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## Introductory experiments on AC

for 14-16

This collection of simple experiments shows that alternating current can be understood using students' prior knowledge of direct currents and voltages.

## The waveform of AC on a demonstration oscilloscope

Practical Activity for 14-16

**Demonstration**

A simple qualitative demonstration of the varying voltage of an alternating supply.

Apparatus and Materials

- Power supply, AC, low voltage variable
- Leads, 4 mm, 2

Health & Safety and Technical Notes

Read our standard health & safety guidance

Procedure

- Set the oscilloscope with the volts/cm switch to 1, the time-base control to 1 ms/cm, and the AC- DC switch to AC.
- Set the output of the power supply to 2 V (approx).
- Connect the AC terminals of the power supply to the input terminals of the oscilloscope. Adjust the time-base anticlockwise until four or five cycles of the waveform appear on the screen. The pattern traced on the screen should remain fixed in position.

Teaching Notes

- This demonstration is largely to provide a talking point.
- Point out the sine wave nature of the waveform.
- You could show the output of other sources of AC in the same way, e.g. the output of a transformer made using C-cores and ready-made coils, or with hand-wound coils. Comparisons of the input and output voltages could be made.

*This experiment was safety-tested in October 2006*

- A video showing how to use an oscilloscope:

### Up next

### Bicycle dynamo and oscilloscope

**Class practical**

Showing students that the e.m.f. (voltage) produced by a dynamo depends on the rate at which it turns.

Apparatus and Materials

- Bicycle
dynamo

assembly - Lamp, 1.5 V in lamp holder

Health & Safety and Technical Notes

The dynamo assembly consists of a simple bicycle generator, mounted and geared so that it can be driven both at speed and slowly – see the illustration. For convenience, a lamp holder may be fitted between the terminals.

Read our standard health & safety guidance

Procedure

- Connect the output from the generator to the oscilloscope input (Y-plates). The time base should initially be switched off and there should be maximum gain on the Y-amplifier. The spot should be in the centre of the screen.
- Connect the lamp across the output of the dynamo, in parallel with the C.R.O.
- Turn the handle with low speed gearing so that the up and down motion of the spot is clearly visible.
- Switch on the time base at slow speed and centre the trace with the X-shift. The gain should still be at maximum. The dynamo is again driven at the slow speed, and the spot will be seen to generate a wave-like trace.
- Gradually speed up the time base. Cut down the gain on the oscilloscope to about 2 volts/cm and drive the dynamo at the high speed. With the time base set at 10 ms/cm, a roughly sinusoidal wave-form will be seen.

Teaching Notes

- A bicycle
dynamo

is one of the simplest of generators and is easily available. It also has the advantage that the armature/coil is stationary and the field moves relative to it, in accordance with standard practice in heavy engineering. The field is normally produced by an 8-pole circular magnet rotating between two coils producing alternating voltages. - Turning the
dynamo

more quickly will increase the e.m.f. - A long-persistence screen would be an asset in this experiment, but is not essential. Alternatively, you could capture the trace using a datalogging system, and display it on a computer screen.
- The wave form will not be sinusoidal; the bicycle
dynamo

was designed for efficiency and not for teaching purposes. Other generators can be found which give a more nearly sinusoidal wave form, but there is greater value here in using a generator as familiar as the bicycledynamo

.

*This experiment was safety-tested in June 2007*

- A video showing how to use an oscilloscope:

### Up next

### Comparing rms value and peak value of AC

**Demonstration**

This experiment helps advanced level students to compare qualitatively the power produced by AC and equivalent DC sources. Root mean square (rms) values of AC voltage are calculated from peak values measured by an oscilloscope.

Apparatus and Materials

- Power supply, low-voltage, AC
- Cells, 1.5 V, 2
- Lamp, 2.5 V in holder
- Rheostat (10 - 15 ohms)
- Two-way switch
- Leads, 4 mm

Health & Safety and Technical Notes

Oscilloscopes contain high voltages and often have ventilation holes which allow access to points which are hazardous live

. Warn classes not to poke anything through holes in the case.

Read our standard health & safety guidance

Procedure

- Connect a 2 V AC supply to a small lamp. Attach a crocodile clip to one lead, to act as a home-made two-way switch.
- Connect the two dry cells and a rheostat to the lamp. The two-way switch gives a choice between the two supplies. Adjust the rheostat so that, with the DC supply, the lamp glows with the same brightness as with the AC supply.
- Connect leads also from the lamp to the y-input of the CRO with the time-base on.
- Switch to and fro between the two supplies, to make the comparison. With DC you will see the trace deflected upward (or down); with AC you will see the waveform. Are the AC waveform peaks higher than the steady DC voltage?
- Switch off the time-base of the oscilloscope, and centre the spot. In the DC case the spot will be deflected a definite amount. In the AC case, a line is obtained, the length of which is 2√2 times the deflection of the spot in the DC.

