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I am trying to understand how amps work exactly. I see variations of the following in various online sources.

From here:

[...] A standard household circuit that supplies your outlets and switches carries 15 or 20 amps (15,000 or 20,000 mA).

And:

This gives you an idea of just how much danger there is in the home wiring system we take for granted, where wires carry 15,000 or 20,000 mA.

Also, from this question (only the wording in the title is relevant for my question):

Is lithium battery charging speed proportional to the amps provided from the power source?

To me, this means that a power source has a fixed number of amps that it provides, similarly to how it has a fixed voltage that it provides. This number of amps is always there, like the voltage is always there.

However, from here:

[...] For example, if you have a 100-watt light bulb in a lamp that is plugged into a 120-volt outlet, it will draw 0.83 amps.

[...] For example, if you plug a 40-Ohm dryer into a 220-volt outlet, the appliance will draw 5.5 amps.

So this makes it sound like if you plug the above dryer in, the wires won't carry the full 15A mentioned in my first link, but will only carry 5.5. The 15A is an upper limit, not what's always there.

Which is it? is the 15A always there, or is it just an upper limit, and what's there is only what is being drawn by a consumer at any given moment?

If it's the second, then, although I am aware that it's dangerous and I have no plans of trying it out, I don't have a clear idea about HOW dangerous exactly. How much would a human body (let's say with a dry finger) touching the wires draw? 100mA? 1A? the full 15A?

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    \$\begingroup\$ Is water supplied or consumed? The current rating for a source is what it is capable of supplying. The current rating for a load is what it will draw. \$\endgroup\$ – DKNguyen Oct 22 '19 at 19:50
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    \$\begingroup\$ Short-circuit that "toaster oven" and it will draw much-much more than 15A (but the breaker in the box will blow). Bypass the breaker in the box and you'll get all the current the main breaker can supply (neglecting the wiring starting on fire). Bypass the main breaker and you'll get all the transformer on the pole can give. I think you are confusing the capacity with the draw. Just because a circuit can supply 15A, doesn't mean the device (or human being electrocuted) is drawing that much. \$\endgroup\$ – Ron Beyer Oct 22 '19 at 19:54
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    \$\begingroup\$ The load determines the 'draw', always. The problem is that wiring heats up if too much current is flowing through it because wires have resistance. This leads to degradation of the wire or in worst cases, fire. So limits are enforced on AC mains to make sure the 'draw' is not exceeded. \$\endgroup\$ – Voltage Spike Oct 22 '19 at 19:56
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    \$\begingroup\$ I would change the first 2 quotes into "can carry" instead of "carries". \$\endgroup\$ – Huisman Oct 22 '19 at 20:06
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    \$\begingroup\$ I would say those quotes using carry/carries are plainly incorrect as they don't continously carry that current. But maybe it's an English way to express it; I'm not a native speaker. \$\endgroup\$ – Huisman Oct 22 '19 at 20:18
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The source is capable of supplying some number of amps, at some voltage, depending on how it is built.

Total Resistance

Consider a 1.5v battery being the total energy source and miles of thin copper wire. Lets say the wire equals 9Ω total resistance, and the battery has 1Ω of internal resistance, so the total resistance is 10Ω:

  • The total Amperes it can supply to a shorted load (0Ω): 1.5v/10Ω = 0.150A
  • The total Amperes it can supply to a medium load (10Ω): 1.5v/20Ω = 0.075A
  • The total Amperes it can supply to a light load (1kΩ): 1.5v/1.01kΩ = 1.485mA
  • The total Amperes it can supply to your dry fingers (100,0010Ω): 14.9985µA

Now lets change things around. Instead of one battery, we are going to use twenty of them, all wired in parallel. And instead of miles of thin wire, we're going to use short copper bus bars. Twenty batteries in parallel is still 1.5v, but the internal resistance (1Ω each) are also in parallel:

$$ R_P = \frac{1}{\frac{1}{R1}+\frac{1}{R2}+\frac{1}{Rn}...}$$

This makes the internal resistance equivalent to one battery with 0.05Ω. Lets say the bus bars are also 0.05Ω, for a total resistance of 0.1Ω. What happens now?

  • The total Amperes it can supply to your dry fingers (100,000.1Ω): 14.999985µA
  • The total Amperes it can supply to a light load (1kΩ): 1.5v/1000.1Ω = 1.49985mA
  • The total Amperes it can supply to a medium load (10Ω): 1.5v/10.1Ω = 0.1485A
  • The total Amperes it can supply to a shorted load (0Ω): 1.5v/0.1Ω = 15A!

If the delicate thing connected to this battery had 15A dumped into it, it would be destroyed.

Household (Mains) Power

Mains power works in a similar way, but is more dangerous mainly because the voltage is much higher (120v instead of 1.5v, or 80 times more voltage!)

What limits this current is both the load resistance and the source resistance. The total resistance is the key.

Now mains power has an intrinsically low resistance. Thick copper wires connect the utility service to the house, and relatively thick wire connects from here to the outlets. So something must be present to prevent current from getting too high, and that's exactly what a fuse and/or circuit breaker does.

If you have an outlet rated for 120vAC/15A and attempt to plug two hair dryers into it (30A load), a fuse or circuit breaker will trip. This may be inconvenient, but it's much better than the wiring in the walls catching fire. I'll let you in on a little secret though. Fuses and circuit breakers are not instantaneous. If you could somehow switch both of those hair dryers on at exactly the same time, you'd see 30A flowing for a very small amount of time. And if you shorted the outlet, at least 100A briefly... that much current is dangerous, and causes wires to melt and vaporize, which is highly unpleasant at best. Research ArcFlash for more info.

