Transformer Isolation
Isolation is often misunderstood for safety or for somehow limiting the power that can pass through a transformer. Although a transformer CAN increase safety, just the presence of a transformer in no way guarantees it.

Isolation transformers provide Galvanic isolation. The principle of isolating functional sections of electrical systems to prevent current flow; no direct conduction path is permitted between them. 







simulate this circuit &ndash; Schematic created using CircuitLab

The circuit above contains an isolation transformer. However as you can see, if you grab both sides of the lamp you will be electrocuted just the same as if the transformer was not there. 

What about this circuit? Is it isolated?







simulate this circuit

If you answer yes it is an isolated circuit you would be correct. Some of you will say, "But they are both connected to the same point!", You are right, however that does not matter, there is no current loop between the left side and the right side, so no current can pass between each ground point. They are simply held at the same voltage.

The isolation part comes into it's own by the fact that you can use different references on each side of the transformer. 







simulate this circuit

Notice in this version, though the transformers are basically the same, we can use a different point as a reference to change how the voltage is biased around ground. This is because the circuit, before we grounded it, was actually floating.

You can do much more interesting things with this too, like the following.







simulate this circuit

In short, an isolation transformer de-couples your signal from whatever zero potential reference you are using on the primary side so you can attach it to a different reference on the secondary side.

Conservation of Energy

The other critical thing about transformers is whatever power goes out one side must come in the other. Whether it be a 1:1 transformer like I used here or a step-down or step-up transformer that rule always holds true. (Within the capability of the windings and core anyway.) 

In reality you have to put a little more in than you get out because of losses due to heating and vibration of the transformer. But it can never be less.

That is why isolation transforms give you no guarantee of safety. They may reduce the voltage or current to a level that will not kill you, but the transformer itself can still be capable of supplying the same raw power. 

Indeed in the case of a step-up transformer, it is usually MORE likely to kill you.