(DANGER: Risk of serious injury or death, do not attempt unless you know what you are doing)
With a 1:1 Isolating Transformer, the voltage on the primary winding is equal to that on the secondary winding. This is particularly useful for safety where an appliance may be used in a wet area or another hazardous location. Usually they are used when someone needs to use a mains powered appliance outdoors such as a power drill or electric lawnmower without the risk of electric shock or death. Typically they come in 120:120 volt or 240:240 volt variants of up to tens to even hundreds of kVA’s. With a slight tweak in the wiring, they can be used to half or even double the input voltage on the output.
Typically the neutral conductor in a mains power system is earthed (grounded) which means that in 120 volt countries the line conductor has a potential difference of 120 volts between the line conductor of your power cord and the ground outside which poses a hazard to the user should a fault occur. This is the same in 240 volt countries except with 240 volts between line and ground. Basically the isolation transformer removes that ground reference which means that there should be zero volts to ground from both the line and neutral pins on the output socket. Note however that touching both pins at the same time is still harmful. The diagram below shows how the transformer is connected.
As you can see above, the “-” terminal is grounded while the “+” terminal isn’t. This means that if a person makes contact with the + line terminal, they would be exposed to a 240 volt electric shock which could very well be fatal particularly if they are outdoors on wet ground.
With the transformer connected, the secondary is isolated from the primary. As the multimeter shows there is around 360 picovolts between the secondary and ground which is highly unlikely to even be felt let alone cause harm. This ensures that any appliance connected won’t shock the user in the event of a fault, unlike if it were connected directly to the mains.
As with most multi winding transformers, their windings can be connected in series to increase the output voltage if they are connected out of phase with each other or decrease voltage when in phase with each other as seen below.
As you can see above, V1 is connected as an isolating transformer with 240 volts going in and 240 volts coming out. V2 has both the primary and secondary in series with the 240 volt supply across both windings. From this 120 volts is present from mains line or neutral to the center point of the two series connected windings. This has the effect of providing 2x 120 volt supplies 180° out of phase with no isolation from the mains which isn’t always desirable. V3 has the 240 volt supply across one winding with the second winding being connected to the line side of the primary from one end only. This means that assuming they are connected out of phase, 480 volts will be present between the neutral conductor and the side of the secondary not connected to the line conductor. As before, this provides no isolation from the mains which may not be desirable depending on the application. This is the same principle that is used in the overwind function of a variac and technically the isolation transformer is being used as an autotransformer which is why there is no mains isolation. If you live in a country with 120 volt mains then a choice of 60, 120, or 240 volts can be derived from a 120:120 volt transformer instead of the 120, 240 or 480 volts that you could get from a 240:240 transformer on a 240 volt supply.
When stepping up voltage the transformer only carries a percentage of the load which is related to the amount of voltage increase. For example I have a 10 kVA load rated for 150 volts and a transformer with a 100 volt input and 50 volt output and my supply voltage is 100 volts. If I connect both windings in series 180° out of phase I get 150 volts out. To run my 10 kVA load, the transformer would need to be rated at 5 kVA instead of 10 kVA as the amount of voltage increase above the supply voltage is only 50% which means the transformer is only going to carry 50% of the full load. Ultimately this can lead to cost savings as smaller transformers are generally cheaper. Only problem with this is the lack of isolation from the mains in this case.