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I found this question about isolating transformers in the NZART question bank, but I can't figure out the meaning of the answer. Either the answer is misleading or I'm fundamentally misunderstanding something:

#10.10 An isolating transformer is used to:

1) ensure that faulty equipment connected to it will blow a fuse in the 
distribution board 
2) ensure that no voltage is developed between either output lead and ground 
3) ensure that no voltage is developed between the output leads 
4) step down the mains voltage to a safe value

The answer is given as:

2) ensure that no voltage is developed between either output lead and ground

Now I understand what an isolating transformer is, but the answer doesn't make sense because if there is no voltage developed between either output and the ground then that necessarily means that the voltage difference between the two output leads is 0 because if there were a different voltage on either output lead then one of them must be a different voltage than ground.

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if Vg = V1 and Vg = V2 then V1 must = V2, making the transformer useless.

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Yeah, it's a poorly worded question/answer. There's no DC voltage developed between either output lead vs ground.

You're absolutely correct that there's AC potential developed, because... well... duh. One of the main purposes of an isolation transformer is to isolate DC potential and the question either doesn't make that clear or is trying to get at a different characteristic of the device.

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I agree it's poorly worded, but with MCQs you have to choose the least incorrect answer. 2 is still the obvious choice, the rest are totally wrong or deliberately opposite to the truth.

What they intended is to say that there is no enforced potential between either output and ground. This is quite different to a normal mains socket, where Hot/Live is at 230 V AC and Neutral is at ~0 V. Also no current, AC or DC, will flow through the transformer, so you will get no leakage to earth from any capacitors in the device under test, for example in the EMC filters.

The question is surely written thinking about the problem of measuring voltages on a valve HF amplifier. With an isolation transformer in place, you are less likely to die if you touch something, and you can safely clip your (earthed) scope ground anywhere. Better than lifting the ground of your scope and hoping its transformer does the job.

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Answer 2 is pretty much the whole point of an "isolating" transformer. It isolates.

And no, there is no voltage between either output and ground (except for the leakage current, which, for an 'isolation' transformer is designed to be 'too small to matter').

There is voltage between the two contacts of the output transformer. That does not mean there is voltage to ground.

Since this is a NZART exam question, you can be pretty sure that they are thinking about the high voltage (AC) output of a radio transmitter, both in test and in use.

That explains the wording of the answer: 'touch'. The danger is that you, or someone, might 'touch' the high voltage AC output of the transmitter, or that it might 'touch' something like your iron roof, and make it live.

Yes, an 'isolation transformer' isolates the inputs from the outputs -- so you can hold one of the inputs and one of the outputs at the same time if you also have an isolated input. But that is not the ordinary use case. Ordinarily, if you already have an isolated input, you don't need another isolation transformer.

The ordinary use case is that you do NOT have an isolated input. At least one side is live to 'something else'. The case, the signal ground, the ac ground, neutral, whatever. As it happens, almost always your non-isolated input is not isolated from 'ground' and other non-isolated elements are also not isolated from 'ground' so even if what you really need is isolation from 'conducted interference', that means the same as 'isolation from ground'.

The other main use of an 'isolation transformer' is to isolate "things" that are different potentials -- for example adjacent buildings connected by ethernet cables or telephone lines -- and in that case, you may deliberately connect one side of the isolated output to ground. It's not isolated any more. But the isolation transformer has done it's work of isolating from ground so that you can connect either side (or any point) to ground.

We aren't all radio engineers, and an isolation transformer will create a floating output that is safe in the presence of one (1) ground fault. You can touch either side of the output, and it's safe, because it was isolated from ground. This may be a DC voltage (solar panel) or an AC voltage (test equipment, or equipment under test).

But the answer is generically true even for cases that don't involve the expectation of 'touch'

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