Electricity Tutorial 9 - Alternating Currents

(A-level only.  This is not on the AS syllabus)

 Contents

What is AC?

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 electrolysis.  Low voltage DC is used in electronic devices.

AC is much more easily distributed than DC.  This is because transformers use AC only; they 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 at a power station.

The symbol for an alternating supply is shown below:

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:

On the CRO the AC waveform looks like this:

Note the peak voltage is V0 (sometimes called Vpk).  Notice also the effective voltage, Vrms.

On a CRO, there is less uncertainty if you measure from the peak to the trough.  This is called the peak-to-peak voltage, and is given the code Vpk to pk

 The peak to peak voltage is twice the peak voltage.  Remember to halve this when you do calculations with the peak voltage.

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

 What is the peak voltage of the 230 V ac mains?

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

The graph shows the idea.

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.

 Question 2 On the diagram below, mark the following: AC waveform DC Period Peak Voltage RMS voltage How does the power vary with time if a current of Irms passes through a heater with a voltage of Vrms? Think about the power when V and I are positive and when V and I are negative.  Sketch a graph to illustrate your answer. How does the peak power compare to the power worked out using the rms values?

 Not every alternating current is a sine wave. The scale on the x-axis is the period, not the wavelength.