Voltage

Note from Akuli:

Voltage is one of the most important concepts in electronics, if not the most important concept. In this lesson, we discussed what exactly voltage is and how it behaves, using batteries and a multimeter as an example. We also learn how to test if a battery is empty.

To follow along, you need:

A multimeter
Two or more batteries (we used AA and AAA batteries, but any type of battery will do)

I also told adder that alligator clip cables might be useful. We talked about them but we didn't end up using them.

Measuring 4 different batteries

adder Ready. Got a multimeter and gator clips with me.

Akuli great :)

adder Right, and different kinds of batteries.

Akuli first, grab just the multimeter, and one battery (doesn't matter which)

Akuli set the multimeter to volt, not the ~ one if you have two voltage settings (I don't remember)

Akuli then, touch the multimeter probes to the battery in all kinds of different ways you can think of, and see what happens :)

Akuli we'll collect some observations, then figure out simple rules to explain them all

Akuli and then some intuition to make the rules not feel arbitrary

Akuli sounds good?

adder Yeah.

Akuli i'll let you play around with it for a while, let me know when you have pretty much done everything you can think of :)

adder So, I managed to get the meter to display ~1.2V when I connected up the probes to both of the battery's ends.

Akuli great :)

adder It doesn't matter which probe (black or red) goes on battery plus or minus.

adder Otherwise just touching the battery body doesn't do anything.

Akuli look at the meter carefully, there's one small difference if you swap the probes

adder Like negative voltage? I paid close attention to see a minus in front of the number, but I didn't see it. Let me try again.

Akuli yes :)

Akuli oops, spoiled it i think

adder Ah, right. This is the minus under "DC".

Akuli yeah, varies meter to meter

adder So I think black on plus and red on minus is negative voltage?

Akuli sounds right to me

Akuli can you make it show anything meaningful at all if you touch just one probe?

adder Sounds arbitrary to me. :)

Akuli this will make sense by the end of the day :)

adder Just 0.001V.

Akuli so basically nothing :D

Akuli i think we've measured pretty much everything i can think of

Akuli now grab another battery, and see what's same and what's different

adder Has the battery "capacity" depleted now? Has some "energy" run out?

Akuli we'll find out, for now just remember the 1.2 volts you got

Akuli see if other batteries are also 1.2 volts ish

adder Smaller AAA battery (previous one was larger) gives out ~1.3V.

adder A bit more than 1.3V.

Akuli alright :) got more batteries? we could do maybe one more

Akuli maybe one that you know is recently charged if rechargeable, or new if not

adder The third one, also 1.246V, but I'm not sure what its status is.

Akuli alright :)

adder Like I don't know whether it's new or rechargeable or whatever.

Akuli hmmm do i have a battery here

Akuli found some new batteries

Akuli i'll measure one and send pic

Akuli this is what a fresh battery looks like

adder So a bit more voltage?

Akuli yeah

Battery	Type	Measured voltage
adder's first battery	AA	about 1.2V
adder's second battery	AAA	about 1.3V
adder's third battery	AA	1.246V
Akuli's battery	AA	1.593V

What does voltage mean?

Akuli now look at your batteries

Akuli there's some text on them

Akuli it should say somewhere what the voltage is supposed to be

adder The AAA says 1.5V.

Akuli yep, how about the AA?

adder Third one (AA) says 1.5V.

Akuli yeah

Akuli mine also says 1.5V, you can see in the pic

Akuli right around the center of the battery

adder First one says 1.2V.

Akuli hmmm

Akuli 1.2V is new to me

adder Says Ni-MH AA 3000mAh 1.2V Rechargeable

Akuli maybe i have some learning to do here :)

Akuli i didn't know some AA batteries are designed to be 1.2V ish only

adder :)

Akuli so, what do the numbers mean? :)

Akuli voltage is basically, how hard is the battery trying to push electricity from the plus terminal to the minus terminal

adder So through the battery body?

Akuli yeah

adder OK

Akuli hmm, not quite

Akuli more like, through whatever you connect between the terminals

adder Ah.

