Alternating currents and voltages
3f1 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.
So far we have
dealt with DC (Direct Current) circuits driven by cells. The electrons
in the circuit flow in one direction from the negative of the battery
to the positive.
This is actually the opposite of "Conventional Current Flow" in which the
current is said to flow from positive to negative. Why the difference.
Well, when Eddyson was doing his experiments on current flow no one
knew about electrons. So he made a guess and said that current
flows from positive to negative. It was only later that the electron was
discovered that it was realised that electrons flow from from negative
to positive. So we just have to remember that conventional current is
said to flow from positive to negative, but electrons actually flow from
negative to positive.
What about alternating current (AC). In AC the electrons are pushed
into the circuit and then pulled back, so the voltage and current are
constantly changing direction. The rate at which the current and
voltage vary is called the frequency. You will be familiar with UK
mains supply which has a frequency of 50Hz. You will also be familiar
with your 7.0MHz transmitter which changes cycle 7 million times a
second.
How do we picture what is happening. The most common way is to
visualise the current flow and the change in voltage as a sine
wave.
In the drawing the red line shows the change in voltage or current over
time.So. if we start at the left-hand side of the graph the voltage (or
current) starts to rise to a peak voltage. This is the amplitude or peak
value. The voltage then decreases to zero and continues until it
reaches a maximum peak negative voltage. It then starts to increase
until it reach zero again. This constitutes one cycle which takes
periodic time T.
To work out T (the time for one cycle) we us the equation:
Where T=time in seconds and f=frequency in Hz
Example - if the frequency is 50Hz, what is T (the time for one cycle)?
T=1/f
T=1/50
T=0.02 seconds
So, a mains frequency of 50Hz takes 0.02 seconds to complete one cycle)
Example 1
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 × 0⋅707).
RMS voltage
If you look at the sine wave and lets image that this is applied to a
resistor that will then get hot . It only reaches a peak positive
voltage once in a cycle. The rest of the time it is less than the peak
voltage. This means that it will not generate as much heat as a DC
signal which is always at the peak positive voltage. The equivalent DC
voltage of an AC voltage is called the RMS (Root Mean Squared) value.
The heating effect of an AC voltage is equivalent to the RMS of the peak voltage.
From Example 2 it can be seen that you get the same amount
of heat out of a resistor by applying either 20v peak AC or 14.4v DC
Example 2
3f.2 Recall that by repeatedly charging and discharging in alternate
directions, a capacitor can pass alternating currents, but cannot pass
a direct current.
If a DC voltage is
applied to a capacitor, it will charge up the plate of the
capacitor to the point at which it at the same voltage as the power
supply. At this point current will cease to flow to the plate of the
capacitor. At no point has current flowed across the capacitor. So, the
capacitor appears as a high resistance to a DC voltage.
If an AC voltage is applied to a capacitor the charge will increase and
then decrease as the AC voltage changes from the positive to the
negative half of the cycle. This will cause a corresponding charge to
build up and decay in the opposite plate. This alternating rise and
fall in charge will cause current to flow in the circuit attached to
the opposite plate. So, the capacitor appears as a low resistance to an
AC current.
All of this means that you can use a capacitor to stop DC flowing in a circuit, but continue to allow AC to flow.
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. Reactance in capacitors
We already know that in a DC circuit with a voltage and a resistor V=IR.
i.e. the voltage is equal to the current multiplied by the resistant.
In an AC circuit with a cell and capacitor which is starting to store energy we call resistance REACTANCE
Reactance in capacitors is measure in Ohms (Ω)
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.
Reactance in Inductors
In an AC circuit with a voltage and inductor which is starting to
store energy in it's magnetic field we call resistance REACTANCE
Reactance in inductors is also measured in ohms (Ω)
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 with capacitor and
resistors or inductors and resistors when a current flows through there
will be a transfer of electrical energy to heat in the resistors
and energy storage and release in the capacitor or inductors.
In this type of circuit, the ratio of overall potential difference to current is called impedance and that impedance is in opposition to both energy transfer and storage in the capacitors or inductors.
