How Does a Step Up Transformer Illustrate the Conservation of Energy?

[XPTPCREWX]

It is understood that you cannot have something from nothing, but how is this the case with a step up transformer? It seems that stepping up the voltage is stepping up the potential energy and since more windings actually increase the resistance there will be lower current which is how most people explain the conservation of energy in this situation, however what would happen in the case of a superconducter?

 

[Pumblechook]

You step up voltage not energy. Energy out is always less than energy in.

 

[berkeman]

It is understood that you cannot have something from nothing, but how is this the case with a step up transformer? It seems that stepping up the voltage is stepping up the potential energy and since more windings actually increase the resistance there will be lower current which is how most people explain the conservation of energy in this situation, however what would happen in the case of a superconducter?

Just to add a little to Pumblechook's answer... In the case of the step-up transformer, the signal source driving the transformer "sees" the output load impedance attached to the transformer, but it sees it through a ratio related to the transformer turns ratio.

So say you have a 1:1 transformer, with a signal source (and source impedance) connected to the input of the transformer, and a load impedance Z connected to the transformer output. The signal source is driving the magnetizing inductance of the transformer, in parallel with the load Z, because for the 1:1 transformer, the output load is transformed to an equivalent input parallel load directly by that 1:1 ratio.

But if you use a 1:2 step-up transformer, the load impedance Z is transformed across to an equivalent load of Z/4 in parallel with the input of the transformer (the load transforms across by the square of the turns ratio). So if the signal source has a low enough output impedance compared to that load impedance, it will drive about 4X the current through that equivalent load, in order to be able to support twice the output voltage at twice the output current (4X the power). So if you want to get twice the voltage out of a transformer (which also doubles the current through the load Z), you need to drive more input current, and hence the input and output powers are the same (actually less at the output for a real transformer with losses).

The more traditional way of stating all of this is to make the load lighter for the 1:2 step-up case (Z --> 4*Z) , and then you can say that you have twice the output voltage (compared to a 1:1 transformer), and half the current. That is the equivalent power case.