A VandeGraaff generator is a mechanical current-pump attached to a small-value capacitor.
On a good day, the rubber belt is creating perhaps 10uA: a constant ten microamps. The VDG sphere forms a capacitor, with the Earth as the second plate, and the usual capacitor value is well below 50pF. Very tiny!
When we connect our belt-driven constant-current source to a capacitor, the voltage ramps up smoothly. For 50pF and 10uA, the voltage rises by 200KV per second.
Capacitor voltage-ramp for constant current:
Volt/Sec = Ampere/Farad
V/T = 10-5 / 50 x 10^-12 = 200,000 volts/sec
But after a second or two the capacitor voltage stops rising and levels off. It stops rising because, at extreme high voltage, the VDG's sphere becomes a "sharp tip," and it creates some surface-plasma and begins leaking current through the air. When the air-leakage increases to 10uA, the output-voltage stops rising.
A tabletop VDG machine might reach 200KV or 300KV before the voltage-rise is halted by air-leakage.
So, whenever you reach out and touch the VDG sphere, you discharge the 50pF capacitor. SNAP! The high voltage disappears in an instant. (Well, not instantly, since the RC decay-time might be 1 x 10^4 ohms times 5 x 10^-11 farads: a half-microsecond or less.)
The 200,000V is harmless because it only existed on your body for fractions of a microsecond. Between the time that the spark leapt to your hand, and when the voltage finished collapsing to zero, only a few hundred nanoseconds elapsed.
If you grab the VandeGraaff sphere, will you be shocked by the ten-microampere current-pump? Nope. If your skin resistance is typically 10K ohms, then the rubber belt can only develop about 1e-5 * 1e4 = 0.1VDC across your body. Fifteen times less than a 1.5V battery.
In other words, a AAA cell is much more hazardous than a VandeGraaff machine! If your skin resistance is 10K ohms, a 1.5V flashlight battery can create 150 microamps whenever you touch both terminals!!! OMG, it's producing less than a QUARTER OF A MILLIWATT of heating! Heh.
So, the VDG machine is safe because its output voltage is fifteen times smaller than a flashlight battery. That's true whenever a grounded human is touching the sphere.
Now if instead you could increase the belt-speed on your VDG machine, so it was 10,000 times faster, then the current-pump is getting dangerous: 100mA. (But if the belt's normal top speed is something like 5MPH, it's a bit hard to crank it up to 50,000MPH.)
Are VandeGraaff machines hazardous? Sure. HAZARDOUS TO YOUR WALLET. They can fry your new iphone, damage your best laptop. Worse, if you're using expensive medical implants, especially the static-sensitive kind (cochlear implants to aid hearing,) a VDG machine might create several thousand dollars of of fried electronics. SNAP!
TYPICAL VANDEGRAAFF SPECS:
- Output current at max. belt speed: 10uA
- Max terminal voltage: 250,000V
- Average output watts: 2.5W
- Internal impedance: nearly infinite(note 1) (it's a current-source.)
- Effective impedance at max voltage: 25 giga-ohms.
(note 1) The internal resistance of a VDG machine is the resistance of 20" of rubber band, in parallel with 20" of plastic pipe. On a low-humidity day, expect thousands of giga-ohms. On the other hand, during normal VDG operation, the surrounding air becomes full of ions: a weak plasma. The surrounding air is a much better conductor than the rubber and plastic parts of the machine itself. If the ionized air forms a resistor across the VDG output, what's the value of resistance when 250,000VDC is leaking a current of 10uA? That's 25 giga-ohms. If you manage to measure the Z(out) of a VDG machine, actually you're just measuring the resistance of the invisible weak plasma-stream which connects the metal sphere to nearby ground.