Electrical principles

City and Guilds 2365Certificate in Electro-technical

TechnologyLevel 3

Unit 1 Outcome 4 Session 1

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 4Electrical principles

Alternating Current (a.c.)

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.

Sinusoidal Wave

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.

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.

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

1T = f1f = T

where T = time(s)f = frequency (Hz)

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. 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 VoltageIn 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 doesn’t matter what the size of the current or voltage is, the average value is always 0.637 times the maximum value available.

n

Average formulaUse the table to work out the average

VAV = V1 + V2 + V3 + V4 + V5 + V6

6

373.2 divide by 6 = 62.2v. This is the average (Vav) of 100v max (Vmax)

Angle* Voltage (V)0 degrees 030 degrees 50.0060 degrees 86.6090 degrees 100120 degrees 86.60150 degrees 50.00180 degrees 0

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 toa resistor in an A.C circuit.

An easy way to measure power is the RMS method.

R.M.S

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?

Heating effect

100*C

D.C A.C70.7*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= 0.7071

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 valuesThe 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 030 degrees 50.0060 degrees 86.6090 degrees 100120 degrees 86.60150 degrees 50.00180 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 formula

So now we have the squared total, the formula

becomes a little easier to work out.

VRMS = 29999.126

= 4999.85 = 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.

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

Vrms = Vdc All values of a.c voltage and current are given as

RMS values

Exercise

Now have go at completing

the exercise.