Akuli for example, if you hold it in your hand so that your hand touches both terminals, a tiny amount of electricity flows through your hand

Akuli you don't feel it because it's so small

Akuli if the battery was pushing harder (let's say 50V or more), you would feel it and it would be painful :)

Akuli ok?

adder OK

Testing batteries by licking them

Akuli that said, tongue is more sensitive than hands

Akuli (i haven't tried other body parts)

adder :)

Akuli if you manage to somehow touch both terminals at the same time with your tongue, you will feel it

Akuli that's why i suggested a 9V battery yesterday, the terminals are right next to each other

adder Don't exactly wanna do that. :-P

Akuli yeah :D

Akuli not required :)

Akuli my dad tests 9V batteries that way

adder :D

Akuli you can feel how much voltage is left in the battery

Battery voltage decreasing

Akuli so, a fresh battery has slightly more voltage than what's written on it

Akuli as the battery is used, the voltage decreases

Akuli we'll later see that it's a bit tricky to make a power supply that maintains the same voltage in all situations

When nothing is connected to battery terminals, what does the voltage do?

adder Okay, so here's some questions that hold me back from "picturing" voltage. Like, when nothing is connected to the terms, what does the voltage do? Idle? What exactly IS voltage that is idle, electricity?

Akuli the idle state is voltage but zero current

Akuli the battery wants electricity to go from + to -, but it's not going because nothing is connected

adder So voltage is still e.g. 1.2V?

Akuli yes

Akuli it's always there

adder OK

adder So air not a good conductor?

Akuli right

Akuli at least not at such low voltages

Does holding a battery in your hand decrease its voltage?

adder If I held onto both terms with my hands, it would eventually decrease right?

Akuli yes

Akuli that's very slow though, if you're sweaty that speeds it up :)

adder OK

What in the battery makes electricity to go from + to -?

adder So one more question.

adder You said, battery wants electricity to go from + to -.

Akuli right

adder Why is this?

Akuli the direction is arbitrary, and actually wrong

adder What in the battery is doing this?

Akuli the internals of a battery are chemistry go brrr

adder Right, right, but like, why is it behaving this way?

Akuli you'd need to ask someone who does chemistry

adder OK

Akuli for electronics, you're more interested in how it behaves as a voltage source

Electrons

adder The takeawy, electricity wants to go from + to -, possibly reversed.

Akuli electricity wants to go from + to -

Akuli that's a convention though

Akuli let me explain :)

Akuli the things that actually move are electrons, and they physically move from - to +

Akuli but before people knew that's what really happens, the meanings of + and - were already standardized

Akuli so they didn't bother to switch those around

adder OK

Is an electron indivisible?

adder Is an electron already atomically indivisible unit?

Akuli as far as i know, yes

adder Like can we break it up into pieces?

Akuli as far as i know, no

adder OK

Akuli you'd need to ask someone who is really really up to date with modern physics to find out :)

What is a proton?

adder So now I just got one more question.

adder What is a proton?

Akuli a proton, as far as i remember, is one of the things that electrons can spin around to form atoms

adder So is battery + somehow related to protons?

adder Logical plus.

Akuli it sure has many protons :)

adder I'm just trying to grasp wtf makes it flow.

Akuli there's multiple per atom, i think helium or hydrogen or something has just one electron and one proton, but most other atoms have a mix of both

Akuli and neutrons too

adder Ah, right, I remember now.

Resistance (will be covered in more detail later)

Akuli the short answer to what makes it flow: some materials have electrons more loosely attached than others

Akuli metals, in general, don't have their outermost electrons attached particularly tight to them

Akuli so one atom can exchange electrons with another atom that sits next to it

adder I see.

Akuli during this process, the electrons don't flow losslessly along a straight line

Akuli they bump around, they change direction, they wiggle their way through

Akuli that's resistance :)

adder So like resistance is caused by what?

adder Air?

adder Friction?

Akuli basically friction

adder OK

Akuli it's not air, it's just electron movement not being an ideal straight line

adder I see.

Akuli and heat is just vibrations of atoms

Akuli i should mention, i might get some detail wrong, because i don't usually think about stuff at this level

adder You mean, as electrons (atoms?) move, they generate heat?

Akuli yeah

adder OK

Akuli the smoother they can move, the less resistive the material is and the less heat you get

Akuli it also helps to just have more of the same material, so a thicker wire will heat up less

adder OK

How fast do electrons move? Speed vs current. Why a thicker wire has less resistance.

adder So one more question, is there a constant speed at which the electrons move, or is it like spermatozoids, where one is faster than the other?

Akuli the speed depends on the current (which is how much electrons are moving through a wire), and the size of the wire

Akuli it's surprisingly slow, i think i've calculated it at some point in physics class

Akuli but in general, if you have a narrow wire, the electrons will move faster through it for the same current

Akuli --> more heat

adder Sorry, wdym "how much" electrons? Do you mean e.g. it depends on if 1, 5, or 1000 electrons are moving together?

