Is 20 watts of electricity dangerous?

Question

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.

Answer 1

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:

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:

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.

Answer 2

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.