Why does isolation transformer protect from shock?
It's not really meaningful to talk about the voltage between two points that are completely isolated from each other. Any attempt to measure the voltage changes it.
Any real-world voltmeter requires a small current to pass in order to measure the voltage, which means it acts like a resistor. For a modern digital meter, this might be about 10MΩ. So by attempting to measure the voltage between two isolated points, you're changing the circuit by connecting them together.
If you actually tried to measure the voltage between A and G, it probably would be about 0V, but only because you've connected them together through the voltmeter. The same goes for B and G. If you connected two voltmeters at once (A to G and B to G), they would probably both read about 115V.
The keys to understanding this are
- what causes shocks is current through the body.
- the introduction of any extra components into a system can change the voltages. The human body is no exception to this.
Lets consider an experiment. Suppose I have two terminals, one is at ground potential and one is connected to a 230V (relative to ground) supply. Now suppose I have a 10 megohm resistor, lets call the two ends of that resistor A and B. Firstly I connect A to the 230V supply terminal and leave B disconnected for now. Both ends of that resistor are at 230V.
Now suppose I connect my multimeter between end B and ground. My multimeter has a 10 megohm input resistance (this seems to be a de-facto standard on virtually every digital multimeter) so the voltage on B will drop to 115V.
Now suppose (DO NOT DO THIS) I remove the multimeter and touch B and ground. Assuming the resistor is not faulty I do not get a shock because the current will be less than 23uA (the exact value will depend on the resistance of the body which is somewhat variable).
Now getting back to the isolation transformer case. Lets ignore the PC, it just complicates matters.
Suppose there is nothing connected to the output of the transformer. We know the voltage between the two output terminals. We do not know the voltage between the output terminals and ground, with no low impedance path to tie it down it could be virtually anywhere.
Now suppose you touch one end of the transformer and ground. The voltages now shift around so that the end of the transformer you just touched is at damn near ground potential. If you touch the other end then the same thing happens. It's only if you touch both ends at once or you touch one end and the other end inadvertently ends up connected to ground that a significant voltage can be maintained into the load that is your body and hence deliver a current that will give you a shock..