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The Magic Current Factor

When you ask people why you can die of electrocution if you touch a 230-volt wall socket but usually not when you touch an electric fence (those which are used to deter cattle from leaving an area) which can have several tens of kilovolts, they usually respond with the classic "yes, the voltage is very high but the current is very low".

By itself that answer doesn't make any sense. People talk about voltage and current and what can kill a human as if there was some kind of magic current factor involved which would lower the current in certain situations.

Assuming that the resistance of the human body does not change between tests, the current traversing through it is 'I=U/R' where 'U' is the voltage difference between the wire and the ground. It is rather clear from this formula that if 'R' stays the same then increasing 'U' will increase 'I' accordingly.

However, the overly used cliché answer "yes, high voltage but low current" sounds like there would be some kind of magic factor in that formula, like it was 'I=f*U/R' where 'f' is this magic factor: The smaller 'f' is (determined by some unexplained phenomenon) the lower the current, even if 'U' is large.

But of course this is nonsense. The formula is 'I=U/R', period. There's no magic factor. If the resistance of the human body is 'R' and the voltage difference between the wire and the ground is 10 kilovolts, then 'I' will be much higher than if the voltage difference was 230 volts. There's no lowering factor there. Thus the explanation, as it is, is wrong (or at least very lacking and non-explanatory).

The true explanation why the fence is (mostly) not lethal has to do with time. When not connected to the ground the voltage difference is indeed several tens of kilovolts, but immediately when it is connected to the ground (eg. through a human body) the voltage very rapidly decreases down to almost zero.

Thus the amount of current traversing through the human body is indeed really high, but it is this high only for a really small amount of time and it very rapidly decreases to almost nonexistent. While it is enough to give a huge shock, the short duration of the high current makes it non-lethal.

With the 230-volt wall outlet the problem is that the voltage difference, and thus the current, is maintained continuously, and it's this continuous high current that can kill.

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