Episode 123: Alternating current
Lesson for 16-19
- Activity time 85 minutes
- Level Advanced
The aims are to distinguish alternating from direct currents and to remind your students of why AC is so important (they should already have met this at pre-16 level).
- Demonstration: The output of a generator (10 minutes)
- Student experiment: Measuring AC with a CRO (20 minutes)
- Discussion: r.m.s values as equivalent DC values (20 minutes)
- Demonstration: Finding the r.m.s value (15 minutes)
- Student questions: Practice on AC (20 minutes)
Demonstration: The output of a generator
A simple hand-turned generator can be used to create an alternating voltage that can be seen on an analogue demonstration voltmeter (needle swaying back and forth). This can be used to emphasise the ideas of frequency and peak value. Follow up by connecting the generator to a lamp and showing how the brightness depends on frequency of rotation.
Don’t get bogged down with electromagnetic induction but do compare what charges are doing inside a lamp filament when it is connected (a) to a DC supply and (b) to an AC supply (in the first case they drift in one direction in the second they move back and forth).
Student experiment: Measuring AC with a CRO
Measuring the peak value (amplitude), peak-to-peak value, and frequency of an AC supply using an oscilloscope.
This exercise builds on their introduction to oscilloscopes and sets the scene for the next demonstration. Make sure they are able to identify and measure peak and peak-to-peak values and to work out frequency from the time period of the voltage variation.
a lot of oscilloscopes have
calibration positions on their variable y-gain and time base settings. Students will need to be reminded to set these prior to making measurements otherwise they will get systematic errors throughout.
Discussion: r.m.s values as equivalent DC values
Ask the class what the average value of an AC voltage or current is over a whole number of cycles. It is obviously zero. So how can AC transfer energy? Remind them that power is calculated by P = I × V and point out that both I and V change sign together, so power is always positive but varies over the cycle, having a maximum value of IpVp and a minimum of zero. This should also make it clear that the average power is less than IpVp . Good mathematicians may know that the average value of a sine or cosine squared over a whole number of cycles is just 12. Weaker students might be persuaded by the symmetry (either side of V = 12) of a graph of sine-squared or cosine-squared against time. Either way you need to lead them to the idea that average power delivered by AC is:
P = 12 Ip Vp or, P = 12 (Ip)2 R or, P = 12 (Vp)2R
(using V = I × R)
The same power would be delivered by a DC with values I and V if:
P = I 2 × R
P = 12(Ip)2 R
P = V 2R
P = 12(Ip)2R
These lead to the equations:
I 2 = Ip2
I = Ip√
V 2 = Vp2
in turn giving
V = Vp√
This links the DC equivalent values to AC peak values. The point is that a sinusoidal AC supply of peak value Vp delivers the same average power as steady DC of value Vp√ .
We call these
DC equivalent values the r.m.s values for AC and we can use them in the same way as steady DC values: e.g. average AC power
P = Ir m s × Vr m s
You ought to say that r.m.s stands for
root-mean-square but it is only really worth going into the meaning of this in detail with groups who can handle the mathematics.
Demonstration: Finding the r.m.s value
To reinforce the idea of DC equivalence show them a demonstration in which a filament lamp is lit from first a DC and then an AC supply and the supplies are adjusted to make the lamp equally bright (equal powers). From the previous discussion you should be able to coax them to predict that the peak value of the AC (shown on an oscilloscope) is root-two times the steady DC value.
Student questions: Practice on AC
End the session by discussing the mains supply. AC currents and voltages are usually quoted as r.m.s values so 230 V 50 Hz mains AC varies from + 325 V to − 325 V and has a period of 150 (0.02) second. 230 V is its r.m.s value, 325 V is its peak value and 650 V is its peak to peak value.