How Hard Is It To Die Of An Electric Shock?

Being both an electrical engineer and a person with questionable judgement, the occasional high-voltage zap is something I've learned to accept as an unavoidable occupational hazard.  I've suffered dozens of 120-volt AC (wall-outlet-level) shocks, occasionally even directly through the chest cavity (traveling from one hand to the other), as well as more low-voltage and DC shocks than I could easily count, with no noticeable ill effects.  The highest voltage I've been bitten by, so far, was a 9000VAC neon-sign transformer, which zapped me (again, through the chest cavity) during an unfortunate attempt to build high-voltage capacitors out of empty malt liquor bottles and salt water in college (note to budding scientists: if science requires empty malt liquor bottles, that doesn't necessarily mean you have to drink all the malt liquor yourself before getting started).  Aside from firing every muscle in my upper body at once and leaving me sore for days, that one didn't hurt me either.  From these experiences, I can draw two possible conclusions:

1. The human body is more resistant to electric shocks than I'd previously been led to believe.
2. Unlike you puny humans, I cannot be killed by electricity.

In the interest of figuring out which of those it is (smart money's on #2, obviously), I decided to look into what exactly it takes to deliver a lethal electric shock to an average-sized adult human. 

Conventional wisdom about electric shocks is that "it's the current, not the voltage" that hurts you.  That's true, at least in the strictest physical sense; voltage is just a measure of potential energy, while current is a measure of the actual number of electrons using your body as a transmission line.  A reasonable analogy would be getting a rock dropped on your head; while the rock had to be up above you (giving it gravitational potential energy) for it to happen, what actually made it hurt is that the rock got dropped from up there and hit you in the goddamn head.  Same deal with electricity; all the voltage in the world doesn't mean a thing if it isn't driving any current, just like the mere act of someone holding a rock above your head isn't going to give you a concussion.  So yeah, you generally need to run some current through your body to do damage, which begs the question "how much?"  And that's where things get complicated.

This otherwise well-intentioned public service announcement from Electric Six critically misunderstands the voltage/current distinction.

Every EE undergrad knows Ohm's law, which states that V=IR, where V is voltage (in volts), I is current (in amps) for some reason, and R is the resistance of your circuit to having current passed through it, in units called ohms.  So to figure out how much current is passing through something, you just take the voltage across it and divide by the resistance.   It's a simple, handy equation that will tell you what's going on in nearly any electrical circuit (until you start throwing semiconductors into the mix, at which point it all goes to hell, but that's neither here nor there), providing you actually know the value of R.  When you're working with basic circuits (generally containing resistors that have their values printed on the side) that's a no-brainer, but it gets weird when you start trying to add more complex elements like "the sack of meat and water that is a human body" to the mix.

The most basic possible electrical circuit.  A voltage V is applied to a resistance R, the value of which decides how much current (I) will flow through the circuit.  Nobody knows why the symbol for current is I so don't ask. 

The resistance "seen" by a high voltage trying to pass current through your body can vary wildly, depending on the path it takes, how wet your skin is, damage to the skin already caused by current, and lots of other factors.  The inside of your body, being mostly water and electrolytes, has a pretty low resistance (<500 ohms), so the resistance of the entire "meat-resistor" is going to depend in large part on the skin resistance.  While a totally dry-skinned person should in principle have a resistance in the 100,000 ohm neighborhood (meaning it would take 100,000 volts to drive an amp through you), natural moisture on the skin usually brings that down to something in the neighborhood of 1,000-5,000 ohms in most situations (it varies by as much as 2-3X by person), and fully wet skin can cause it to be even lower.  So a reasonable, low-end estimate for the resistance of a human body is probably about 1000 ohms.  Keep that in mind during the next part.

