Understanding Circuits Voltage Resistance and Current in Physics

so i've got a cool little circuit here and when i stick an led in these sides boop it turns on but you didn't know that you could use modeling clay to make electric circuits but if you use the kid's kind that has salt in it totally works now stick another led in it lights up just as bright another led keeps working but if i hook them up in a line that is in series instead of in parallel they get a lot more dim why is that hey i'm diana cowan and welcome to lesson 19 of diana's intro physics review class this is actually the final lesson in this series today's theme is electricity because that's the topic of today's lesson today we're going to explain that strange light bulb dimming we saw at the

start of this video with two new ideas voltage and resistance okay so it's your birthday and your friends just bought you this epic electricity wand that makes metallic shapes seemingly magically dance in the air and you know how this works from the last lesson because charges are building up on the wand and the same charges build up on the metal thing so they repel each other cool so this one required two double a 1.5 volt batteries did it come with them no but now is a great time to stop and think what is a battery and what does it mean to have 1.5 volts or 9 volts how does a battery work let's build one on paper so the simplest battery that i know is the one that we saw last time it looks like this is the parallel plate capacitor

that we described in the last lesson so you know this already we charged it up with separated charges we've got positive on the top negative on the bottom so it's two conducting plates with charges on them this is the simplest battery i know of and we know from the last time that there is a constant electric field between the two plates going from the positive to the negative that's our electric field e and this is the simple setup we're going to use to develop our new tools for today so think about what happens if i put an electron in here a free electron and i put it near the negative side is it going to feel a force yes it's a charge in a non-zero electric field so it's gonna feel for us which way negative charges over here pushing

positive charges over here pulling so it's gonna go this way so electric field exerts a force on the charge and it's gonna accelerate quickly across the capacitor now moving charges around in electric fields is a lot like it's a lot like lifting weights in gravitational fields if we took out our little nano tweezers if we push the electron in the field toward the negative side we would feel some pushback like lifting weights in the air you have to do some work because you are force times distancing in physics terms forces here's gravity force here is the electromagnetic force and just like you store gravitational potential energy by getting swole in gravitational fields and lifting the weights up in the air you store electric potential energy in

electric fields by pushing charges around in electric fields specifically the way they don't want to go so we're going to get to the equations to describe all of this in a bit and we're going to come back to our electric potential energy or p e whenever it is like a little e so you know it's electric potential energy one of the new concepts for today and that is what a battery fundamentally is it's a device for storing electric potential energy but the fields in this battery or this battery don't look like this they're not coming from simple two plate capacitors like this they're actually generated by the electric potential energy difference between materials like copper and zinc so that means you could stick copper and

zinc into a lemon and that makes a battery there it is because the sink and the copper then change their chemical state once you connect them with a wire and complete the circuit the loop which allows electrons to flow through the wire connected to the metals so the lemon itself doesn't release the energy or provide the energy it's just providing an environment where the metals can provide the energy and once you let electrons flow between the metals you're decreasing the electric potential energy and that is simply what a battery does i highly recommend that diy project i did it for the first time this year it's really fun and also some people think that when you use a battery you use it up like you use up the

materials and maybe it gets lighter but think about your phone is it lighter when the battery is dead doesn't seem to be in a battery all the materials are still there once it's discharged you've just moved some charges around so the mass is almost exactly the same as at the beginning i said almost because there's a negligible bit of mass loss because of e equals m c squared but that's beyond this course although it is cool but all of the atoms all the materials are still there so anyways there are fancier batteries than these ones uh like the batteries in your electric car that are made with more exotic materials like silicon coated with an elastic ion conducting polymer and impregnated with lithium but they rely

on the same principle as these batteries an electric potential energy difference between the metals that's how battery works okay so build a battery you've got a way to make electrons move but what is this voltage business nine volts one and a half volts okay so i'm gonna try to explain this using a gravitational analogy so with a gravitational field if i lift this dumbbell up i've got some gravitational potential energy now so even if i don't lift up a dumbbell i still have some potential for energy i still have a gravitational field and the same is true here i can push these charges across and store some electric potential energy but even without the charges moving around or pushing them around i still have the

potential to get some energy or to do work and get some stored electric potential energy now what if i want to quantify that potential for energy not the potential energy but the potential for getting some energy well in a gravitational field i could say okay here's my potential energy and i just divide out the mass so then i have a number okay let me write that down so i've got gravitational potential energy is mgh if i just divide out the mass i get gh but why would i want this number this gravitational potential if you want to calculate how much energy would take to escape earth's gravity in a rocket given a mass so you could take gh and multiply it by the mass of your rocket and that tells you how much energy you need i can

