Transformer turns ratio and impedance matching

 Using a 120 volt to 12 volt transformer what is the turns ratio? 120 / 12 = 10. What is the reactance ratio for the coils?

Look at the inductance formula. The number of turns is squared. Each turn reacts (has mutual inductance) with the rest so adding one turn to the first row of turns will not have as much effect as adding one turn to the second layer. Look at it this way, if all factors are held equal except the number of turns changing the turns count from 10 to 20 would produce four times the inductance. If the 19 turn coils was 100 uh the 200 turn coil would be 400 uh. When designing a transformer the cross section of the former determines the area for winding the coil After finding the desired number of turns the wire is sizes to fill the space available. Look at the example again.

The transformer windings are 10h and 10mh with a 10:1 turns ratio. Using the formulas the 10:1 turns ratio produces a 100:1 inductance ratio.
consider the voltage and current in the circuit and apply Ohm's law.
R = E / I
I = 12 / 8 = 1.5amp on the secondary
The 10:1 turns ratio tells us we have 1.5 amp / 10 = .15 amp in the primary
R = E / I = 120 / .15 = 800 Ohm
So our 10:1 turns has a 800 Ohm to 8 Ohm impedance match.

Another way of looking at it is R = E / I and when we reduce the voltage we have a higher current available. Reducing E reduces R AND increasing I reduces R.