As Edison so ably demonstrated back at the turn of last century, low-frequency alternating current (AC, the kind that comes out of our walls) is by far the most likely type of current to electrocute you.  That's because the frequency of the wall current (either 50 or 60 Hz, depending on where you live) is close enough to your heartbeat frequency to scramble your sinoatrial node (the heart's pacemaker) without much trouble, a condition known as fibrillation.  When your heart stops due to fibrillation it's not going to start again without a defibrillator or some very good CPR; basically, you're pretty screwed.  As a result, you really don't need much of this stuff to die; the "death current" is generally considered to be in the range of 0.1 to 0.2 amps.  To put that in perspective, that's 100-200V if we use our 1000-ohm estimate of the resistance of a body.  The standard home line voltage in the US is 120V, so that's more than capable of delivering a lethal shock under the right conditions.  Oddly enough, AC current above 0.2 amps usually isn't lethal, since that much current will cause all your heart muscles to "clamp," preventing the heart from going into fibrillation by just plain stopping it until the shock ends.  Obviously stopping your heart is bad and will eventually kill you, but if the shock is short-duration your heart will probably restart normally afterward without the need for CPR or anything

DC current, which is "always on" and has no frequency associated with it, will have a much harder time killing you but can still get the job done.  The end result is similar; enough current = stopped heart.  In this case the clamping (seizing of all the heart muscles) effect we also see at high AC currents is the culprit; too much DC voltage will stop your heart, which as most people know will eventually make you die.  Fortunately, it takes way more DC current to cause clamping than it does AC current to induce fibrillation; typical fatal DC currents are usually about a factor of two higher than AC (so 0.2-0.5 amps), meaning the associated voltage has to be about twice as high assuming identical skin resistance.  Clamping, as I previously mentioned, is also a reversible condition; if you can get yourself off the circuit before your heart is off long enough to do damage, it'll probably restart and you'll be fine. Even so, a modest DC voltage (a good example is the 48V power applied to certain types of microphones) is perfectly capable of murdering you under the right conditions.

The Neumann U87 patiently awaits its prey

So what are "the right conditions"?  Obviously the electricity is going to need to pass through the heart to stop it, so you need to put your body in the circuit in a way that that's possible (having the current run from one arm to the other is a good way to do it).  Contact area is important; if you're touching a live wire with a fingertip, the total resistance of the circuit formed by your body is going to be much higher than if you grab it with the entire palm of your hand, meaning the shock is much less likely to be lethal.  Similarly, since most of your body's resistance comes via the skin, being wet or damp will bring your total resistance down considerably, reducing the "kill voltage" needed to produce a fatal current.  Conversely, if there's some other source of resistance in the circuit besides your body (a thick pair of rubber gloves, for example) that's going to increase your electrocution-voltage threshold by a lot.  Finally, there's duration to consider; as we know, clamping will take a little while to kill you, and even fibrillation takes a few seconds to take effect, so if you can pull yourself off the source of the shock within a second or two you'll probably be OK.  Interestingly, this is where low voltages can be more lethal than higher ones; voltages (both DC and AC) between 50-500V will usually cause your muscles to contract when shocked, which can result in you involuntarily gripping something that's slowly electrocuting you.  Higher voltages, as I've empirically discovered, tend to just cause all the muscles near the contact site to fire uncontrollably, which usually has the useful effect of throwing you out of the circuit almost instantly. 

So that's the easiest way for electricity to kill you.  Beyond just stopping your heart though, it can also cause nasty internal burns at even sub-lethal currents.  The reason for that is that as current passes through a resistor (or meat-resistor in this case), it loses electrical potential energy, or voltage. This energy gets lost in the form of heat, which means whatever the current is passing through will heat up.  Even currents of less than 50% of the "death threshold" can dump enough heat under the right conditions to cause internal burns.  Interestingly the shorter the path taken through your body the more severe the burn, since the same amount of energy is being distributed as heat over a smaller distance.  When you go to really high currents (like the electric chair or subway third rail) you're going to die of organ failure caused by being literally cooked from the inside out long before your heart ever gets a chance to go into fibrillation or clamping.  In extreme cases, like lightning strikes, it's possible to be completely vaporized from the resistive heat alone.

So to bring this back around to the personal: why didn't my 9000V shock kill or injure me?  My meat-resistance was probably extremely low due to both hands being covered in highly conductive salt water, so even the short time I was connected to the power supply should have caused some really nasty internal burns even if it didn't get a chance to stop my heart.  The thing that saved my life was that the power supply was current-limited; it had a resistor inside with a value set so that the total output current, even in a full short-circuit condition, could never exceed 0.03 amps.  That's not enough current to do much more than tickle a little even in the most idiotic of circumstances (like this one), so I really wasn't in any danger.  So the question of whether or not I can be killed by electricity will, unfortunately, remain unanswered until the next time I do a dumb thing involving malt liquor and high voltages.

The majority of the specifics of this one came from here, although I did a lot of googling around to figure out the exact mechanism by which DC current kills.