do the same thing with my battery same concept the electric potential for energy is the number the quantity that tells me how much energy i would get if i multiply not by mass but by the amount of charge that i have i can find some number where i take my electric potential energy i would divide by my charge this time instead of mass i should have written a little delta and i get the potential for energy if i just multiply my charge like maybe it's just the charge of one electron or maybe it's a charge of 10 000 electrons then i get out the amount of energy i stored so this is what i use to quantify the potential for energy this is called voltage v it's the potential energy per

charge so this side this over here is its own thing so we know that we get a potential for energy from here to here but what voltage is just generalizing that difference in energy for any unit of charge so you could multiply that number that voltage quantity by charge and get out the energy now how do you change voltage in a battery well in a battery like this one you can change the type of material the dimensions the size of it the construct and so forth and that'll determine your voltage your electric potential difference so then does a 9 volt battery have a lot more energy than a one and a half volt battery not necessarily because it's the energy per charge that's the voltages okay so all these batteries in series i now have

imagine they're all connected i've got one and a half volts times 10 so i've got 15 volts now from here to here that's a potential difference of 15 volts but what if instead i lined them up like this and connected them all across this side instead of plus or minus it's all plus the plus on this side and minus to minus and i connected all these wires to one side of my circuit and all these wires to my other side of my circuit i would end up with still just a one and a half volt drop so same batteries same amount of energy but very different voltages in fact 10 times different and i could use a million of these batteries and connect them like this with all the wires on one side and i would still only have one and a half

volts unless i line them up like this then for a million i'd have one and a half million volts which would be insane you could have a one and a half volt battery that can give its energy to a bunch more charges but the energy per charge is going to be lower than the 9 volt battery it's a bit different than gravity because we don't ever run out of gravitational potential there's no gravity battery that runs out but that is the case with batteries okay cool so batteries store electric potential energy and we can quantify that per unit charge with their voltage and we can use this potential energy to power our phones and our cars and our laptops and you probably have noticed that sometimes these toys get hot

why is that we have to think about our next two big ideas first what is current so batteries make electrons move we saw that and moving electrons that's current as simple as that current is the rate of charges so it could be electrons or other protons or whatever but is the rate of charges flowing through something and that medium could be metal it could be air like this singing tesla coil made by the band architect so normally charges don't freely flow through air like this but if you make a super high voltage like in a lightning storm charges flow as a strong electrical current because that's what lightning is it's just charges flowing through air and then obviously creating some light

as they go now in most of our devices the medium that current is flowing through is usually metal like the metal wires and cables because metals unlike air are really good at letting the current flow so the second idea is why electrons flow more easily through some materials and not others and why that current makes things hot so electrons typically in most materials don't flow perfectly efficiently there's always at least some interaction between the electrons and the atoms and the medium because they're flowing through and they're bumping into the atoms and jostling them around passing off some of their kinetic energy to the medium and that's why the material heats up it's

gaining some of that kinetic energy at the atomic and molecular level so the metal filament in your light bulb actually uses this principle it heats up because electrons are flowing through the filament jostling the metal atoms in it around and getting them so hot that they reach glowing hot temperatures and that's how incandescent light bulbs work fluorescent light bulbs are different so as you might guess those interactions that cause the heat also have the effect of resisting the flow of charge because electrons are bumping into things it slows them down it resists the flow and that's what we call resistance to the current so materials that allow electrons to flow more freely have lower resistance so metal has a lower

resistance to current wood has a higher resistance to current some ceramics have low resistance to current actually fun fact resistance in a material can depend on temperature so for some materials if you drop the temperature low enough the resistance goes away not just get small it goes to zero which now that i'm saying it sounds impossible but that's what we call a superconductor and the search for materials that can be super conducting at near room temperatures is a big field in modern physics and actually just a couple months ago in october 2020 the first room temperature superconductor was discovered at about 15 degrees celsius it's this material made of hydrogen carbon and sulfur but it only works at about 2.6 million times

atmospheric pressure at sea level so it's not that useful okay so that's current and resistance so now we know the concepts that we're dealing with let's get to our tools our mathematical tools to describe all this and be able to work with it so let's think again about pushing our charge around in the capacitor imagine that i push it over here and let it go it's going to accelerate back if i could push it back and let it go would it keep going over and over yes phew as long as i keep putting the work in there to give it electric potential energy to then convert into kinetic energy but what if i push it over here really fast does that change how much electric potential energy it gets well what's a way of

figuring that out actually move all of this now well energy comes from work and work comes from a force and the force here depends on two things you learned from last time the force depends on the charge and the electric field so let's translate that into the math that we can use so energy comes from doing work which is work which is a force times a distance you remember that from our work lesson and then the force on the charge from last time is the magnitude of the electric field times the charge so putting this all together i get work equals my charge i'm going to put the force in here my charge times my electric field times my distance that's the work i've done and so therefore that's the potential energy