Akuli let's say that the current is 1000 electrons per second

Akuli we could calculate how many amperes that would be

Akuli but amperes are literally electrons per second, scaled up to make the numbers nicer to work with

Akuli ok?

adder OK.

Akuli so if all the electrons move through a narrow spot, that spot becomes really busy

Akuli but if you have a bigger wire, they can spread out all over it

adder OK.

Akuli so that's why thicker wire has smaller resistance

Can a wire be too big? Why chinese alligator clip cables have high resistance

adder Can a wire be too big?

Akuli yes, it just becomes expensive and inconvenient

adder Like so big electrons can't move?

Akuli no

adder OK.

Akuli usually real-world wires are some tradeoff between the resistance you want and money

adder OK.

Akuli for example, the alligator clips cables you and me have are surprisingly high resistance, because they're made cheaply in china

adder Meaning what, that the "teeth" are thin?

adder Or that the wire in between the pair of teeth is thin?

Akuli it's not about the clip itself, because the clip is plenty thick

Akuli it's about the 0.5m ish wire connecting the two clips

adder Right.

adder It's too thin?

Akuli yes, the wire inside the yellow plastic is too thin

Akuli and made of bad materials

Akuli pure copper is the traditional material for such wires, but it's really expensive now, so many new wires are a mix of all kinds of other stuff

adder I see.

Akuli there's even some iron in them, that's easy to test by bringing a magnet near the wire

adder Let's not open up electromagnetism yet. :D

Akuli :)

Note from Akuli:

I highly recommend this video by Matthias Wandel if you want to learn more about the resistance of cheap alligator clip cables.

Summarizing what voltage means

Akuli so, voltage is how much a battery wants electrons to go from minus to plus

Akuli but for historical reasons we think of electricity as going from + to -

Akuli voltage doesn't mean anything is moving though

Akuli it just sits there ready to go

Akuli ok?

adder OK.

Negative voltage

Akuli now the minus sign should make some more sense

Akuli the meter is like, yes it wants to move like this, but in the opposite direction

Akuli one very common color convention is that plus is red and minus is black

Akuli so if you follow that, the meter gets the "usual" thing and shows no minus sign

Akuli if you swap it, it notices that the direction is reversed

adder When you say "direction", do you mean like a direction down the wire, from one end vs vice-versa?

Akuli i mean the direction along the wire that electricity wants to go

adder Yeah.

Akuli so if the meter notices that electricity wants to go in through the red probe and out the black probe, it shows a positive number

Akuli and if that's reversed, it still shows the voltage but puts a minus sign

adder So in your pic we have negative voltage, meaning what?

Akuli i put the probes backwards

adder Battery releases electrons through the red probe?

Akuli yes

adder OK.

Akuli the meter says that electricity wants to come in through the black wire and go out the red wire

Akuli (i.e. the same but opposite wires for raw electrons)

adder So wait.

adder Usually, forget the conventions, let's talk about what actually happens.

adder We have a battery with + and -, that is with a bump (+) and a flat bottom (-).

Akuli yep

adder IN REALITY, electricity wants to flow from flat bottom out of the bump?

Akuli yes, electrons want to go from the flat bottom to the bump

adder OK.

Akuli so if you invert the meter reading, you get what the electrons want to do

adder Which, does not really matter for electronics?

Akuli right

adder OK.

Akuli it's a convention, and when you work with existing components (which is always), you just follow the same conventions that the people who made the components

adder OK.

Vacuum tubes

Akuli the one situation where this does matter is vacuum tube technology, which is largely obsolete by now

adder OK.

Akuli in a vacuum tube, electrons jump from one metal plate to another

Akuli before semiconductors (basically diodes and transistors), this was used to do what semiconductors do now

Akuli for example, my dad's old guitar amplifier has a vacuum tube for converting AC to DC

adder I see.

Akuli which sounded ridiculous to me when i learned about it :)

Akuli nowadays you would "of course" use diodes :)

Akuli anyway, we'll come back to all that later

Summarizing what a battery does

Akuli do you have more questions about what happens with one battery and a multimeter? (great questions so far!)

adder Well, I'm not sure.

Akuli the tl;dr is, battery wants to put out electrons from its flat end to the little bump, which we call voltage from the little bump to the flat end

adder I think we can continue and then if something needs worked on, we can always return.

Akuli sure :)

Voltage is always between two points

Akuli so a couple key things

Akuli note that voltage is always between two points

adder In this case between flat bottom and bump?

Akuli yes

Akuli typically two metal objects, but any conductive material could be used to reasonably measure a voltage

adder OK.

