5VDC and 10VAC on the same PCB - what happens on 10V goes to 5V ground?

Question

Me and a colleague (we are both EE-trainees) had a chat the other day about mixed voltages on the same PCB. She pointed out an interesting question that I was not able to solve.

Imaging having a PCB that use a ground plane for the 5VDC and the 10VAC/50Hz somewhere else on the board (not interconnected with any 5VDC-part whatsoever). That is, they are two completely separate voltage lines on the same board. The 5VDC is not derived from the 10VAC in the power supply, everything is separated.

Now, my colleague blurted out this one:

Imagine I make a mistake when soldering, so that one of the two 10VAC-cables also gets attached to the ground-plane (for 5VDC). Nothing will happen to the 10VAC-circuit since only one of the cables is misplaced, but how will this single cable affect the 5VDC-ground?

After two days I am still not able to answer that question. I cannot grip this question theoretically and I do not have any equipment to try it out practically.

I'm thinking on the one hand: 5VDC will be unaffected since there is no path to the second 10VAC-cable, so there will be no short or anything like that.

And I'm also thinking on the other hand: Will the 10VAC induce noise to the 5VDC-ground, making all 5VDC-circuits unusable?

What will happen?

EDIT: added pseudo circuit schematic

^{simulate this circuit – Schematic created using CircuitLab}

Answer 1

Well it depends, but just about every device running off a floating (rather than earthed) DC power supply already has both of its power input potentials relative to earth oscillating at mains frequency and at a good portion of mains voltage, merely staying at a fixed potential relative to each other - and obviously these devices are still operational. Designing a device that is too sensitive to mains frequency interference will make it generally inoperable in normal household conditions. If the device was operational before, you should expect it to be operational after you short one of the floating AC lines to DC.

The oscillating potential is not measurable, as the moment you connect your voltmeter between the power supply outputs and the earth, the voltmeter resistance of maybe 10 or 20 MOhm will pull the potential in question to ground.

It's a bit more difficult to predict what will happen due to higher frequency AC. Some common mode noise current may be induced, but again this is always something to contend with, and fundamentally same as proximity with no short. The DC power supply actively drives one of the outputs with low impedance to maintain a fixed voltage.