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Electrical principles
Outcome 4
Electrical principles
Session 1
a.c circuits
Objectives:
 To know how alternating current is produced
 To understand what average and RMS values are,
in relation to A.C and D.C supplies
Alternating current or a.c. is the supply most common in the UK; this
is due to a large number of economic and electrical factors.
An alternating current is
produced when a coil is
placed within a magnetic
field and allowed to rotate.
The coil is free to rotate within the magnetic field, as the coil turns
current is induced in the coil. This is tapped off at the slip rings.
The current in the coil varies depending on how much is being cut.
The coil starts at a position where no magnetic flux is being cut.
The magnetic flux is shown by the lines between the magnets.
At this point if we were drawing a sinusoidal wave or sine wave
this would be the 0 on the wave form diagram.
1. It moves from zero up to a maximum
in one direction.
A standard sine wave.
2. It then moves from the maximum,
back through zero
3. Then on to a maximum in the
opposite direction,
4. Then to zero.
When a sine wave has completed one of these sequences, it is then ready to
begin another the same.
Each complete wave is called a ‘cycle’ or ‘period’.
The quantity of cycles in one second is called the ‘frequency’.
A simple formula is attached to this
The quantity of cycles in one second is called the frequency
The formula for frequency is;
1
f
1
f=
T
where T = time(s)
T=
Frequency in the
UK is 50Hz.
f = frequency (Hz)
Time is usually measured in seconds or milliseconds
The maximum or peak value cannot be the total useful current, power or voltage,
as so much of the wave is less than the maximum. This is the average value.
This cannot be done over both positive and negative half cycles, as this would
produce an average value of zero.
So to look at the average value of current or voltage we must only look at one of
the half-cycles.
In this instance, the average value is when a series of readings are taken at different
points on the half-cycle and then averaged.
Points at which readings
would be taken.
In the above example, the values are taken every 10 degrees. You could also
take the values every 1 degree or even 30 degrees.
The average value is found from this formula;
Value (VAV) = V1 + V2 + V3 + V4 +…………Vn
n
It does not matter what the size of the current or voltage is, the average
value is always 0.637 times the maximum value available.
Now try and find the average of the previous example
Average value (VAV) =
V1 + V2 + V3 + V4 + V5 + V6
6
373.2 divide by 6 = 62.2v. This is the average
(Vav) of 100v max (Vmax)
In D.C circuits, the powered delivered to a resistor
is given by the product of voltage across the
element and the current through the element.
However, this is only true of instantaneous power to
a resistor in an A.C circuit.
An easy way to measure power is the RMS method.
R.M.S stands for, root mean square. This is
the effective value of a waveform.
The ‘Root Mean Square’ of an alternating current
is the value of equivalent direct current that would
produce the same amount of heat in a fixed
resistive load.
In the U.K, the single phase voltage is 230v. This is the RMS
voltage.
Multifunction meters (mft)
measure RMS values.
The RMS value is found using this
formula;
Mathematically the RMS voltage (VRMS) of a
sinusoidal waveform is determined by
multiplying the peak voltage(Vmax) value by
0.7071
Angle*
Voltage (V)
Voltage (V2)
0 degrees
0
0
30 degrees
50.00
2500
60 degrees
86.60
7499.56
90 degrees
100
10000
120 degrees
86.60
7499.56
150 degrees
50.00
2500
180 degrees
0
0
Using a table will help you simplify the RMS formula
For this example the total squared figure is 29999.12
So now we have the squared total the formula
Becomes a little easier to work out.
VRMS =
29999.12
6
=
4999.85
= 70.71v
So when we say the main supply to a domestic
property is 230V RMS, the maximum value would
be 325.3V and the average value would be 207.2V.
In an A.C circuit the average value is
63.7% of the max value
In an A.C circuit the RMS value is
70.71% of the max value
AC voltage is produced when a coil rotates through a magnetic
field.
Frequency is the number of cycles that occur every second

The maximum value of a waveform is Vpeak or Vmax

The average value of a waveform = 0.637

The RMS value of a waveform = 0.7071
The A.C RMS value is the same as the D.C value
You now have 5 minutes to complete
the exercises I have given you.