Teaching Notes

- If, you measure from the zero axis, then the AC peak value should be √2 the DC value for the same brightness of the lamp.
**Frequency**is the number of complete cycles of current or voltage per second measured in hertz. The frequency of the AC mains is 50Hz.**Peak voltage**is measured from the zero axis to the top of the curve and in the case of the UK mains supply is 324 volts (√2 x 230 V).**Average voltage**is zero.**Root mean square (average) voltage**- the alternating current does not warm up a lamp as well as a direct current of the same value as the peak AC, so you need to work out how to find the equivalent DC voltage for the AC situation. The experiment shows the same heating effect from an AC peak voltage √2 times bigger than the equivalent DC voltage. The constant voltage giving the same power dissipation as the time-averaged power dissipation of a sinusoidal AC voltage is called V_{RMS}.
Vpeak = √2V

_{ RMS }

*This experiment was safety-tested in January 2007*

*Thanks to Vijay Herwade for pointing out unclear text this page, now corrected. Editor *

- A video showing how to use an oscilloscope:

### Up next

### Ohm's law with alternating current

**Demonstration**

An ohmic resistor is equally ohmic when used with alternating current.

Apparatus and Materials

- Power supply, AC, low voltage variable
- Rheostat (10 - 15 ohms)
- Ammeter, (0-1 A), AC
- Voltmeter, 0 to 15 V, AC
- Leads, 4 mm, 6

Health & Safety and Technical Notes

Read our standard health & safety guidance

Procedure

- Set up a simple series circuit using the AC terminals of the low-voltage supply in series with the ammeter and the rheostat, used here as a fixed resistor.
- Connect the voltmeter in parallel with the resistor. Adjust the voltage so that a current of about 1 A flows.
- Record a series of values of the current and potential difference as you gradually reduce the voltage applied.

Teaching Notes

- You can calculate the value of the resistance from the root mean square (rms) readings of current and voltage.
- The resistance will be the same value as in an experiment carried out with the same resistor using a DC supply.

*This experiment was safety-tested in October 2006*

### Up next

### Why teach about AC?

It would be easy to leave AC as a slightly mysterious version of the direct currents that you deal with in simple DC experiments, and to suggest that detailed studies belong to later work in engineering. But AC is our standard form of supply. It is far more economical in distribution than DC because of the efficiency and simplicity of transformers.

Students are likely to be interested in the characteristics of AC. There are obvious ones (such as giving the same heating effect as direct current yet failing to move a DC ammeter visibly), and surprising ones involving phase differences. It is important to point out the differences between peak values, average values, and root mean square averages.

For elementary purposes, alternating current can be thought of as a current which is, at any instant, flowing in one direction or the other. As the alternating voltage changes direction, so does the current it pushes through a resistive circuit.

### Up next

### Explaining rms voltage and current

There are many ways of explaining root mean square (rms) voltage and current at different levels of complexity, to advanced level students.

- For the simplest level, say that you sample the current (or potential difference) at tiny intervals of time. Square each value, add up the squares (which are all positive) and divide by the number of samples to find the average square or mean square. Then take the square root of that. This is the
root mean square

(rms) average value.
For example, suppose there are 8 time intervals as shown in the diagram above:
- For those who are familiar with the graphs of sine and cosine functions, then the following algebraic method can be attempted.
*I*=*I*_{0}sinω*t*and*I*^{ 2}=*I*_{0}^{ 2}sin^{2}ω*t*- The heating effect depends on
*I*^{ 2}*R*, and so an average of*I*^{ 2}is needed and not an average of*I*. - To find the rms value, you need the average value of sin
^{2}as time runs on and on. - The graph of sinω
*t*and the graph of cosω*t*look the same, except for a shift of origin. Because they are the same pattern, sin^{2}ω*t*and cos^{2}ω*t*have the same average as time goes on. - But sin
^{2}ω*t*+ cos^{2}ω*t*= 1. Therefore the average values of either of them must be 1/2. - Therefore the rms value of
*I*_{0}sinω*t*must be*I*_{0}√ 2 - The rms value is 0.707 times the peak value, and the peak value is 1.41 times the value the voltmeter shows. The peak value for 230 V mains is 325 V.
- Alternatively: Plot a graph of sin
^{2}θ. Cut the graph in half and turn one half upside down, or copy onto a transparency and fit together. The two halves fit together exactly, showing that the mean value is 1/2. - Note that, when using
unsmoothed

rectified AC from a simple power supply, the estimate of the power obtained by multiplying the readings of a moving coil DC voltmeter and a moving coil ammeter is likely to be nearly 20% too low. This is because each moving coil meter measures the simple time-average of the half-cycle humps, not the rms average.
The rms values of current and voltage multiplied together give the actual power. This is a vital fraction when trying to do quantitative power and energy experiments such as specific thermal capacity. The values are only 80 % of the value at best

Values | 7 | 10 | 7 | 0 | -7 | -10 | -7 | 0 |

Squares | 49 | 100 | 49 | 0 | 49 | 100 | 49 | 0 |

*(peak value)*√ 2 =

*peak value*1.41 = 0.707

*peak value*