Akuli so technically, there's no such thing as "voltage of this point", though i myself use that phrase a lot, we'll talk about what that means soon

adder OK.

Voltage from a point to itself (mathematically)

Akuli i guess you tried touching both probes to the same point too?

adder Yep.

Akuli inventing some notation here, V(A -> A) = 0

Akuli where A is any point

Akuli ok?

adder ok

Voltage backwards (mathematically)

Akuli you also noticed: V(A -> B) = -V(B -> A)

Akuli if you swap the wires, the sign changes :)

Akuli ok?

adder OK.

Akuli mathematically, the first note is actually a consequence of the second

Akuli if you plug in A in place of B, you get: V(A -> A) = -V(A -> A)

Akuli looks like x = -x

Akuli solve that in whatever way you like, you get x=0

Akuli ok?

adder OK.

Akuli so you could say we've made just one observation so far, V(A -> B) = -V(B -> A)

Akuli ...and discussed what it means, of course

Akuli ok?

adder OK.

adder It reminds me of vectors, and how vec(AB) = -vec(BA).

Akuli yes :)

Akuli very similar :) just one-dimensional instead of 2D or 3D

adder I see.

Akuli and a one-dimensional vector is just a number... so we use numbers for voltage... yeah

adder Cool.

Two batteries

Akuli let's make another observation that isn't covered by that

Akuli take two batteries

Akuli put them on the desk so that the plus of one battery touches the minus of the other

Akuli (you may have seen this arrangement in some battery-powered devices)

Akuli again, measure all the voltages you can think of :)

I generally want black probe on minuses, and likewise, red on pluses?

adder Holy crap.

adder So just one question.

adder When I work in electronics, I generally want black probe on minuses, and likewise, red on pluses?

Akuli yes

adder If I want a somewhat sane result displayed on the meter?

Akuli it's no big deal if you get it wrong

Akuli you can always ignore the minus sign

adder OK.

adder So...

adder We chained up two batteries, and we increased the voltage.

Akuli yep

adder I'm not sure whether this was expected. :D

Akuli :)

Akuli measure the batteries individually too

Akuli see if you notice a pattern in the numbers you get

adder They sum up to total voltage?

Akuli yes :)

adder OK, so first question, is this mathematically precise sum, or is anything here "lost"?

Akuli this is a mathematically precise sum, as far as anyone designing any electrical device is concerned

adder I see.

Akuli some modern physics person might insert an achthually, but i don't think even they would

adder lol

Akuli try flipping one of the two batteries around

adder Guess: it's gonna be the same total voltage, but negative.

adder Let's see.

adder Oh so they cancel out?

Akuli yeah

Akuli does this contradict the adding thing?

adder No.

Akuli right :D

adder It's consistent.

Akuli you're just adding a negative number

Akuli now flip the other battery around too

adder Like chained up nose-to-butt but in the other direction or?

Akuli yes

adder Negative voltage.

Akuli yep :)

Akuli now you're adding two negative numbers :)

The important equation

Akuli so: V(A -> B) + V(B -> C) = V(A -> C)

Akuli ok?

adder OK.

Akuli this is a really important fact

Akuli a lot of electronics boils down to how does one voltage spread among multiple components

adder OK.

Akuli mathematically, our earlier two facts are actually consequences of this new fact...

Akuli put A in place of B and C

Akuli V(A -> A) + V(A -> A) = V(A -> A)

Akuli looks like x + x = x, solution is x=0

Akuli so V(A -> A) = 0

Akuli ok?

adder OK.

Akuli with similar trickery you can derive V(A -> B) = -V(B -> A)

Akuli i think just put A in place of C and you should get it

Akuli ok?

adder OK.

Akuli so, basically everything we did today, in one equation

Akuli (and a lot of understanding about what it all means of course...)

Akuli ok?

adder :)

adder OK.

Akuli this equation is basically the first thing i say when i'm explaining electronics to math people

Akuli basically, "every metal object has a voltage, and it follows this law"

Akuli or rather, "between any two metal objects there is a voltage, and it behaves so that..."

Akuli this equation is so important that just knowing that much gets you very far :)

adder OK. :)

Floating

Akuli there's actually a corner case here that looks like a contradiction, but isn't really

Akuli the tl;dr is that the important equation is always true even though i'm about to show a case where it appears to be false

Akuli ok?

adder OK.

Akuli take two batteries

Akuli let's call them A and B

Akuli let's call the terminals A+, A-, B+, B-

adder OK.

