3.
Technical Basics
Alternating currents and voltages
3f.1 Understand the sine wave curve as a
graphical representation of the rise and fall of an
alternating current or voltage over time and that both the
frequency and the amplitude must be specified.
Recall that the time in seconds for one
cycle is the Periodic Time (T) and the formula T=1/f and
f=1/T where f is the frequency in Hz.
A
sine wave is a pure wave and contains no harmonics. Any
deviation from the pure sine wave curve is indicative of other
products mixed in with the signal e.g. harmonics.
To fully describe a
sine wave both the amplitude and the time for 1 cycle
( also called the periodic time ) or the number of cycles per
second, the frequency in Hertz Hz must be specified.
However voltage
quoted could be a peak to peak value or might be the RMS
value.
The
time taken for one complete cycle is known as the Periodic
Time (T)...however frequency is the more commonly used term.
The
relationship between Periodic Time (T) and Frequency ( f in
Hz) can be expressed like so:
T =
1/f or transposing it to give f = 1/T where f is in Hertz.
It
is worth pointing out that in earlier times the frequency was
measured in Cycles per Second ...these days Hertz, abbreviated
to Hz is now used.....in honour of an early experimenter in
the electrical field.
Recall that the power dissipated (in a
resistive circuit) varies over the cycle and that the RMS
current or voltage is equal to the current or voltage of a
DC supply that would result in the same power dissipation as
that of the AC sine wave current or voltage.
Recall that the RMS value of a sinusoidal
voltage is given by Vpk/√2 (Vpk x 0.707).
When
dealing with D.C the power dissipated in a resistive circuit
is constant and one way it can be calculated is to multiply
the applied voltage by the current flowing in the circuit.
However when using an AC waveform the voltage is not constant
but varies with the frequency. It follows that the current
must also vary with the frequency of the applied voltage.
Therefore the calculation of power dissipated in an AC circuit
is not straight forward. To calculate the power dissipated in
an AC circuit the RMS (Root Mean Square) voltage must be used.
The RMS voltage
is one that will the produce the same equivalent heating in
the circuit as would an equivalent DC voltage. RMS
voltage measurements can be assumed unless otherwise stated.
How
do we calculate the RMS value of a waveform if we only know
the Peak value (Vpk)
You need to be able
to recall that RMS value of a sinusoidal voltage is given by
Vpk/√2
then √2 = 1.414
and 1 / 1.414 = 0.707
So RMS (Vpk x 0.707).......
Simple just multiply
the peak value by 0.707
3f.2 Recall that by repeatedly charging and
discharging in alternate directions, a capacitor can pass
alternating currents, but cannot pass a direct current.
Recall that the ratio of the RMS potential
difference to the RMS current as the capacitor stores energy
in its electric field is called the reactance of the
capacitor and is measured in ohms.
Applying a DC voltage across the plates of a capacitor will
charge the capacitor with electricity. The capacitor can hold
a charge for a long time...indefinitely in the case of a
perfect capacitor with no losses.
When
the DC voltage is applied there is an in rush current that
charges the capacitor. Once the capacitor is charged no
further current will flow....in fact all current flow stops. A
capacitor cannot pass DC once it is charged.
When
an AC supply is applied to the plates of a capacitor there
will be an in rush of current just as on DC, however once the
supply changes polarity as the waveform reverses then the
capacitor must discharge and then recharge in the opposite
polarity. When the supply again changes polarity as the
waveform reverts back the capacitor must again discharge and
recharge again in the opposite sense. So when you apply an AC
waveform to a capacitor current is constantly charging and
discharging the capacitor and flowing around the circuit.
The
ratio of the AC voltage to the current flowing in the circuit
as the capacitor stores energy in its electric field is called
the reactance of the capacitor and is measured in ohms.
3f.3 Recall that an inductor will take time
to store or release energy in its magnetic field.
Recall that the ratio of the RMS potential
difference to the RMS current as the inductor stores energy
in its magnetic field is called the reactance of the
inductor and is measured in ohms.
Just
like a capacitor can store energy in its electric field
(between the plates of the capacitor) an inductor (a coil of
wire) stores energy in its magnetic field. An inductor has a
strange quality (inductance) which makes it oppose any change
in the current flowing through the inductor. So when you apply
a voltage (AC or DC) to an inductor the current can only build
up slowly as the inductor fights the change in the "status
quo".
Just
as in a capacitor, the ratio of the AC voltage to the current
flowing in the inductor circuit as the magnetic field builds
up and collapses in time with the frequency is called the
reactance of the inductor... and is also measured in ohms.
3f.4 Recall that in a circuit comprising
capacitors and resistors, or inductors and resistors, a
current will result in energy transfer (into heat) in the
resistors and energy storage and release in the capacitors
or inductors.
Recall that in such a circuit the ratio of
the overall potential difference to current is termed
‘impedance’ and that this name denotes an opposition to both
energy transfer and energy storage in the circuit. Recall
impedance is measured in ohms.
In a
circuit comprising capacitors and resistors, or inductors and
resistors, the current that flows on account of the AC voltage
applied will result in energy transfer in the resistors (they
will get hot!) and energy storage and release in the
capacitors, as an electric field, or in the inductors as a
magnetic field. Storing energy of course does not consume any
power...but forcing current to flow through a resistance (as
the name implies) does consume power!
In
such circuits containing resistance and or capacitance and or
inductance the ratio of the overall potential difference to
current flowing is termed 'impedance'. This name denotes an
opposition to both energy transfer and energy storage in the
circuit. Note this impedance to the flow of AC is measured in
ohms.
