If a voltage source is current limited does this actually mean that the voltage across the load is limited?

Question

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.

Answer 1

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:

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%.

Answer 2

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.

Answer 3

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.