Electrical principles
Outcome 4
Electrical principles
The aim of today is to understand the average and RMS
values in an AC circuit.
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
An alternating
current (a.c) is
produced when a
coil is placed
within a magnetic
field and allowed
to rotate.
As the coil turns current is induced in the coil.
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.
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.
2. It then moves from the maximum,
back through zero
3. Then on to a maximum in the
opposite direction,
4. Then to zero.
Each complete wave is called a ‘cycle’ or ‘period’.
The quantity of cycles in one second is called the
‘frequency’.
The formula for frequency is;
1
T=
f
1
f=
T
where T = time(s)
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.
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 doesn’t matter what the size of the current or voltage is, the average
value is always 0.637 times the maximum value available.
Use the table to work out the average
Angle*
Voltage (V)
0 degrees
0
30 degrees
50.00
60 degrees
86.60
90 degrees
100
120 degrees
86.60
150 degrees
50.00
180 degrees
0
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.
What does RMS stand for?
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.
D.C
100*C
70.7*C
A.C
The heating effect of 1A max d.c across a resistor
is100*C. But the heating effect of 1A max a.c is 70.7*C.
Heating effect of 1A maximum a.c
Heating effect of 1A maximum d.c
= 0.7071
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
=
4999.85
6
Remember this value!
= 70.71v
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
Vrms
All
= Vdc
values of a.c voltage and current are given as
RMS values
Now have go at completing
the exercise.