> Assume I'm running an gasoline powered generator which produces 120VAC for a single outlet. As far as I can tell, this is an ungrounded isolated system analogous to the isolated transformer. If I'm barefoot and standing on wet concrete, and stick my wet finger into only one side of the plug, will I receive a dangerous shock?

Theoretically, no. Your generator isn't going to pick up large static voltage from the atmosphere the way a power grid does, so it's theoretically safe to leave it ungrounded.

However, I would strongly advise against actually doing this experiment unless you are absolutely certain that your generator is isolated from the ground, and even then I would advise against it. Some risks are not worth taking even in the name of science.

> However, I would strongly advise against actually doing this experiment unless you are absolutely certain that your generator is isolated from the ground, and even then I would advise against it.

A safe version of the experiment would be to take a standard incandescent lightbulb and run one wire to an earth ground and one wire to one side of the plug on the generator. My guess is still (although with more doubt based on how many intelligent people here have opined otherwise) that because of the enormous capacitance of the earth, the light bulb would still light up even though no clear circuit is formed.

In my quite possibly flawed mental model, electrons will be pulled and pushed from the earth across the filament, causing it to heat up. Whether this actually works (in my mental model) depends on the frequency and the capacitance of the generator, but I'm guessing that at 60Hz whatever is inside the generator is enough to get an effect. Unless someone has already done this, I guess I'll have to get a generator and try it.

> My guess is still ... that because of the enormous capacitance of the earth, the light bulb would still light up even though no clear circuit is formed.

Your statement implies that you are viewing the earth as a huge, perfect, capacitor. And by "perfect" I mean no series resistance.

In reality, the earth is a relatively poor electrical conductor (i.e., a high resistance [1]) and so where your mental model breaks is omitting that resistance from consideration in your model.

I.e., the equivalent circuit your 'experiment' produces would be:

   G-----bulb------R--C 

The "R" and "C" above are the capacitance and resistance of the earth. Yes, there is an amount of C present, but there is also a quite large series "R" present as well. And it is that resistance that results in a very limited current flow from your theoretical experiment. Too low of a flow to illuminate the bulb.

[1] https://en.wikipedia.org/wiki/Soil_resistivity

Your mental model is correct, but there's a matter of orders of magnitude, as I explained above. A standard incandescent lightbulb isn't going to light up until you have tens or hundreds of milliamps going through it, so it's possible it could still be dark at a current where you would be dead. At the microamp levels you'll actually see in this situation, you might be able to get an NE-2 neon bulb to light up. (Don't forget the ballast resistor.)

A good example are the helicopters with workers inside that work on high voltage lines while they are charged.

The workers touch the lines to bring themselves (and the whole helicopter) to the same voltage and then get to work. That high of voltage should be fatal, but voltage is relative. They are at the same voltage and there's no path for the electricity to follow.

In a truly ungrounded system, if you touch one of the wires in the system, your body will match the voltage of that wire and nothing "bad" will happen. Only if that voltage has a connection back to the other side of the system will current flow through you, either by touching the other wire or if one of the wires is grounded and you touch the "hot" side.

It's a great example, but a very different one. In the case of the helicopter, there truly is no path to ground. In the case of a person standing barefoot on wet ground, they (potentially) become the ground. If the human touching the wires is ungrounded (as in the case of the helicopter), there is no difference in this case whether or not the system itself is ground connected. The question is how much difference it makes for the system to be grounded if the human is also acting as a ground.

Note that I am not encouraging you to conduct this experiment :)

You are correct that there will be at least 60V that exists between your body and at least one of the wires from the generator. What isn’t guaranteed to exist is a low impedance loop for that current to flow through your body back to the generator. You’re in bare feet on the concrete, but the generator has a plastic body with rubber feet.

People repeat that old “it’s the current that kills you” line and often in a misguided and dangerous way, but it’s actually true in this case. If there’s no way for the current to flow back to the generator, the voltage on its own will likely not do much.

If you were to touch both wires while wearing rubber gloves, you’d be in a similar situation. 120V exists across your body, but because the gloves have a very high resistance, no current can flow (I=V/R)

"it’s the current that kills you" isn't the relevant point. The point is that the current through your body that kills you (specifically, the current through your heart, not merely through your fingertipes). Touching a high-current wire doesn't send high current through your body (same as high-voltage across your body) unless there is a circuit (as you correctly wrote).

Capacitive coupling within small portable generators is a bit of a rabbit hole. Send me an email and I can discuss.

Edit: kragen has good overview of this below from the generator in a puddle.

Now in practice, most small generators that you buy as a consumer are "floating neutral," which means that the generator chassis, EGC, and generator GSC (i.e. neutral) are NOT bonded together. Floating neutral generators are another, very long post.

