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The Van De Graff generator can generate voltages in the kV and MV range.

I have read that if I touch the Van De Graff generator producing, say 50kV, with one hand (myself being insulated from ground by plastic stool) and the other hand to the grounding rod, I don't get shocked because the current passing through me is small.

But if I grab live and neutral wires in each hand from a home AC electric service, which carry 120V or 220V, I might get fried because even though it has low voltage, it delivers high current.

My questions:

  1. What factor determines the current flow through the human body in the case of the Van De Graff generator and of the AC wall socket?

  2. Why is the current less in the generator case and why is it high in the AC wall socket case? Doesn't high voltage mean high current? And low voltage mean low current? What am I missing here? Is the missing thing the internal resistance?

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    \$\begingroup\$ Do NOT start any practical experiments. \$\endgroup\$
    – Solar Mike
    Jun 15, 2020 at 5:35
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    \$\begingroup\$ One has a very small charge (and is static), the other can generate enough current to melt thyristors (and is alternative). \$\endgroup\$ Jun 15, 2020 at 6:08
  • \$\begingroup\$ Ok But what determines the current in each case? \$\endgroup\$
    – user220456
    Jun 15, 2020 at 6:24
  • \$\begingroup\$ I am not able to understand when you say "One has a very small charge" ? How come a Van De Graff generator which can produce some kV ranges have small charge? Can you please explain the relation between the charge and voltage in general with respect to your comment \$\endgroup\$
    – user220456
    Jun 15, 2020 at 6:26
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    \$\begingroup\$ Q=CU=It. Even a small charge can provide a huge voltage when it's stored to extremely small capacitance. \$\endgroup\$
    – Justme
    Jun 15, 2020 at 9:06

3 Answers 3

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When you are stood on the insulating plastic stool, you are preventing a continuous DC current flow and your body quickly acquires the same potential as the sphere of the generator. Your scalp hairs might start to separate because of charge repulsion (see gold-leaf electroscope) but there is no more current flowing - your body has become charged to (maybe) 1 million volts. You body has roughly 100 pF capacitance to ground (see human body model) and 1 million volts and 100 pF is a charge of 0.1 mC. If your body acquires a voltage of 1 MV in 0.1 seconds then the current is: -

$$i = C\dfrac{dv}{dt} = 1 \text{ mA}$$

You might feel this little surge but only for a fraction of a second.

On the other hand if you connected your body across 220 V, it's the resistance of your body that determines the current and, this current will therefore continue to flow. If the voltage is big enough to breakdown the surface resistance of the skin, then your body resistance might be in the region of 1 kohm. 220 volts / 1 kohm = 220 mA (continual and rapidly lethal).

Do you see the difference?

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  • \$\begingroup\$ But isn't the 220V AC? Is AC capable of doing this? I thought only DC was harmful \$\endgroup\$
    – user220456
    Jun 15, 2020 at 11:57
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    \$\begingroup\$ DC can be more damaging (sometimes) due to it causing a muscle contraction that can grip a conductor harder and thus be nearly impossible to remove yourself from. AC will not cause a unidirectional muscle contraction but can upset muscle co-ordination and cause the heart to stop or not work at all properly. DC can also cause the heart to stop but, given the prevalence of AC around the home, AC is regarded as the most common to kill. \$\endgroup\$
    – Andy aka
    Jun 15, 2020 at 12:12
  • \$\begingroup\$ what happens when i touch the VDG sphere and ground rod at the same time? My body may not act as a capacitor but a resistor right? And it just now occurred that you used capacitor type approach for VDG and resistance type approach for the wall socket example. Could you please explain why is that too? \$\endgroup\$
    – user220456
    Jun 16, 2020 at 10:47
  • \$\begingroup\$ @Newbie if the VDG is capable of charging the sphere with a current of 1 mA then you will get a continuous current of 1 mA flowing through your body to ground. It will tingle a bit but not be dangerous however, I would do this for very long. However, the VDG might only be capable of 100 uA or less so it's not really a health issue. I used the resistance approach for the AC socket because that will dominate over the human body capacitance current by a mile. \$\endgroup\$
    – Andy aka
    Jun 16, 2020 at 10:52
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    \$\begingroup\$ @Newbie When my high school physics class did the VdG experiment, the chairs we stood on had plastic bodies, but metal legs, secured to the bodies by metal rivets. After a few seconds of touching the sphere, arcs would start jumping between our feet and those rivets, and you could feel every spark like someone punching you in the arm. It was really something. \$\endgroup\$
    – hobbs
    Jun 22, 2020 at 8:27
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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!

enter image description here

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!

. enter image description here

.

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.

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enter image description here .

(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.

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  • \$\begingroup\$ Thank you for the clear explanation ! Really appreciate it \$\endgroup\$
    – user220456
    Jun 15, 2020 at 12:13
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the answer is simple. The AC plug have high power. the current flow through your body still lower than AC inlet power. For Van De Graff the power is low due to small generator. It have high voltage but very low current so it take time to charge up capacitor (the metal surface act like capacitor). when you discharge it the current flow through your body is more higher than charging current there for voltage will drop immediately. If you got high power Van De Graff's generator, it's different story.

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