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I have a few circumstances which invlove someone being shocked with 20 watts of electricity and whether it would be deadly. So here they are:

  1. Would 1000 volts at 20 miliamperes of AC (2MHz frequency) be dangerous or deadly?

  2. Would 1000 volts at 20 miliamperes of DC be dangerous or deadly?

  3. Would 10 Kilo volts at 2 miliamperes of AC (2MHz frequency) be dangerous or deadly? and

  4. Would 10 Kilo volts at 2 miliamperes of DC be dangerous or deadly?

Thanks for everyones help.

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    \$\begingroup\$ You're missing very important thing: For how long? I'm pretty sure all of the options above would be very deadly, if sufficient energy is used. \$\endgroup\$ – AndrejaKo Mar 7 '15 at 8:38
  • \$\begingroup\$ It doesnt matter too much, A relatively short time though \$\endgroup\$ – Boris Deletic Mar 7 '15 at 8:41
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    \$\begingroup\$ RF voltages can be awfully painful, I know from personal experience with a 450MHz transmitter. I had a hole punched in my thumb for just grabbing on N-connector while the transmitter keyed. Range of 100 kHz to 5 MHz RF can be used for surgery and is used because of the fact that it largely instantly stops bleeding. en.wikipedia.org/wiki/Electrosurgery \$\endgroup\$ – jippie Mar 7 '15 at 8:58
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    \$\begingroup\$ possible duplicate of How much voltage is "dangerous"? \$\endgroup\$ – Roger Rowland Mar 7 '15 at 9:02
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    \$\begingroup\$ Boris - LISTEN. Heart muscle current tends to be the killer. Various things initiate it. I would not trust my life to ANY source that can possibly produce 20 mA or more across my chest. | In very exceptional cases people have died with current from a 12 volt source. Wattage is an interesting thing to calculate along the way - current is the key focus.| Also - once VF (ventricular fibrillation) is induced there is no certainty that it will stop and that normal heart operation will resume when the current is removed. So "a short time" is long enough to kill you once VF has started. \$\endgroup\$ – Russell McMahon Mar 7 '15 at 10:09
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Don't try this at home - my answer is only based on internet research not medical knowledge.

Only the 20 mA DC looks lethal, the rest are probably OK, might just cause some skin burns.

Voltage and current

The voltage is not all that important, as long as it's enough to drive that much current. Current is what is dangerous to humans, and all discussions about safety end up discussing the current.
In fact, as skin resistance is some 1-100 kOhm, a voltage of 10 kV will always drive more than 2 mA through a human, but if you specify 10 kV limited to 2 mA then the voltage will drop as appropriate.

Time of exposure

The length of the exposure to current is the first factor. Wikipedia has a nice graph: Current danger

Log-log graph of the effect of alternating current I of duration T passing from left hand to feet as defined in IEC publication 60479-1.
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

Frequency of the current

This Answer has a good overview of current and safety. I've copied across the best table from the answers there, the results of experiments by Charles Dalziel:
Table of current dangers
Due to the way that nerves conduct information as a series of almost digital impulses, the body is much more sensitive to 60 Hz AC than DC. 10 kHz is also less dangerous, presumably too fast for the nerves to respond to.

At much higher frequencies, many MHz to GHz, the skin effect becomes important. This causes the current to be concentrated on the outside of the body. It's why your microwave oven only heats the outside inch or so of the food. 2 MHz is quite low, so this probably isn't the most important effect here. Also, most of your nerve endings are in your skin, so having the current concentrated on the surface should mean that you feel it more.

Finally, for interest, I'll quote an experiment, showing the drop in nerve sensitivity with higher frequencies:

The unstoppable Don Klipstein, now 20 years on the net, performed an experiment on himself, where he reported

I connected a variable frequency sinewave generator to an audio power amplifier, which drove a step-up transformer. With one wet hand, I touched the two high-voltage-side terminals of the transformer. With the other hand (insulated), I varied the voltage and frequency the first hand was getting.

Results:
Low audio frequencies 80 Hz and less seem most shocking. As frequency was increased above about 80-100 Hz, the burning/pain sensation decreased but the "tingly" shocking sensation did not lose much of its intensity until the frequency reached 500 Hz. Roughly at that point, the shock began to be less intense in all ways as the frequency was increased further. It was noticeably less intense at 1 KHz than at 500 Hz, and a fraction as intense at 5 KHz as at 500 Hz. At 20 KHz, there was almost no sensation of shock at voltages where lower frequencies are painful.