---

Source: 6 years ago, when the NEC changed substantially for small portable generators, I wrote a multi-part series on all of this for a trade magazine in the pro audio industry, who make prolific use of portable power distribution systems, and generators, in the 3kW to 500kW size range.

In the course of writing that series, I dealt directly with the EE who works for PGMA, the portable generator manufacturer's trade organization.

So, it's true that the capacitive coupling of the system to ground allows some current to flow. If you connect yourself between one point in the circuit and ground in the way you describe, you become a resistor of about 1kΩ between that point and ground, and so you bring that point in the circuit to very nearly ground by virtue of flowing a current through your body. The question is, how big is that current?

It turns out that that current is precisely equal to the current flowing through the impedance between the other side of the circuit ("neutral", if you're connected to the "hot" side) and true ground. If we suppose that that impedance is purely capacitive, the question is just how big the capacitance is, because that tells us how big the impedance ((2πfC)⁻¹) is, and thus the current.

If it's 0.1 pF, the impedance at 60 Hz is 27 GΩ, and the current is 4.5 nA.

If it's 100 pF, 27 MΩ and 4.5 μA, which is still too small for you to feel. Megohms to tens of megohms is a typical resistance range for protection in the kind of neon-bulb testers that use your body to detect hot wires, because microamps are still enough to light up a neon bulb visibly.

If it's 0.1 μF, 27 kΩ and 4.5 mA. At this point you will probably yell and let go rapidly, but you will retain control over your muscles; this is still uncomfortable rather than hazardous.

If it's 1 μF, 2.7 kΩ and 45 mA. At this point your muscles will spasm and, depending on how you happen to be connected, you may be unable to let go until somebody else pulls you off. You will probably not die or suffer any permanent damage but it may be a few days before you feel okay again.

If it's over about 3 μF, and your body's resistance has become the limiting factor in the situation; for the purposes of electrical safety, it's not really any safer than if you had the generator grounded to start with.

So, the question is, how much capacitive coupling are you going to have between your gasoline generator and the actual earth, or rather, the wet concrete you're standing on? And this depends on geometry. Let's suppose the generator has a steel base, connected to its neutral wire, that is ¼m² and suspended on rubber feet of 10 mm above that same wet concrete floor. In this situation C = εA/d ≈ 220 pF, so you're down in the microamp range, three orders of magnitude away from an uncomfortable shock. If you instead have the generator on a dry wooden pallet or a dry concrete floor, you'll have about an order of magnitude less capacitive coupling. If it's on a dry wood floor elsewhere in the house and you're down in the basement standing on the wet concrete, you'll have about two orders of magnitude less capacitive coupling.

So in this situation what you need to worry about is not really the capacitive coupling; it's that maybe one of the rubber feet has a steel screw in the middle that has made conductive contact with the puddle.

Higher voltages make capacitive coupling more dangerous; you've probably seen the video of the lineman coming in on a helicopter to repair a live 100kV line, finishing by flying away while a meter-long arc connects his helicopter to the line. That's tens of milliamps of displacement current flowing across the helicopter's capacitance to the Earth, even though the helicopter is considerably further from the Earth than our hypothetical generator is from your wet concrete.

Is that helpful?

> Is that helpful?

Yes, this is tremendously helpful for putting numbers on my intuitions. To understand the details, I'll need to think about it more tonight when I'm less distracted. As a starting question, does the capacitance internal to the generator matter, and what level might this typically be?

Also, how did you estimate the 1KΩ resistance to ground? Mostly as an aside, I presume you are familiar with the possibly apocryphal story of electrocution with a 9V battery? https://darwinawards.com/darwin/darwin1999-50.html

> does the capacitance internal to the generator matter, and what level might this typically be?

It might, but it can only make the situation safer. For example, if the "neutral" wire's only connection to the chassis is through its capacitive coupling to that chassis, then the impedance from that capacitance is in series with whatever the chassis-puddle capacitance is. Typically such capacitances are going to be much smaller, because the chassis and hypothetical puddle have much larger surface areas than anything else in the generator. Some can be larger, but their impedance isn't going to go below zero. (A sufficiently large tuned inductance could go below zero, but it would have to be very carefully tuned to lower the impedance rather than increase it.)

> Also, how did you estimate the 1KΩ resistance to ground? Mostly as an aside, I presume you are familiar with the possibly apocryphal story of electrocution with a 9V battery?

Mostly by sucking on ohmmeter leads in the past, although it's also common in textbooks. Yes, I've heard the story; if I had heard it earlier, I might have been more reluctant to suck on ohmmeter leads, although modern digital VOMs use smaller currents that are probably not dangerous.