electrical principles. session 1 a.c circuits objectives: to know how alternating current is...
TRANSCRIPT
Electrical principles
City and Guilds 2365Certificate in Electro-technical
TechnologyLevel 3
Unit 1 Outcome 4 Session 1
Session 1a.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
Outcome 4
Electrical principles
Alternating Current (a.c.)
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.
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.
An alternating current is produced when a coil is placed within a magnetic field and allowed to rotate.
Sinusoidal Wave
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.
Complete Sinusoidal Wave
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.
A standard sine wave.
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’.
Frequency
The quantity of cycles in one second is called the frequency
The formula for frequency is;
Time is usually measured in seconds or milliseconds
1T =
f1
f = T
where T = time(s)
f = frequency (Hz)
A simple formula is attached to this
Frequency in the
UK is 50Hz.
Labelling a sine wave
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.
Average Value of Current or Voltage
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
Average Values
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.
n
Average formulaNow 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)
Average ValuesIn 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.SR.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.
R.M.SIn the U.K, the single phase voltage is 230v. This is the RMS
voltage.
Multifunction meters (mft) measure RMS values.
R.M.S 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
R.M.S tableAngle* Voltage (V) Voltage (V2)
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
0
2500
7499.56
10000
7499.56
2500
0
Using a table will help you simplify the RMS formula
For this example the total squared figure is 29999.12
R.M.S formulaSo 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.
Remember
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
Re-cap
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