
The unit called the hertz (Hz), is used for cycles per second. Then
60 cps = 60 Hz. All metric prefixes can be used. As examples
1kilocycle per second = 1 × 103Hz = 1kHz
1megacycle per second = 1 × 106Hz = 1MHz
1gigacycle per second = 1 × 109Hz = 1GHz
The entire frequency range can be considered in two broad groups:
1. audio frequencies (af)
2. radio frequencies (rf)
audio frequencies (af)
These includes frequencies of electrical signals that can be
heard as sound waves by the human ear. The range is approx.
16 to 16,000 Hz.
radio frequencies (rf)
These are frequencies of electrical signals that cannot be heard
as sound waves by the human ear. The range is from 16,000 Hz
up to several megahertz
Sonic and Ultrasonic Frequencies
Refer to sound waves due to variations in pressure generated by
mechanical vibrations, rather than electrical variations.
Sonic frequencies
These are sound waves in the audible range of frequencies
below 16,000 Hz. The term “audio” is reserved for electrical
variations that can be heard when converted to sound waves.
Ultrasonic frequencies
These are sound waves above the audible range of
frequencies. The range is from 16,000 Hz up to several
megahertz.
Period
This is the amount of time it takes for one cycle.
1 1
T = or f =
f T
I Its symbol is T for time.
I The higher the frequency, the shorter the period.
Examples
1. An alternating current varies through one complete cycle in
1
s. Calculate the period and frequency.
1000
2. Calculate the period for the two frequencies of 1 MHz and 2
MHz.
Wavelength
This is the length of one complete wave or cycle when a
periodic variation is considered with respect to distance. The
wavelength depends upon the frequency of the variation and its
velocity of transmission:
velocity
λ=
frequency
where (the Greek letter λ) is the symbol for one complete
wavelength.
Wavelength of Radio Waves
The velocity of electromagnetic radio waves in air or vacuum is
equal to the speed of light; that is 3 × 1010 cm/s. Therefore,
3 × 1010 cm/s
λ(cm) =
f (Hz)
Examples
1. Calculate λ for a radio wave with f of 30 GHz.
2. The length of a TV antenna is λ/2 for radio waves with f of
60 MHz. What is the antenna length in centimetres?
Non-sinusoidal AC Waveforms
Any waveform that is not a sine or cosine wave is a non-sinusoidal
waveform.
Important differences and similarities to consider
In all cases;
1. the cycle is measured between two points having the same
amplitude and varying in the same direction.
2. peak amplitude is measured from the zero axis to the
maximum positive or negative value.
3. the rms value 0.707 of maximum applies only to sine waves
because this factor is derived from the sine values.
4. phase angles apply only to sine waves because angular
measure is used only for sine waves.
5. all waveforms represent ac voltages; positive values are
shown above the zero axis, and negative values below
the axis.
Harmonic Frequencies
A non-sinusoidal waveform, e.g. a 100-Hz square wave has a
fundamental rate of repetition of 100 Hz.
Exact multiples of the fundamental frequency are called
harmonic frequencies.
The 2nd harmonic is 200 Hz, the 3rd harmonic is 300 Hz, etc.
Even multiples are even harmonics, and odd multiples are odd
harmonics.
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