Electrical injuries - Doorknob vs powerline

Question

This is something that has bothered me since high school physics. I have a medical and engineering degree, yet I can't for my life answer this question in a way that's logically consistent in my head. The question essentially boils down to the following:

A high voltage line is about 20,000V. This is considered a "high voltage" injury if you touch this line and get shocked. Yet, the voltage between you and a door knob when you get shocked is also about 20,000V. The reason you don't die from the doorknob, is because the current from the doorknob is microscopic compared to that of the power line. But if $V=iR$, and the $V$ is fixed, and the $R$ (my body) is also fixed, what's allowing the higher current?

I know there's something wrong with my oversimplification of the situation that prevents me from fully understanding this but I can't seem to get my brain around it.

Now of course the damage you receive is actually determined by the total energy transmitted which is $W = Pt = iVt = i^2Rt$, so time plays an obvious role in the damage received from electrical injury. However, I still can't wrap my brain around the idea that you can generate more current with the same voltage.

An analogy I guess is putting batteries in parallel, which increases their current handling. Yet if you hook up a single 1.5V battery to my body, and 6 1.5V batteries in parallel to my body, the current - by Ohm's law - should stay the same, no? What am I missing here?

So can someone finally explain to me how the powerline kills me but the doorknob just gives me a tickle?

Answer 1

The Key to your question is the distinguation between ideal and real sources of voltage and current. If we stay at the batteries: At the moment you attach batteries paralell to your body, what happens is that one part of the body has another electric potential than the other one, thus (Ohms law) a current will flow in your body. At this point the current will be determined only by the potential-difference between the body points.

BUT: In the moment the current flows, the Voltage of the batteries will drop, when they are a real source of voltage: If you simply assume the batterie as two boxes with charges in it, and you open the boxes and take some charge out, then the charges remaining will have fewer attraction towards each other and thus, the voltage between the ends of the batterie will drop. This effect isn't large (and in batteries, the charges are "restored" chemically", but this will lower the current in your body. And here is what you have asked for: The more batteries you use to attach to your body paralelly, the lower will this voltage drop be, and the more "ideal" will the source of power be: If you use 100 batteries, then there won't be mutch change for them, if a little bit current flows out of them. Instead if you use one tiny battery (like really tiny!) then it will be empty in 2 seconds.

In an Ideal Situation: You apply voltage, it will generate a current by Ohms'law.

In a real Situation: You apply voltage, it will generate a current by Ohm's law, the current will decrease the voltage, this will change the current, and so on and so on. This will system will reach an equilibrium somewhen, and this equilibrium will have higher current if the source of voltage is more ideal.

In short: Just because Ohms law states that to a voltage attached to a resistance belongs a current, doesn't say anything about how mutch charge is provided that CAN flow through your body.

For you doorknob: The voltage that is applied to your body is 20.000 V, yes. But in the moment you touch the Doorknob, and current flows through your body, this 20.000 V will immideately decrease, and after the little shock that you get, (which is the current), the voltage will be 0, because all the charges are gone from the Doorknob. The Powerline doesn't care if you touch it, it is made in a way to have all kinds of stuff be attached to it and draw some power away, mixers, an oven, computers .... it maybe won't have 20.000 V anymore, but 18.000 V (I didn't calculate that, it's only for the purpose of explaining this that I choose this number), but that's still enough to maintain a current high enough to fry you.

Answer 2

The powerline can supply large amount of current, whereas the doorknob cannot. Each power supply comes with voltage and max rated current. Let us say body resistance is 5M ohm. Then current flowing through the body when you touch powerline is 20k/5M = 4mA. Now powerline can easily supply 4mA of current. But the doorknob cannot supply 4mA. So the actual current flowing when you touch the doorknob is very less(may be of a few microamps).