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Let's say I have a 230v version of a AA battery resting on a table say, I touch the + terminal, think of me as a resistor of 1 ohm, the circuit needs to close, and can take infinitely many parallel paths, which is a bit confusing, but let's think of it as a single path to the - terminal.

The ground acts as a resistor, the resistance of the floor under my feet, up through the table legs through the air and into the - terminal. Think of the floor, table legs etc as another resistor with an enormous resistance, we now have a circuit with 2 resistors, first the me resistor of 1 ohm (say, just for a sense of ratio) and then the ground resistor of 1000000 ohms or some huge number, now the current through the circuit is miniscule and the voltage difference between my hand and the floor should be tiny no?

Equally, if I get one of the table legs, and use it to touch the + terminal with instead, I would expect this to be very safe? But what has changed, the resistance in the system hasn't changed much (ok now I force the circuit to mostly go through a table leg, but I don't think this is significant as it was always going to have most of its current through a table leg), so the current should be the same?

Equally equally, what's so different if I am levitating instead, now the circuit has to go through the air to reach the floor and air presumably has a really big resistance, several orders of magnitude greater than wood, but I already felt the resistance of the ground should be very big so I don't know I care too much?

To clarify, my question is, why isn't the current through me miniscule when touching a live wire as I imagine the resistance of the path to complete the circuit to be very high? In diagrams I often see all the grounds joined together to one vertex, but does this really make sense? to get from one ground point to another ground point you have to go through a lot of resistive material incurring a high resistance, no?

daniel purdew
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    It's not clear what your actual question is here. Can you [edit] to improve it? Your body resistance will be in tens of kilohm so you're a bit off there. See https://incompliancemag.com/article/experiments-of-dc-human-body-resistance-i/. – Transistor Mar 21 '21 at 16:48
  • why bother touching the positive terminal of the battery? ... just stand in the same room as the battery – jsotola Mar 21 '21 at 16:54
  • @Transistor thank you I have edited it, noted re the body resistance, I have clarified I say '1' just as some perspective of proportion – daniel purdew Mar 21 '21 at 17:14
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    your whole writeup makes no sense ... the lowest path of resistance is directly between the two battery terminals ... your contact with one if the terminals does not change it much – jsotola Mar 21 '21 at 17:21
  • @jsotola is that really so? why should this be the lowest path of resistance? There it has to pass through some air the length of the battery, passing through me it can avoid going through so much air by going through me, through the floor, up the table and then through a smaller bit of air from the table up to the - terminal. Depending on how much more resistive air is this could be a lower path of resistance? I am sorry that my writeup makes no sense, but that I don't understand is why I am asking a question. – daniel purdew Mar 21 '21 at 17:25
  • @danielpurdew the distance between the positive and negative terminals of an AA cell is less than 1 mm – jsotola Mar 21 '21 at 17:39
  • @jsotola hmm OK that makes sense thank you, what are the implications of this? that circuit is parallel to the circuit passing through me and into the ground etc and is lower resistance, so most of the current from the + terminal goes through this path, but this again makes me think there shouldn't be much current going through me? Does it mean I am safe to touch the + terminal of the 230v battery in the given scenario? And that one of the mistakes in my question has been conflating this situation with that of touching a live mains wire? – daniel purdew Mar 21 '21 at 17:50

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Body resistance varies depending on the path and quality of contact (dry or wet, size of contact, etc.) with the voltage. It’s in the multi-kohm range, so not so high that direct contact with 230V won’t possibly be fatal.

Ground, by definition, has practically no resistance. In practice electrical systems take great pains to minimize their resistance to ground, including driving large copper spikes into the earth to form a good low-resistance connection. The power panel ground will have a resistance to earth 25 ohms or less if it meets codes.

You’re also overlooking a detail: with AC, the current will find its way through any capacitance present as well. This means that, even if you are insulated from ground by say, wearing rubber boots, touching live AC will charge and discharge through your body to the dielectric that’s doing the insulating. So even with those rubber boots you’ll still receive a shock, though not as much as if you were standing on the ground with bare feet.

This is why power poles use large stand-off distances for the high-voltage wires. This decreases the capacitance as well as increasing the insulation resistance. This is done for safety as well as reducing line losses.

Your ‘levitation’ case is the classic bird on a wire: the bird assumes the potential of the wire with no direct path to ground, and a very large insulation distance, so very little current flows through the bird.

Related: Professor said no current flows to ground

hacktastical
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  • The key detail seems to be that you are saying somehow the resistance to earth aims to be less than 25 ohms, I don't understand how this is achieved, I am standing on a wooden floor right now and I know that there are no conductive materials withing several meters of me on the floor, if I touch a live mains wire hanging from the ceiling, it has to at least go through the floor and up the walls and into the neutral wire. Is this not a lot of resistance? Do I just have no notion of the numbers involved? – daniel purdew Mar 21 '21 at 17:28
  • @daniel purdew 25ohms if we use suitable large copper conductor, whose one end is inside the earth and other connected to wire (May be your body) directly – user215805 Mar 21 '21 at 17:38
  • The wood floor would be an insulator, sort of. Wood resistance isn’t perfect and depends on a lot of factors, such as moisture, density, thickness, distance to source. If you also touch something metal that’s grounded, all bets are off. This is why safety grounds are used: you can’t count on the body always being insulated. – hacktastical Mar 21 '21 at 17:40
  • I think you may neglect capacitance. It is very low with any gloves or boots. And electricians really use insulating boots and gloves when working with low (240-1000V) voltage systems. – AlexVB Mar 21 '21 at 17:44
  • @danielpurdew if you stand on clean dry wooden floor you probably can touch a wire and survive. But one day it may be not so dry and 100mA is enough. – AlexVB Mar 21 '21 at 18:01
  • Don't forget that AC has the unhealthy habit of going through capacitances. You might have a big series resistance, but if you are capacitively coupled to a return path in parallel to that... – Sredni Vashtar Mar 21 '21 at 19:29
  • @danielpurdew earth has low impedance between two points despite typically higher resistance per cross sectional area times length because it has immense cross sectional area. The two points are connected through the earth in a straight line, but in addition to this they are connected in parallel to each other in every other direction. This gives you a conductor with effectively infinite thickness with the caveat that each layer of thickness has some added length from having to go around the more direct conduction paths. – K H Mar 22 '21 at 04:14
  • Similarly, wood is not a great conductor, but once you add stain or varnish and coat it, your conductivity could change. The part of it touching the bottom of your feet is rather large by conductor standards, and the part of it that is thin is still minimum 5/8 thick, typically includes glue that could be more conductive, and is in contact in every other direction with a large amount of wood and metal (including G wires), all that branching out and connecting down to an immense surface of actual ground. The way it branches out gives it low inductance (which objects to fast current change). – K H Mar 22 '21 at 04:20
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It's not really possible to analyze what's going to happen without reasonable approximations for all the resistance values.

A person will typically be a few thousand ohms, depending on how damp their skin is. It's the skin that's the best insulating part of a person. The resistivity of wood varies a lot depending on whether it's wet or dry. Dry wood is a pretty good insulator. A metal chair would be a really good conductor. But if it has plastic feet on the bottom, it will make very poor contact with the floor.

When looking at circuits diagrams, don't assume that "ground" is always the Earth. The two tend to get mixed up in confusing ways. Sometimes "ground" is no more than a common conductor that links all the things at 0V together.

Simon B
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