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  • \$\begingroup\$ "skin effect" isn't relevant to mixed materials. I have a post on that. \$\endgroup\$ – JonRB May 9 '16 at 21:47
  • \$\begingroup\$ @jonrb my answer made it sound like Don Klipstein's quote was because of the skin effect, which was not the case. The effect still happens in any conductor, the equations don't mind if it's meat or metal. But skin depth is much deeper in meat. I also had a long answer with some figures. \$\endgroup\$ – tomnexus May 10 '16 at 4:46
  • \$\begingroup\$ Not with meat (the key is humans are not a slab of meat... Layers). Ill find my post \$\endgroup\$ – JonRB May 10 '16 at 6:25
  • \$\begingroup\$ BEST: A shock that makes you voluntarily or unvoluntarily pull away from the source. WORSE: An uncomfortable shock that has you cursing and screaming while locking your muscles to the source. WORST: One you do not perceive as very uncomfortable while it has catastrophic health effects... \$\endgroup\$ – rackandboneman Aug 28 '17 at 1:02
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    \$\begingroup\$ Oh, and: If doing stupid experiments, do not rely on a measurement of skin resistance made with a low-voltage multimeter.... \$\endgroup\$ – rackandboneman Aug 28 '17 at 1:05
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The relationship between voltage, current and resistance is the well known Ohm's law, or V = I R.

You are stating levels of both voltage and current. The skin resistance is also relatively constant (depending on whether it is dry or wet). So you are essentially trying to specify values for all three variables in the equation at once, and Georg Ohm doesn't appreciate that. Given a set skin resistance, you can specify only the voltage or the current but not both.

The National Institute for Occupational Safety and Health (NIOSH) did a study on dangerous electrical currents and voltages.

Here are the effects of different currents on the human body:

     1 mA Barely perceptible
    16 mA Maximum current an average man can grasp and “let go”
    20 mA Paralysis of respiratory muscles
   100 mA Ventricular fibrillation threshold
     2 Amps Cardiac standstill and internal organ damage

Note these are independent of voltage. Contact with 20 milliamps of current can be fatal, due to the paralysis of the respiratory system. The NIOSH don't specify the duration of the current, (just "an extended time") but it would have to probably be at least a minute or two (sort of like involuntarily holding your breath). So short (a few seconds) of exposure is unlike to kill you, but it would be uncomfortable.

To get the voltages needed to generate such current, it is necessary to know the skin resistance. The NIOSH says under dry conditions, the resistance offered by the human body may be as high as 100,000 (100K) Ω. Wet or broken skin may drop the body’s resistance to 1,000 (1K) Ω.

So 120V / 100 KΩ = 1.2 mA, barely perceptible. 120V / 1 KΩ = 120 mA and you're dead. So don't play with electricity in the bathtub.

Now you used two examples of 1 kV and 10 kV. Now you've got something else going on. Voltages over 600 volts can rupture human skin, greatly reducing the skin resistance (down to 500 ohms or so).

1000 (1k) volts / 500 Ω = 2 A, cardiac arrest. 10,000 (10k) volts / 500 Ω = 20A, welcome to the barbecue.

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  • \$\begingroup\$ A shocking answer +1 \$\endgroup\$ – Andy aka Mar 7 '15 at 9:36
  • \$\begingroup\$ Thank you, but I beg to differ concerning one part of what you said. you said that if you were to make contact with 120V at 1 Kilo Ohm of resistance, then you would recieve 120mA which would kill you. But what if, like in my examples above, the total power provided by this 120v source is 2.4 watts. Then the total possible current could only be 20mA, it wouldnt be possible for you to be zapped with 20A because there isnt that much current provided by the source. \$\endgroup\$ – Boris Deletic Mar 7 '15 at 10:01
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    \$\begingroup\$ @BorisDeletic Please re-read the first couple paragraphs of my answer. You're still trying to specify both the current and voltage at the same time -- you can't do that. The current is all based on the voltage divided by the skin resistance. If you are telling me a voltage and power (which indirectly tells me the current), then you are arbitrary assuming a specific skin resistance. That's only useful if you are trying to determine what skin resistance would be needed to pass 20 mA at 120V for example. That's a fairly useless question. \$\endgroup\$ – tcrosley Mar 7 '15 at 10:21
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    \$\begingroup\$ @tcrosley Ok, my question was answered a while ago, but I'd like to explain what I clearly said to you previously. You say that at 1000v, the current = V/R. Let's say, that your skin is wet and has a resistance of 1k Ohm. Then the current would be 1000/1000 = 1A, and your dead. I understand that. BUT. If the source of electricity only supplies a maximum of 1mA at 1000v, then it is clearly not possible to supply 1A at 1000v, no matter what the resistance of the circuit/ body is. In my original question and comment to you, I did state the maximum current that could be drawn. \$\endgroup\$ – Boris Deletic May 26 '15 at 6:46
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    \$\begingroup\$ The problem with that course of logic Boris, is assuming there is no capacitance on the HV wiring and it is instantly current-limited. Most sources of HV are either high-power, or filtered using relatively large capacitances. The latter implies that even though the maximum sustained current would be 20mA, the initial "spark" could be much more, and still incite arrhythmia or paralysis. There are many factors to consider when it comes to safety and high voltages. \$\endgroup\$ – rdtsc May 9 '16 at 21:24

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