that i got my change in potential energy electric potential energy so the work the field will do on the charge is the amount of charge times the magnitude of the field times the distance between the plates that's if i move the charge the whole distance so as long as we keep going the same distance in the field we will get the same work and therefore the same electric potential energy that can be converted to kinetic energy and that gives us the same speed just like lifting a rock up in the air one meter and dropping it will always hit the ground with the same speed no matter how fast you lifted the rock so now that we know the difference in potential energy for an electron between here and here

between the two plates we can figure out the mathematical tool we need for voltage it's our potential energy per charge right and i just figured out what my potential energy is going to be so it's that energy per dumbbell so we take our potential energy which is the work we did q e d and we divide it by charge so the charges cancel and i get the electric field strength times the distance so that's the amount of potential energy available per charge so that is our voltage so ed that's my voltage or my potential difference so voltage is a measure of potential difference and by the way the unit of voltage is called a volt so another way i could write what i just did is that voltage that potential difference times q i'm just bringing up

this q that's equal to my potential energy so our next tool current as we said current is the rate of charges per second so we actually use the symbol i for current and it is in units of coulombs per second because it's charge per time but this is also called an ampere or an amp so one amp here is one coulomb per second so in a circuit voltage is generally proportional to current which makes sense higher voltage more charges are going to flow per second voltage is proportional to current in a circuit interestingly though increasing the current doesn't always mean increasing the speed of an individual charge because you might think that electrons moving through a wire are zipping around right but no the

average speed of an electron is on the order of micrometers per second it's just the number of charges passing through per second that typically increases so the bigger voltage the bigger the current it can create metaphorically it's like more pent-up pressure ready to push the air so higher pressure more air could be pushed similarly with voltage higher voltage means more charges will pass through in a second and that's current so lastly we've got our tool for resistance and we can think about what the equation might be for voltage current and resistance by thinking about what resistance does so voltage is the energy per charge higher resistance means more of that energy is likely lost to heat therefore we would get a lower current

so we define resistance as the ratio of voltage to current because increased resistance means decreased current and the units of resistance are volts per ampere which is actually something called ohms and we use the greek letter omega to represent ohms so if i bring back this i over here delta v equals ir you'll see why i'm going to do this in a second because this is the famous ohm's law this is the famous equation for electrical circuits this is like f equals m a level of importance when it comes to circuits voltage is current times resistance understanding that and using that tool is incredibly important for electricity and physics now the hardest concept in all of this i think is voltage so let's do a practice problem to practice

thinking about voltage use an old-school tv old-school tvs were made where they would shoot electrons from the back of the tv to the front of the tv which would hit this chemical that glowed that's how it worked here's the back of the tv in front of the tv so say we shot our electrons across a potential difference or a voltage of a thousand volts so i want to know how fast the electron would be going once it accelerated across this voltage and hit the other side just like a falling rock problem start with potential energy it gets converted to kinetic energy and we use that kinetic energy to find the velocity so how do we find electric potential energy well that was the whole point of the voltage in my opinion that electric

potential energy will just be the voltage which we know times the charge of the electron electric potential energy and i'm going to end up with some kinetic energy and i'm going to use that kinetic energy to find my speed at the end because that's ultimately what i want to know so now we know that this electric potential energy is just going to be the voltage times the charge of the electron and here it gets interesting if we were doing this in a gravitational potential energy problem where we would set this potential energy equal to kinetic energy we would have mgh equals one half mv squared we would see the m's the masses cancel you know what that means mass is cancelled means that all objects

fall at the same rate in a gravitational field which we know here i get my voltage times my charge equals one-half mv squared and the mass does not cancel so charges with different masses will end up with different velocities that's interesting but in a gravitational field the speed it's going at the end does not depend on mass but with charges it does so we need to work out the math using the mass and the charge of the electron and so let us plug in some numbers and work it out real quick so i've got my voltage which i gave you that was the beginning of the problem 1000 volts times the charge of the electron something you'd just either know or look up which is 1.6 times 10 to the minus 19 coulombs and that equals my one half

mass of the electron same thing i just looked it up 9.1 times 10 to the minus 31 kilograms and that's times my v squared i'm solving for v squared do all this math out and i get v equals 1.9 times 10 to the 7 meters per second whoa we found something like 20 million meters per second or almost 10 percent of the speed of light that is fast so even though the energy we gave the electron was tiny why did it go super fast because the mass is really tiny too with a small mass it's easier to accelerate you here's another problem and this one is gonna help us think about why our phones get hot and also it's gonna help us think about the power in circuits so check out our simple i'm gonna draw a little battery here

a plus and a minus and then it's going to go through a little light bulb okay so there's a potential energy drop between the two ends of our battery say this is 9 volts so our potential energy drop our voltage drop between this positive and negative side is 9 volts and this drop this potential energy drop makes the current flow through the wire and where does the energy go well the light bulb is a big resistor and you can literally feel the energy from the voltage drop heating up the material you can feel it heating up the light and then you can see the resistor is radiating the energy away as light and if i wanted to know how long my battery is going to last maybe how fast it's using the energy if i wanted to know the rate of energy

