I see a lot of talk about “what the source voltage is” and “what the source current is” etc. This type of talk can be very misleading to a lot of people.
So I’ll start at the beginning…
Let’s say there is an electrical power source. This can be a wall outlet, output of a power supply, battery – anything.
You walk up and touch one of the terminals. Is it going to hurt you? Kill you?
First of all, we must determine what components make up the “circuit.” They are as follows:
- Electrical power source
- Your body
Electrical power source
As mentioned above, the electrical power source can be pretty much anything. For the sake of discussion, let’s assume it’s a DC supply w/ two terminals ( “+” and “-” ). Let’s also assume it’s a non-isolated supply, i.e. the “-” output is tied to earth ground. Furthermore, the electrical power source can be modeled as an ideal voltage source in series with a known resistance. (This is a 1st-order model, but good enough for this analysis.) The voltage source is really called the Thevenin equivalent voltage source, and the series resistance is called the equivalent source resistance or, more accurately, *Thevenin resistance. *
During an electrocution incident, your body can be 1st-order modeled as a 2-terminal resistor. Of course, the actual value of resistance depends on a lot of things, and can vary wildly from person-to-person. Very dry non-broken skin can be as high as 500,000 ohms from hand-to-hand; wet skin can result in a hand-to-hand resistance less than 1,000 ohms. Sweaty hands typically register between 20,000 and 40,000 ohms. For broken skin, an arm or leg is typically 500 ohms, while the trunk is 100 ohms. Again, this depends on a lot of factors, and actual resistance may be very different from the values I stated. Also, I believe your body resistance is somewhat non-linear (i.e. the resistance is not constant with current), but we’ll ignore this factor.
This is the resistance between your body and the “-” terminal of the power supply. I’ll call this the “ground resistance.” It can be very low, e.g. if you’re standing barefoot in a puddle. In can even be zero, e.g. if your left hand touches the “+” side of the power source, and your right hand touches the “-” side. Of course, it can also be very high, e.g. if you’re wearing rubber-soled shoes.
So here’s what the circuit model looks like:
Positive terminal of Thevenin voltage source connected to Thevenin resistor.
Other end of Thevenin resistor connected to your body.
Other end of your body connected to ground resistor.
Other end of ground resistor connected to negative terminal of power supply.
With me so far?
Now the risk factor to your body depends on the current through your body. This is because body resistance can be just about anything (see above), thus voltage value alone is doesn’t tell you a whole lot. (I = V/R). Currents above 10 mA are considered “bad” for an adult, though it is possible to receive a lethal shock from currents below 10 mA. The GFCI outlet in your bathroom is designed to break the circuit when it detects a leakage of current of 4 to 6 mA.
So given the model I described above, what determines the current through your body?
- The value of the Thevenin voltage source = Vs (volts)
- The value of the Thevenin resistance = Rth (ohms)
- Your body resistance = Rb (ohms)
- The value of the ground resistance = Rg (ohms)
The current through your body (Ib, in mA) is thus:
Ib = 1000 * Vs / (Rth + Rb + Rg)
Therefore, for a given voltage source, the way to decrease the current through your body is to increase Rb and/or Rg. (You usually don’t have much control over Rth.)
Consequently, the voltage across your body (Vb, in volts) is:
Vb = (Vs * Rb) / (Rth + Rb + Rg)
So what does all of this mean? Let’s look at some examples.
Let’s say you put one hand on the “+” terminal of a car battery, and the other hand on the “-” terminal. Vs = 12.6 V, Rth = 0.01 ohms, Rb = 100,000 ohms, Rg = 0 ohms. The current through your body is 0.126 mA. No problem here. Notice that the maximum current capability of the car battery (about 500 A) makes no difference, except for the fact that more current capability = lower Thevenin resistance.
Let’s say you have a skin break in each hand, and do the same as the previous example. Vs = 12.6 V, Rth = 0.01 ohms, Rb = 1000 ohms, Rg = 0 ohms. The current through your body is 12.6 mA. Not good.
Let’s say you’re very well grounded and you touch a Van de Graaff generator. (This type of device generates a “static” voltage using a motor-driven belt and combs. As a result, it can generate fairly high voltages, but the Thevenin resistance is extremely high. It’s also very non-linear, but we’ll ignore that fact for this analysis.) Let’s say it can generate up to 10,000 volts… Vs = 10,000 V, Rth = 1,000,000,000 ohms, Rb = 100,000 ohms, Rg = 0 ohms. (I’m guessing at these values.) The current through your body is 0.01 mA. Definitely no problem here. Also notice that the voltage across your body is only 1 V. Because the Thevenin source resistance is so high, 10,000 V is never actually across your body. In other words, before you touch the Van de Graff generator, the voltage is indeed 10,000 V. But it drops to 1 V as soon as you touch it. Of course, this is with Rg = 0. To get the notorious “hair raising effect,” Rg must be very high. (Wear rubber-soled shoes!) This means your entire body will “float” at a fairly high voltage above ground, but the current through your body is (still) extremely small.
Now let’s talk about AC. Assume you have rubber-soled shoes on and you touch the hot side of a 120 VAC outlet. Vs = 173 V (max), Rth = 0.001 ohms, Rb = 100,000 ohms, Rg = 10,000,000 ohms (due to the shoes). The maximum instantaneous current through your body is 0.017 mA; you probably won’t feel a thing. (But because you’re a capacitor, you might feel a charging current. But that’s another topic.) Now let’s say you’re standing barefoot in a puddle and you touch the hot side of a 120 VAC outlet. Vs = 173 V (max), Rth = 0.001 ohms, Rb = 1000 ohms, Rg = 100 ohms. The maximum instantaneous current through your body is 157 mA. You’re dead. (I have also read that 60 Hz is more lethal than DC.)
So there you have it. To re-cap:
- Too much current through your body is bad.
- The value of the current is determined by 4 things: Thevenin voltage source, Thevenin resistance, body resistance, and ground resistance. Thus, voltage is a factor, but not the only one.