# Lethal Voltage vs. Current: Exploring the Truth Behind Electrocution

• Metallus
In summary, the conversation discusses the concept of voltage and current being lethal to humans. It is determined that it is the combination of both and not just one factor alone that can cause harm. Furthermore, the source impedance is taken into account, as well as the duration of the shock. It is also noted that the amount of electrons is not the determining factor, but rather the amount of charge. Overall, the exact workings and effects of voltage and current on the human body are complex and require further study.
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?

Metallus said:
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

Metallus
davenn and 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.

@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

Metallus said:
@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.

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.

https://en.wikipedia.org/wiki/Electric_shock said:

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 and berkeman
@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?

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.?

anorlunda said:
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?

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.

anorlunda said:
, 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.

sophiecentaur said:
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.

anorlunda said:
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.

sophiecentaur said:
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'.

## 1. What is the difference between voltage and current?

Voltage is the measure of the potential energy difference between two points in an electrical circuit, while current is the flow of electric charge through a conductor. In other words, voltage is the force that pushes the electrons, while current is the rate at which the electrons are moving.

## 2. Can voltage or current alone cause electrocution?

No, both voltage and current are required to cause electrocution. Voltage determines the severity of the shock, while current determines the path the electric current takes through the body.

## 3. How does the human body respond to different levels of voltage and current?

The human body is a good conductor of electricity, so when exposed to voltage and current, the body will allow the current to flow through it. Low levels of voltage and current may cause tingling sensations, while high levels can cause severe burns and damage to internal organs.

## 4. Is it true that higher voltage is more dangerous than higher current?

While both voltage and current can be dangerous, higher voltage is generally considered more dangerous than higher current. This is because higher voltage has the ability to overcome the body's natural resistance and cause more damage to the body's tissues.

## 5. Are there any safety measures that can be taken to prevent electrocution?

Yes, there are several safety measures that can be taken to prevent electrocution, such as using ground fault circuit interrupters (GFCIs), keeping electrical equipment away from water, and following proper safety procedures when working with electricity. It is also important to have a thorough understanding of the dangers of electricity and to use caution when working with electrical equipment.

• Electromagnetism
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