it's power it's wattage it's our energy change our energy over time so that's going to be our power is our change in energy over change in time what's our change in energy well we just work through some equations for electricity our change in energy is going to be our voltage delta v times q because remember electric potential energy is our voltage times our charge per time that we could rewrite as just our voltage times charge per time that's our current and so now we have our two basic circuit mathematical models p equals iv and we've got v equals ir power is current times voltage and voltage is current times resistance mathematically these are basically all the tools you would need but since i'm a physicist i like to play with my models

and so to figure out other relationships like if i don't know the current then i could just substitute in v over r for current and i could get p equals v squared over r or if i didn't know the voltage then i could just replace voltage here and i would get p equals i squared r lots of things i can do with these two tools and there's also really interesting intuition you can get if you just keep looking at these equations if my current goes up obviously i'm using more energy per time if my voltage goes up but i have the same current then i'm using more power so that tells you a little bit more about what voltage is just a lot of stuff in here really cool so now we can use these new tools to

answer our original question about the light bulbs dimming when we hook up light bulbs in series they got dimmer we're gonna figure out why so i'm gonna draw my circuit here it's similar to this one but instead i've got a battery and the voltage drop on my battery i've got my light bulbs in series so the current flowing across both of these light bulbs is going to be the same because no matter what the same number of electrons have to keep moving around the circuit because the electrons don't just disappear and if it's a different number of electrons across each bulb then they're going to bunch up somewhere and that doesn't happen so that's one important point to always remember in situations like this the

current across both light bulbs is the same and a second important point is that there's a voltage drop across each light bulb because i've got this potential here and then that voltage drops across each of these light bulbs that is because the overall voltage does some work on each light bulb so each light bulb sort of uses up some of that voltage some of that stored energy and the voltage drop across the two light bulbs adds up to the total voltage of the battery so my voltage drop one plus my voltage drop two is the voltage of the battery so that right there is enough to convince me why the light bulbs will get dimmer they have to share the potential drop of the battery but

there's another way that we could have hooked up the light bulbs we could have hooked them up parallel to each other so what would that look like we have our battery one here and then another one parallel to that this is my one this is my two so the current could either go this way or it could go this way so in this case now the currents flowing through the light bulbs are not necessarily equal because the electrons flowing through the circuit gets split into these two paths and the resistance of the light bulbs might not necessarily be the same if the resistance of them is the same is the current the same yes but there's a fork in the road here and if one path is easier to travel than the other so easier would mean less

resistance then more charges are going to go that way but the total current of this circuit equals the current through bulb 1 plus the current of bulb 2 since again we're not losing electrons or they're not bunching up anywhere so my total current is going to be current one plus current two and it works out that the voltage drop across each of the two light bulbs have to be the same they balance out so that's my voltage drop it's going to be the same as the battery and that equals the voltage drop across light bulb one and it's the same as the voltage drop across light bulb two and so again right there we can see that the bulbs in parallel should have the same brightness as a bulb all by itself

because each bulb sees the entire voltage of the battery it just may happen that you use up the battery faster than if you only had one bulb connected and that's our lesson on circuits when they asked what you learned on youtube today here are your two key takeaways one voltages are all about potential energy and potential energy comes from the work which is the potential difference or the voltage times the charge and two ohm's law v equals ir and here are the problems that we solved in the lesson so you can go over them on your own because that's one of the best ways to learn physics and a short disclaimer this series has aimed to review topics covered on the ap physics 1 test but just before recording it was announced that circuits

electrostatics and waves will no longer be covered so there's that this is the end y'all i don't know who's happier you or me if i have one more piece of unsolicited advice it is that i learned so much physics by making this course and i've learned so much physics by tutoring for the last 10 years and i'd say what i found is that when you have to teach something you learn it incredibly well so that's my pitch for you trying to teach something to somebody maybe tutor people that's how you're going to learn the best way possible and i want to give a couple last shout outs to people who really deserve it i would not have been able to do this course without my high school physics teacher jeff brock who was the

lead writer on this course and without my crew hope and levi have been here for the whole filming and all of the other wonderful people who worked on this course all their wonderful names are in the credits but i truly hope that this is not the end of your journey with physics or other science and engineering fields in the words of past diana i hope i do hope i hope you do continue on with physics with physics i do hope you continue with physics i really hope you do and here's one final message for you from some special guests hi i'm craig and i'm mitch and we are asap science now we spent a lot of time in universities studying biology and chemistry but honestly didn't take that many classes in physics and now that

we're older we're obsessed with cosmology the expanding universe the laws of nature all governed by physics so good luck on your course keep watching physics girl and we hope you enjoy it see ya