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 Outcome 4 Electrical principles

As the coil turns current is induced in the coil. The current in the coil varies depending on how much is being cut. An alternating current (a.c) is produced when a coil is placed within a magnetic field and allowed to rotate.

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. 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’.

Frequency The formula for frequency is; Time is usually measured in seconds or milliseconds Frequency in the UK is 50Hz.

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 (V AV ) = V 1 + V 2 + V 3 + V 4 +………… V n It doesn’t matter what the size of the current or voltage is, the average value is always times the maximum value available. n

Use the table to work out the average V AV = V 1 + V 2 + V 3 + V 4 + V 5 + V divide by 6 = 62.2v. This is the average (Vav) of 100v max (Vmax) Angle*Voltage (V) 0 degrees0 30 degrees degrees degrees degrees degrees degrees0

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. What does RMS stand for?

100*C D.CA.C 70.7*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 =

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 (V RMS ) of a sinusoidal waveform is determined by multiplying the peak voltage(V max ) value by

Angle*Voltage (V)Voltage (V 2 ) 0 degrees0 30 degrees degrees degrees degrees degrees degrees Using a table will help you simplify the RMS formula For this example the total squared figure is

So now we have the squared total, the formula becomes a little easier to work out. V RMS = = = 70.71v Remember this value!

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 =  The RMS value of a waveform =  Vrms = Vdc  All values of a.c voltage and current are given as RMS values

Now have go at completing the exercise.