Alternating Currents

Direct current  from a battery moves in one direction only, from positive to negative.  In alternating current the direction is changing all the time.  The charge carriers are moving forwards and backwards many times a second.  In Europe it is 50 Hz (cycles per second); in the USA 60 Hz.

AC and DC are equally good at heating, lighting, or running motors.  DC is essential for chemical processes such as electrolyis.  Low voltage DC is used in electronic devices. 

AC is much more easily distributed than DC.  This is because transformers use AC only; the cannot work with DC.  So electricity is distributed at very high voltages (275 kV) at relatively low currents.  As a result only a small proportion of the transmitted energy is lost as heat in the wires.  The picture shows a transformer.

The graph below shows the difference between AC and DC.

• One complete alternation is called a cycle (NOT wavelength).

• The frequency is the number of cycles per second.  Units are hertz (Hz).

• The period is the time taken for one cycle.  It is measured in seconds.  f = 1/T.

• The current follows exactly the same wave form as voltage.

• The graph is called a sinusoidal waveform or a sine wave.

These features are shown on the graph:

Root Mean Square Value

The values of voltage and current are constantly changing in AC, unlike in DC in which they are steady.  We can measure AC voltages in two ways:

• Measure the peak to peak voltage, easily done on a cathode ray oscilloscope (CRO).

• Measure the root mean square (rms) value, or the effective value.

We use the rms value because its use allows us to do electrical calculations as if they were direct currents. 

How Does the Power Vary?

We know that:

Power = volts ´ amps = Vrms ´ Irms

so:

Peak power (positive) = (Vrms ´ Ö2) ´ (Irms ´ Ö2) = 2P

Minimum power = 0

Peak power (negative)= (-Vrms ´ Ö2) ´ (-Irms ´ Ö2)  = +2P

Notice that power varies from a maximum of +2P to a minimum of 0.  Therefore the average power is P.  We never get a negative power, since that would imply that the component was creating energy.

The Cathode Ray Oscilloscope

The CRO is connected in exactly the same way as a voltmeter, i.e. in parallel with a component.  The input resistance is very high indeed and the electron beam acts as a pointer of negligible inertia.  It is also robust and not easily damaged by overloading.

  The CRO can be used as a DC voltmeter.  We get a horizontal line or a dot, depending whether the time base is on.   If it is used as an AC voltmeter, it will show the sinusoidal waveform.  It will, of course show more complex waveforms of audio signals, but we won't worry about these.

The CRO can also be used to measure the voltage across a resistance of known value.  Therefore it can be used as an ammeter.

The CRO is shown in the picture below:

The most important controls that we use are:

• The vertical sensitivity or y-gain setting, calibrated in V/cm.

• The time base, in s/cm.

  The CRO is a perfect voltmeter as its input resistance is very high indeed.

  Remember:

• We measure the voltage on the vertical  axis.  We can adjust the sensitivity by turning the knob marked y-gain or voltage gain.

• The horizontal direction is determined by the time base setting.   We can change this by using the time base knob.

  As well as analysing the waveform, there are two measurements we can make with the CRO:

• We can determine the peak voltage of the AC waveform shown below. 

• We can also read the period, which in turn allows us to work out its frequency. 

Notice that:

• The peak to peak voltage is 12.8 V.  Often engineers read the peak to peak voltage off the CRO as the determination of the 0 level is not always easy.  The peak voltage is half of the peak to peak voltage.

• The root mean square voltage, which we use in electrical calculations, is the peak voltage divided by Ö(2)

• Therefore the Vrms = 6.4 ¸ Ö2 = 4.5 V

 

Question 2

Look at the CRO display: The time base is set at 2 ms/cm and the y gain at 0.5 V/cm (a) What is the peak to peak voltage? (b) What is the peak voltage? (c) What is the rms voltage? (d)  What is the period? (e)  What is the frequency?

ANSWER