Lethal Voltage vs. Current: Exploring the Truth Behind Electrocution

[Metallus]

Hi there,
I have very big doubts about this. I keep hearing that it's not the volts that kill you but rather the amps. 60 mA are supposedly enough to kill a person.

Let's consider a person with 100.000 Ω resistance. If V = R⋅I, then V = 0.06 A ⋅ 100.000 Ω = 6000 V, and that would be the voltage required to generate 60 mA in the human body.

However, static electricity can accumulate over 25 kV. According to the above calculation, that would be 4 times overkill, yet no one gets electrocuted by a discharge after touching his/her car or rubbing a carpet. At the same time, voltages as low as 100V with 60 mA current can be lethal.

Why is that? How does it exactly work? Why some people can survive a lightning which supposedly carry 100.000 kV? How can you mathematically justify this?

 

[berkeman]

However, static electricity can accumulate over 25 kV. According to the above calculation, that would be 4 times overkill, yet no one gets electrocuted by a discharge after touching his/her car or rubbing a carpet. At the same time, voltages as low as 100V with 60 mA current can be lethal.

The difference with static charge is the source impedance. Typical source impedance for a person (the "Human Body Model" for ESD) is about 100pF and 1500 Ohms in series. There is not much energy in that.

However, having been shocked accidentally by an ESD gun during product testing, I can tell you that taking such a shock arm-to-arm hurts like hell, and definitely came close to putting my heart into fibrillation...

https://en.wikipedia.org/wiki/Human-body_model

 

[phinds]

@Metallus this question has been asked (and discussed) here several times before. I suggest a forum search.

For example:

https://www.physicsforums.com/threads/does-current-or-voltage-kill.757376/page-2

Most basic questions have been asked here many times so a forum search is always a good way to start when you have a question.

 

[Metallus]

@berkeman: how does that enter the formula? If the source has a large internal resistance, then that would mean that the total resistance is not 100.000 Ω but more. Still, it would need to be 4 times higher to reduce the current below 60 mA. Please, help me understand it from the mathematical point of view.

@phinds: I've read several topics about this issue and I was never convinced and that is why I created a new topic. Even the video in that topic shows big current with low voltage and viceversa, but the "high voltage" is 4 V. In fact he says that both voltage and resistance are necessary, and that is okay. I understand it and it makes sense. But then I'd also expect hundreds of kV to be lethal even with big resistance (and it is not always the case).

If 60 mA is the lethal current and you need 100 V baseline to get through human skin, then 6000 V should be enough to kill in all cases, unless some other variable comes into play. If it does, as berkeman mentioned, I would like to know how it affects the general formula V = RI and how it would "adjust" the real value of current or voltage to make sense.

Thanks

 

[berkeman]

@berkeman: how does that enter the formula? If the source has a large internal resistance, then that would mean that the total resistance is not 100.000 Ω but more. Still, it would need to be 4 times higher to reduce the current below 60 mA. Please, help me understand it from the mathematical point of view.

It's the small capacitance of the HBM that limits the energy delivered by the static shock.

 

[anorlunda]

Current and time are what is plotted below. Consider an electrostatic shock as the OP mentioned. It has a very high voltage, but the shock only lasts a few microseconds (nanoseconds?), not long enough to be lethal.

Log-log graph of the effect of alternating current I of duration Tpassing from left hand to feet as defined in IEC publication 60479-1.[19]
AC-1: imperceptible
AC-2: perceptible but no muscle reaction
AC-3: muscle contraction with reversible effects
AC-4: possible irreversible effects
AC-4.1: up to 5% probability of ventricular fibrillation
AC-4.2: 5-50% probability of fibrillation
AC-4.3: over 50% probability of fibrillation

For DC, the same article says.

The current may, if it is high enough and is delivered at sufficient voltage, cause tissue damage or fibrillation which can cause cardiac arrest; more than 30 mA[6] of AC (rms, 60 Hz) or 300 – 500 mA of DC at high voltage can cause fibrillation.

 

[Metallus]

@anorlunda: so it's not actually the current (meant as rate of electron transfer, Q/t) but rather the amount of electrons itself, Q, that can be lethal? Because from that graph I see that 60 mA (danger current) corresponds to AC-4 only at 1s.

Therefore a spark from static electricity, even with a I = 25 kV/100 kΩ = 250 mA would not be lethal because for t < 20 ms it would fall under the green area AC-2 (Q < 0.005 C). This would also come into agreement with what berkeman said, because if the capacitance of the body is only 100 pF, then even if I have accumulated 25 kV, I can only carry 2.5⋅10^-7 C and that is the amount I can discharge at 250 mA (so t = 1 μs).

Did I get it right?

 

[anorlunda]

You got it mostly right, but the part about the number of electrons goes too far.

Who knows how those curves are shaped off the scale of that graph.?

 

[Metallus]

You got it mostly right, but the part about the number of electrons goes too far.

Who knows how those curves are shaped off the scale of that graph.?

Are you referring to the statement "Q = amount of electrons" or to the fact that I assumed those curves kept their trends below 10 ms?

In the former case, is it wrong to assume that Q is the amount of electrons? I mean, Q would be the amount of charge equivalent to that carried by 6.242×10¹⁸ protons (which is the equivalent to that of electrons changing sign), but we know that it's actually electrons that move. Is it wrong to affirm that?

 

[anorlunda]

Current times time has the units of charge, correct. What I meant is that it is wrong to think the biological effects are linearly proportional to any electrical quantity. Biology is highly nonlinear.

 

[sophiecentaur]

, but the part about the number of electrons goes too far.

There is a wide range of conditions where the green curve agrees with the simple rule that it's the charge that counts.

 

[anorlunda]

There is a wide range of conditions where the green curve agrees with the simple rule that it's the charge that counts.

Do you mean the green straight line segment? That's not lethal. Constant charge would make a hyperbola on an I versus t plot.

 

[sophiecentaur]

Do you mean the green straight line segment? That's not lethal. Constant charge would make a hyperbola on an I versus t plot.

The scale is log/log and it looks to me that an increase of a factor of 10 corresponds to a decrease of about a factor of ten. So the threshold is pretty much based on total charge - I think.

 

[anorlunda]

The scale is log/log and it looks to me that an increase of a factor of 10 corresponds to a decrease of about a factor of ten. So the threshold is pretty much based on total charge - I think.

my mistske, I missed the log-log.

But I think that it is a dangerous concept to publish on a public forum that a trivial calculation of charge is all that is necessary to determine safety. We should always refer laymen to safety codes and discourage them from attempting their own calculations.

 

[sophiecentaur]

Agreed. Particularly because it is pretty well impossible to build into any system you might design a metered dose of shock. Basically the recommended level should be ZERO! and leave the protection to 'the regs'.