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For the past while I've been struggling to wrap my head around electricity.

One thing that has puzzled me to no end is the relationship between current and voltage.

On paper it's a really simple linear relationship. More voltage over a fixed resistance? That's more current. More resistance with a fixed voltage? Less current.

However, it seems to me that this rule is often broken. For example, Van de Graaff generators can create millions of volts across the human body, yet somehow with this massive voltage there is a limit to current. There is a quite popular video where a professor explains this is because current is low. However, if the human body is say 200k ohms shouldn't that be multiple amps?

It wasn't until a few days ago while daydreaming that I think I figured it out.

If current is limited by a series resistance then that means as the resistance of the load drops, the series resistance of the supply makes up a larger portion of the total resistance, and thus the voltage across the load drops, thus decreasing the overall current.

Does this mean then that a high voltage source with low current is actually low voltage across the load?

This seems to be the only way I can think of that current could be limited while obeying ohms law. Basically current limiting = voltage across the load limiting.

I am fully aware this post is probably full of painful misconceptions and so I would love any help anyone can provide. I feel electronics is often talked about in various forms of abstraction that make it extremely hard and frustrating for me to understand the fundamentals of what is happening. I struggle to live in a land of abstractions.

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  • \$\begingroup\$ You're pretty close to right, but you're missing a few things--one important one is that ohm's law only applies to purely resistive things, and many things are not purely resistive. There's also the fact that the voltage at the source isn't necessarily constant either, if the source is a charged capacitor for instance. \$\endgroup\$
    – Hearth
    Jun 23, 2021 at 2:43
  • \$\begingroup\$ Current limited means you only get a large voltage for a range of resistances. Try to put a small resistance and the voltage drops to keep the current low. That can be implemented with a series resistance as you said or with an active circuit that monitors the current and lowers voltage adaptively (e.g. current limited power supplies). \$\endgroup\$ Jun 23, 2021 at 2:43
  • \$\begingroup\$ You are definitely on the right track. The key is to model the source correctly. For example ESD is often modeled as a 100 pF capacitor discharging through a 1.5 kOhm resistor. The capacitor is charged to several thousand volts (exact charge depends on the specific protocol being followed). \$\endgroup\$
    – mkeith
    Jun 23, 2021 at 2:46
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    \$\begingroup\$ The high voltage produced by such a generator can result in a high current going trough the human body, but because the charge is typically very small the event is extremely short in duration, thereby not causing any damage. \$\endgroup\$ Jun 23, 2021 at 2:46

3 Answers 3

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A Van de Graaff generator is more like a capacitor than a battery. When a capacitor discharges through a resistor the initial current is \$V/R\$ as Ohm's law says it is, but the outgoing current quickly decreases the voltage on the capacitor. The result is a rapid decrease in the current provided by the cap.

A battery's voltage is (in the ideal case) unaffected by the current it provides.

If current is limited by a series resistance then that means as the resistance of the load drops, the series resistance of the supply makes up a larger portion of the total resistance, and thus the voltage across the load drops, thus decreasing the overall current.

This is, in fact, a pretty accurate view of most voltage sources - including batteries and power supplies - and it's the way voltage sources are modeled when you want to get realistic results.

Here's what a capacitor's discharge curve looks like:

enter image description here

Source: https://binaryupdates.com/how-capacitor-works-with-dc/graph-of-capacitor-discharging-current-and-voltage/

It's an exponentially falling curve. The time constant is \$R\times C\$ where \$C\$ is the capacitance and \$R\$ is the resistance of the discharge path. After one time constant the capacitor's voltage (and current) reduces by 63%.

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  • \$\begingroup\$ I see, so what I'm gathering is with a Van de Graaff generator there is very temporary high voltage and thus high current but because it's so short it is effectively low current. I guess my question then would be why we call it high voltage if the high voltage is also a short burst. \$\endgroup\$
    – WavePhaser
    Jun 23, 2021 at 2:59
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    \$\begingroup\$ @WavePhaser The fact that there's only a small charge and the voltage will quickly drop when loaded doesn't change the fact that it is a high voltage while unloaded. \$\endgroup\$ Jun 23, 2021 at 3:04
  • \$\begingroup\$ I see thank you for the help I think I understand a little better now! \$\endgroup\$
    – WavePhaser
    Jun 23, 2021 at 3:05
  • \$\begingroup\$ Nitpick: A capacitive discharge into a purely resistive load looks like that, but into other loads it can look very different. \$\endgroup\$
    – Hearth
    Jun 23, 2021 at 13:08
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When a source is current limited, it the voltage will be adjusted to whatever level is required for said current.

Van de Graaff generators can create millions of volts, in open-circuit, but low current, whenever a human touches, current starts to flow and the voltage drops.

Keep in mind that a system can never have higher output power than input, the law of conservation of energy, if a system creates millions of volt, it cannot produce more power (thus amps) than the energy that is supplied to it.

Generator will have an IV (current-voltage) curve and will have characteristics at Voc (Open circuit), Isc (short circuit) and anywhere in between.

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It's not always a series resistor. Sometimes, it's closer to a hard limit.

Consider a solar panel in the sunlight. Each photon that hits a silicon wafer in the right place will knock one electron off, and that electron can generate a current. One ampere is about 6.25 x 10^18 electrons per second. So a solar panel generating 1 amp must be hit by 6.25 x 10^18 photons at the right wavelength and in the right place every second (the efficiency of a solar panel may be around 20%; 80% of the photons fail to produce electrons). Try to draw more than 1 amp from that panel, and the voltage will rapidly collapse.

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