How Efficient is a Transformer?
When teaching about transformers, their efficiency definitely should be discussed. As well as being incredibly useful, transformers are probably the closest humans have come to designing a 100% efficient machine. Transformers that are used in the national grid, for example, can be as good as 98 or 99% efficient. This is why the equation Power In = Power Out (or VₚIₚ = VₛIₛ) often gets used, since it's not as unreasonable to assume a transformer is 100% efficient as it would be to assume that, say, a petrol engine were 100% efficient.
However, it's not always that simple. You probably tell your pupils that transformers are used in the 'chargers' that we connect phones and laptops to, since this is a use which will be very close to their hearts. You might then be tempted to look on the label of such a charger, since they often quote the normal working V and I for both input and output, like this (top left):
Assuming the stated input current (1.6A) is a maximum value which will occur when the input V is a minimum, we have Vₚ = 100V, Iₚ = 1.6A, Vₛ = 19V and Iₛ = 3.42A. This gives Power In = 160 W but Power Out as 65W - in other words, an efficiency of a mere 41%.
This explains why transformers like this get so hot when you're charging your laptop or phone. But it's pretty poor, when you consider how good transformer design can be. So why aren't they better? I've never found a really satisfactory answer to this, but I suspect it's because laptop chargers are designed to be as small and light as possible because they need to be very portable. This puts lots of constraints on the design which means the efficiency suffers. The huge transformers used in substations in the national grid don't need to be portable, but there's a big requirement for them to be efficient so their design is intended to maximise efficiency - which it does very well.
An additional complication is that chargers like the one above usually use a switch-mode power supply. This means the transformer operates at a very high frequency (maybe 50kHz rather than the usual 50 or 60Hz of the mains supply) so that the charger can be made much smaller. There will also be the fact that the inductance of the coils and the capacitance of the smoothing capacitor will probably make V and I not vary exactly in phase. All these factors add more complications which probably explains why the manufacturer's data sheet claims an efficiency more like 87% as opposed to the 41% calculated above.