current and ohms law going to be the topic of this lesson in my new General Physics playlist which when complete will cover a full year of University algebra based physics now this is the first lesson in a new chapter on current and resistance uh and we're definitely going to focus on current and OMS law but we'll also talk about the power dissipated across resistors we'll also talk about resistivity uh as well as the temperature dependence of resistance my name is Chad and welcome to Chad's prep where my goal is to take the stress out of learning science now if you're new to the channel we've got comprehensive playlists for General chemistry organic chemistry General Physics and high school chemistry and on Chads prep.com you'll find premium Master courses for the same that include study guides and a ton of practice you'll also find comprehensive prep courses for the DAT the MCAT and the oat now we're going to start this lesson off by defining electrical current uh it's going to be a mathematical definition but before we get there just think about where you might use the word current in your everyday life and it's probably going to involve like wind currents or ocean currents or river currents but it's probably going to involve the flow of either air or water well with electrical current we're talking about the flow of charge so and we give it this mathematical definition we use the capital I to represent electrical current and it is the change in charge over the change in time or the flow of charge over time if you will so let's say you had a circuit and you had a gate on a wire in the circuit and as charge was flowing by that gate so you had some way of counting the charges it went by that's effectively what Cur is it's a measure of that change in charge or flow of charge per unit of time the SI unit we call the Ampere or the amp for short so symbolized with a capital A and if we look at what that reduces down to so the SI unit for charge is the Kum the SI unit for time is the second and so 1 ampere equals 1 K per second all right now a couple things you should know so we talk about it as generically the flow of charge but if we're talking about the flow of charge in a conducting wire well really it's the flow of electrons going around that wire but as we talked about in the last chapter if electrons are flowing this way so versus some sort of positively charged species flowing the opposite way you get the same result and so in the early days a couple hundred years ago all they knew was the result and they didn't know if it was the flow of positive charges in One Direction or negative charge in the other direction and they chose it backwards they just talked about it being the flow of positive charges now in certain Solutions you might get the the flow of ions and it could be both positive and negative ions flowing so it's not completely wrong to say that we could have the flow of positive charges in one sense but in a conducting material the protons are confined to the nucleus it is the loosely held electrons that are actually flowing through the wire and so actual current is the flow of electrons but for historical reasons we Define what's called conventional current which is kind of like the imaginary flow of positive charges as long as you're talking about a conducting wire uh which is pretty much the most common context that will be brought up in this course so keep in mind we talk about conventional current and current in general and less specified it's usually we're talking about conventional current it is the imaginary flow of positive charges just keep in mind that real current is really the flow of electrons in the opposite direction so now we're going to transition and talking about one of the most important laws in all of second semester physics it's rather simple one here this mathematical expression but Delta V equals IR your potential difference equals your electrical current times your resistance uh in a resistor so a resistor resists the flow of charge it resists the current in a circuit hence the name uh we can better see that if we rearrange this a little bit but also oh rearrange this to provide a definition for resistance and so resistance R is equal to the ratio of the potential difference over the electrical current and he called the SI unit for resistance the ohm which we symbolize with the Greek capital omeg omeg GA now if we rearrange this and solve for current we can get a better idea of why we call it resistance so current's going to equal Delta v/ R and we can see that your electrical current is directly proportional to your potential difference across a resistor you double that potential difference you also double the current but it's inversely proportional to the resistance if you double the resistance you would cut the current in half and so the greater the resistance the lower the electrical current the resistors is functioning to lower the current it's resisting the flow of charge uh again and hence the name all right now a resistor uh in some cases we actually just have resistors manufactured as structural elements to put inside circuits to function as resistors but much of the time we're talking about uh many of your electrical appliances actually functioning as resistors like light bulbs and toasters those are just resistors and their job is to turn electrical energy into some other usable form of energy like in the case of a light bulb it's turning electrical energy energy into heat and light now the goal is the light the heat just kind of comes along for the ride and the greater the amount of light per unit of heat the more efficient we say that light bulb would become and LEDs do a great job incandescent light bulbs not so great so but they dissipate power in this case they give off energy per unit of time uh and that's one of the functions of a resistor is to give off this power now we can talk about this power dissipated in a resistor as well and that power it turns out is equal to the potential difference times the current so simple relationship if you know these two properties across a resistor you can get the power being dissipated very quickly and it will come out with units of Watts or jewles per second and so a volt ampere must equal a jewel per second again the same thing as a watt and indeed it does now a couple other ways you might see this expressed is we can use ohms law and substitute it right in here and get two other equivalent expressions for the power dissipated in a resistor as well if we just take 's law directly and then substitute in for Delta v i * R well you get I * R * I which overall simplifies down to i^2 * R and that's another equivalent way of getting the power dissipated in the resistor instead if you actually took and substituted Delta V over R in for I right here you'd have Delta V time Delta V / R which would give you Delta V ^ 2/ R so three different ways to calculate the power being dissipated in a resistor now one thing you need to know it's the power being dissipated in a resistor and that's going to involve the potential drop just across that resistor now if you only have one resistor in a circuit typically the EMF uh of the power source is going to be the uh the potential drop across the resistor they'd be one and the same but if you got more complex circuits that have many resistors that's typically not going to be the case and the rookie mistake some students will make is they'll just look at you know their circuit diagram and they'll see the