# Transformers – something for nothing?(Challenge)

### Transformers use the idea of compensation

Wrong Track: The changing potential difference across the primary coil is 12 volt and this gives 120 volt across the secondary coil. So, since volts tell us the number of joule / coulomb, there must be a 10 times gain in energy from the transformer!

Right Lines: The point to remember is that, if the potential difference across the secondary coil goes up by 10 times, the current through the secondary coil goes down by 10 times.

### Working through an account using a numerical example

The basic assumption in thinking about the working of a transformer is that there must be a power balance across it. The input power and output power must be equal. In other words, it is impossible to get more energy out than is put in. With this in mind, let's consider the following transformer set up: input turnsoutput turns = 110

The potential difference across the primary coil is 12 volt.

The current in the primary coil is 2 ampere.

Teacher: OK! So what's the power input to the input coil of the transformer?

Al: Is it 12 times 2, that's 24 watt?

Teacher: Exactly: 12 volt  ×  2 ampere! Well done! And what does 24 watt tell us?

Susan: 24 joule inverse second is delivered to the input side of the transformer.

Teacher: Excellent! Now, there are 10 times the number of coils on the output coil as compared to the input coil, so what must be the potential difference across the output?

Greg: 120 volt.

Teacher: Good! Now, if we assume that the transformer is 100 % efficient, what does that mean?

Shapi: That the power out is the same as the power in.

Teacher: OK. If we assume that there is 100 % efficiency, who can tell me what the current in the output coil must be? The power output must be 24 joule inverse second, the potential difference is 120 V, so what's the current?

Gail: 0.2 ampere?

Teacher: Yes, exactly right! 0.2 ampere. The potential difference goes up by 10 times and the current goes down by ten times to keep the balance of power across the transformer. The same number of joule second-1 come out as go in.