Skin Resistance

Now contact with fingers is a whole other story. Just like the "variable load" used above ranges from 0Ω to 100kΩ, so can your skin. Dry skin with a small contact area is relatively resistant to electricity. But wet skin and contaminants (sweat) greatly reduces the contact resistance, perhaps as low as 1kΩ. This net effect is a combination of factors:

  • Dryer the skin - higher the resistance.
  • Smaller the contact area - higher the resistance.
  • Lower the voltage - less damage it can do.

Now this is only for the skin. Underneath the skin (inside the body) is very wet and so has a low resistance, perhaps a few Ohms. So if the voltage is high enough to break through the skin and reach inside, then LOTS of current can flow. This is why high voltage is so dangerous around humans - skin offers little protection.

You can however, touch a 12v car battery's terminals without as much as a sensation, even though that battery can deliver 1000A for a short time. Your skin protects you from that. But the skin cannot protect you from a high voltage source, such as an 18,400v power line. It only takes 10mA (0.01A) to be a risk of life.

See? Amps, Ohms, Volts - they are all related, and why it is called Ohm's Law. One is meaningless without the others.

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The whole plumbing analogy for electrical current flow breaks down pretty quickly, but in this case it may just work:

You walk up to your kitchen faucet. It's off. There's pressure behind the valve (40-ish PSI), but no flow. That's like an electrical outlet with nothing plugged in.

You open the faucet just a bit. Water flows just a bit. That's like plugging a night-light into that outlet. You open the faucet a lot. A lot of water flows. That's like plugging in a light fixture, or turning on a vacuum.

Beyond that the analogy breaks down: electricity has to flow in a circuit, while the water that goes down the drain may take centuries to fall as rain again; your pipes don't burn up if you flow water through them too fast, etc. But that's the basic idea.

It's complicated, but:

  • usually a source will provide a fairly constant voltage unless the load is asking for too many amps.
  • A load will almost always pull a certain current for a given input voltage, or maybe the current will change with the state of the load (like a battery charging, and using less current as it gets more charged).
  • An unprotected source will often heat up, burn up, or otherwise be unhappy if you pull too much from it -- power wiring has fuses on it to prevent this from happening, because the inconvenience of changing a fuse or flipping a breaker is usually less than the inconvenience of rebuilding a burnt-down house.
  • Etc. There's more, but -- it's complicated. Hopefully this gives you a start.
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Is lithium battery charging speed proportional to the amps provided from the power source?

Many devices draw only the current they need, and the power source just has to be able to deliver it when required. This does not apply to batteries. A battery is itself a power source, so it is designed to have a low internal resistance to keep the output voltage (relatively) constant at both low and high currents.

When a battery is charged its low internal resistance will not limit current to a safe level if the charging voltage is significantly higher than the battery voltage. Therefore the charger must limit the current, and charging speed is proportional to the current it provides.

Note that USB (and some other) 'chargers' are actually just power supplies. The charger is built into the device it powers. The device may sense the maximum current capacity of the USB supply and adjust its charging current to suit.

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Any circuit will provide or draw only as many amps as the physical laws force it to provide or draw at a particular point in time. No more, no less.

The wordings that you refer to are not "perfect" and the reader is supposed to interpret the wording with regards to context.

  • A household circuit carries 15 or 20 amps should be read as "can carry up to 15 or 20 amps" - it isn't providing or carrying any current until there is a load.
  • charging speed proportional to the amps provided from the power source. When charging a lithium battery there are two phases: a constant current phase followed by a constant voltage phase. In practice the source is "current limiting" and "voltage limiting". So the source will provide "up to" a certain amount of amps. This current will flow if the lithium battery voltage is lower than the voltage limit, the charging source will provide the current that it was set to. There is an exception: the lithium battery also has an internal protection (very low voltage protection, thermal protection) - when the protection is active, the battery will limit the current and the source will no longer provide "the current". In fact the voltage at the battery terminal will increas to the maximum voltage of the source without drawing any current.
  • the light bulb will draw 0.83amps. This is a common wording as the light bulb is the client of the power source that has a low impedance and is capable of providing an virtually unlimited amount of current (until the fuse breaks to avoid overheating, etc). The fact that the light bulb is there doesn not noticeably influence the power source. When the light bulb is drawing 0.83 amps, the source is providing 0.83 amps. But that is rarely the wording that is used for the source. We rather say: it provides 20 amps to indicate the maximum current that it can provide, not the current that it is actually providing.

How much would a human body draw?

It depends. How dry is your finger? How hard are you grasping the wire? How well are you "connected" to ground (conducting shoes, floor, etc)? About 20mA can be deadly. An electrical chair where conductivity is favorised passed 7 to 12 amps through a body at about 2000V source:quora. The internal resistance of a human body is about 300 Ohms so that seems about right. At 250V, I'ld guess that you are indeed under one amp, and under dry conditions well under that, but still quite dangerous. I know some people that are not very precautious that "touch" live wires more often than any person would with "dry" fingers - I gues they are only "drawing" a few milliamps on those occasions. I went through similar experiences a few times too, but I can't remember "direct" contact, only through some other "insulator" like paper or through a wet casing or wire which I found already impressive enough - much more than when holding your tongue on a 9V battery to taste if it is still good enough.

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