What ultimately kills you is a large current passing through your heart.
However, for that large current to exist, you need enough voltage to counter-balance the resistance of your body. If you’ve got a 12V source, it’s basically impossible to die because your skin resistance is 1k+. So the maximum current that could be passing through your body (given Ohm’s Law) would be 12 / 1k = 12mA. Since it takes about 50mA before you’re in truly dangerous territory, you’re mostly safe (if you reduce skin resistance such as by wetting the skin, this can still be a problem).
On the other hand, even with extraordinary high voltages you could also be safe if the power source has insufficient power. When we refer to the ‘current’ of a power source we’re really talking about the maximum current we can draw from the power source instead of what is actually flowing out of the power source (this misuse of ‘current’ is why so many people get confused).
If you had a power source with 1kV but only able to provide 1W of power, then the maximum current – regardless of resistance in the circuit – that could occur would be 1 / 1k = 1mA.
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