# The efficiency of a transformer

1. May 14, 2017

1. The problem statement, all variables and given/known data
A step-down transformer has an efficiency of 90%, the voltage of it primary coil is 200V and its current is 0.5A, and its secondary coil has a voltage of 9V and a current of 10A and its number of turns is 90 turns.
Calculate the number of turns of the primary coil.

2. Relevant equations
η =VsIs/VpIp * 100

Vs/Vp = Ns/Np

Is/Ip = Np/Ns

3. The attempt at a solution

I solved the problem in two slightly different methods, the first one:

And the second one:

The solution in the first method (Np = 1800) is the correct one, but I don't understand why the second one is wrong. I thought that both will lead me to the same answer, but apparently they didn't, could you explain it for me, please?

2. May 14, 2017

### cnh1995

The transformer is not ideal.
Hence,
this is not true.

3. May 14, 2017

OK, but why (Is/Ip = Np/Ns) is true?

4. May 14, 2017

### cnh1995

It is because of the mmf balance in the core. (Magetizing current is neglected as it is very small compared to the load current).

5. May 14, 2017

I didn't know about the MMF balance in my text book, but I googled it and understood it. Many thanks!

6. May 14, 2017

Good!