Akuli just let the batteries sit on the table without touching each other

adder Sideways?

Akuli doesn't matter

Akuli as long as they don't touch

adder OK.

Akuli measure the voltage from A+ to B+

Akuli what is it?

adder ~0V.

Akuli yep

Akuli zero

Akuli the batteries push electrons from minus to plus

Akuli they have nowhere to go from the minus so there's no "i want to move" to be observed

Akuli ok?

adder OK.

Akuli now measure the voltage from A- to B+

Akuli what's that?

adder 0V, too.

Akuli yes

Akuli same story, other end of the battery is not connected so nothing can move

Akuli ok?

adder OK.

Akuli now measure the voltage from A+ to A-

adder 1.226V

Akuli let's try the important equation

Akuli V(A+ -> B+) + V(B+ -> A-) = V(A+ -> A-)

Akuli 0V + 0V = 1.226V

Akuli ...what?

Akuli ok?

adder OK.

Akuli the problem is that the multimeter shows zero when nothing is connected

Akuli if you had two multimeters, and you measured V(A+ -> B+) and V(B+ -> A-) at the same time with them, you would get some pair of numbers that adds to 1.226V

Akuli but if you measure them individually, the meter just shows 0 as a sort of weird default

adder OK.

Akuli so... what is the voltage really?

Akuli the voltage really is zero when the meter says it's zero

Akuli it just changes to zero wherever you put the meter

Akuli the presence of the meter affects the thing you're trying to measure

adder I see.

Akuli basically, the meter has a small tendency to make whatever you put between the probes be zero

Akuli it's so small that you can usually ignore it

Akuli but in this corner case, it shows

Akuli ok?

adder OK.

Akuli this problem is usually called floating

Akuli as far as battery A can tell, the whole battery B is floating

Akuli meaning disconnected

adder OK.

Akuli measuring voltages between any reasonable place (in battery A world) and B+ is just going to produce weird results

Akuli so, a floating thing basically means a disconnected thing

adder OK.

Akuli sometimes it can be a challenge to notice that something is floating

adder Yeah.

Akuli other times your circuit is noisy enough that any floating part just picks up noise from nearby parts and you see that noise :D

adder :)

Akuli so, any weird signal that isn't what it should be at all: something is likely floating

Akuli the reason why that is called floating will become clear when we talk about ground

Akuli but i think i'll leave that for next time :)

adder OK. :)

Summary

Akuli that's all i have for today :)

adder Cool.

adder Thank you.

Akuli :)

adder I might have some questions later if you're still here, if something pops up.

Akuli tl;dr: V(A -> B) + V(B -> C) = V(A -> C) explained, caveats, applications

Akuli ...and how to check if a battery is empty!

adder Wait, how?

Akuli measure voltage with the multimeter you already have

Akuli more than what it says on the battery? good

Akuli slightly less than what it says on the battery? not freshest, but fine

Akuli way under? likely unusable but can depend on device

adder Ah, obviously.

adder Brain farted.

Akuli or lick it if it's a 9V :D

adder :)

Caveat with measuring batteries

Note from Akuli:

This conversation actually happened at the start of the next lesson. I placed it here because it is essentially a correction to what I said above.

Akuli before we begin today's actual topic i'd like to add an achthlually to last time's stuff

Akuli the way i taught you to measure if a battery is empty can be misleading

Akuli i'll explain how

Akuli ok?

adder OK.

Akuli to illustrate this, i took my dead batteries pile, and measured 14 batteries in it

Akuli (i have many more, but some of them have leaked, so i didn't want to dig deeper into the pile)

Akuli ok?

adder OK.

Akuli 11 of them showed a voltage that was clearly way too small

Akuli 3 of them showed a voltage that looked quite ok

Akuli one of them was a 9V battery that measured 8.7V

Akuli so, voltages like that, a little low but looks usable

Akuli ok?

adder OK.

Akuli so what's going on? did i really throw away good batteries?

Akuli the thing is, battery voltage decreases under load, i.e. when you actually try to use the battery

Akuli a simple multimeter check measures the voltage of the battery with no load attached

Akuli but the actual voltage while using the battery will be lower

Akuli ok?

adder OK.

Akuli in a fresh battery, the voltage doesn't drop much

Akuli in a dead battery, it typically drops more

Akuli and this effect can be so big that a dead battery appears fine when measured with multimeter

Akuli so, if multimeter shows a very low voltage, you know the battery is dead, but if the multimeter shows a slightly low voltage, you don't really know and you may want to try a fresh battery anyway

Akuli ok?

adder OK.