"RCDs operate by measuring the current balance between two conductors using a differential current transformer.
This measures the difference between current flowing through the live conductor and that returning through the neutral conductor.
If these do not sum to zero, there is a leakage of current to somewhere else (to earth/ground or to another circuit), and the device will open its contacts.
Operation does not require a fault current to return through the earth wire in the installation; the trip will operate just as well if the return path is through plumbing, contact with the ground or any other current path. Automatic disconnection and a measure of shock protection is therefore still provided even if the earth wiring of the installation is damaged or incomplete.Residual-current detection is complementary to over-current detection. Residual-current detection cannot provide protection for overload or short-circuit currents, except for the special case of a short circuit from live to ground (not live to neutral).
For a RCD used with three-phase power, all three live conductors and the neutral (if fitted) must pass through the current transformer."
-----------------
I don't totally buy into some of the copy paste wiki info above,
if anyone is game to try an RCD sold in Australia on a TRUE isolation transformer, they may be surprised that it won't work,
because there is no leakage to earth/ground or anywhere else in most cases to create an imbalance and make it trip
and any RCD sure as hell won't trip on a LIVE to Neutral BANG! unless it's an RCBO or combined RCD/MCB type
extra surprise surprise: if an RCD does trip when used with an isolation transformer, then that particular transformer is NOT truly/fully isolated
i.e. even if you THINK you know what you're doing, and have all the right gear, some combination of the above may bite you