EMF source and it'll say 12 volts and no matter what what calculation they're doing on the problem they're going to plug in 12 volts every time they see Delta V and that's where you got to be careful it's just the Delta V off the resistor of interest in a problem not necessarily the same thing as the Delta V of the EMF Source in most cases so you got to be careful so I personally like this middle definition because it's impossible to make that rookie mistake but again technically any one of these three should give you the power dissipated across a resistor and let's jump into doing a little bit of pluggin and chugging so uh first question here says says a current of 3.0 amps flows through a 2.0 ohm resistor what do the potential drop across the resistor first question what is the power dissipated across the resistor second question all right so the potential drop here is just straight up ohms law Delta V equals I * R and in this case it's given so I is 3.0 amps R is given as 2.0 ohms and 3 * 2 Delta V is going to be 6 0 volts that is the potential drop across the resistor so typically uh when you convert electrical energy into some other form of energy the amount of potential energy stored in the charge that's flowing is going to go down and again if we're envisioning the imaginary flow of positive charges here so potential energy of those positive charges goes down as potential goes down and so typically we're going to associate Delta v as a potential drop now we're just going to put an absolute value of six FTS here in this case but in more complex problems we really will reflect it as a drop of 6.0 volts in the future all right the second part of the question was what is the power dissipated across the resistor so and we've got three different equations we could use now that we know Delta V here and we know all three we could actually use any one of these three but I like the one that doesn't involve squaring anything because it usually involves lower numbers that's what I'm going to use here so Delta V time I which in this case is that 6.0 volts times our 3.0 amps and that is a power being dissipated of 18 Jew per second or watts and you can see how the other two formulas would have let us to the same place so i^ 2 * R would have been 3^ 2ar which is 9 * a resistance of 2 ohms would have got us 18 Watts or Delta V ^2 over R would have been 6^ s or 36 all over R of two would give us 18 Watts as well so again any one of these three should work if they don't all three give you the same calculation you might be making that rookie mistake next we want to talk about what is known as the resistivity and it's related to the resistance for a substance uh and it's indicative of some conducting substance typically is the context is brought up in uh but before we get there I just want to kind of allude to a simple circuit for a minute uh so we don't get kind of confused of we're going to talk about resistivity and then we're largely going to ignore it for much of the next two chapters so if we take a look at a simple circuit here so we uh talked about in the last chapter that two parallel lines with one's short and one's long that is a battery or a source of EMF uh and then this Jagged line right here that is the symbol for a resistor and so in this simple circuit we have one source of EMF and we have one source of resistance or so we think now it turns out your load resistor is usually the greatest contributor to resistance in a circuit but we'll find out that batteries themselves often have or typically have an internal resistance that we usually ignore but also the wires themselves that are made of a conducting material typically have some sort of resistance associated with them as well depending on what material they're made out of but also depending on kind of their design so how fat is the wire and how long is the wire as we'll see in just a second but we usually ignore that as well and so usually on a simple circuit diagram like this we ignore the fact that the battery has any internal resistance we ignore the fact that the wires themselves have resistance which we're about to talk about and we pretend that the only source of resistance is the resistors that appear in the diagram so just keep that in mind all right all right so resistivity here is talking about the resistance in the wires typically so and it turns out it totally depends the resistance of a wire let's say depends on how long the wire is and it turns out the longer the wire the greater the resistance but it also depends on the uh cross-sectional area of the wire as well the larger the cross-sectional area the smaller the resistance to the flow of charge and you kind of think of this analogous as kind of water flowing through a hose now if you've ever had to gas uh and maybe you have and hopefully for completely legal reasons uh you've had to siphon some gas so couple things I recommend use a short hose so if you use a long hose you're going to get greater resistance and it's going to be harder to get that gas flowing from out of the gas tank in most cases to the other end of that hose so if I used a hose that was one mile long I put the hose in a gas tank and I went to the other end one mile away and I start sucking on it you're not getting any gas out of that thing there's just not going to happen so because it's going to have such great resistance to the flow of water and in the same way the longer a wire the greater the resistance to the flow of electrical current as well now it turns out resistance going to be inversely proportional to the cross-sectional area now the other thing I would recommend doing if you're siphoning gas is to use a pretty good size hose if you use like the really thin IV hose like you might find in the hospital hooked up to an IV uh it's really thin and narrow and so instead of you know using a short hose use long one but now you use a really thin one you're just sucking on that thing all day long and it's going to be tough to get the gas flowing in that one as well you want to use a much larger cross-sectional area hose because it's going to have lower resistance when it has a larger cross-sectional area and you're more likely to get gas flowing through it so to speak same thing here a larger cross-sectional area uh for a wire and you're going to have greater I'm sorry less resistance and greater current flowing through that wire all right and then the Greek letter lowercase row here that is the resistivity and that is the part that is going to be characteristic of that particular conducting material and you can look up these resistivities for all sorts of materials typically like conducting metals and stuff like this and you can see which metals are more conductive than others as a measure of that resistivity now again the shape and length of that wire is going to matter so but you got to get an idea of well if I want the most conductivity which conducting material should I use in principle and things of that sort all right now we'll find out also that this resist ity also has some temperature dependence as well but typically the values that you're going to find reported are going to be kind of reported at some standard temperature like 20° C or something like this now you might be involved in doing some simple plug and chugging with this equation for resistance and resistivity or you might just simply have to understand the relationships now one thing to note since uh resistance and current are inversely proportional then any relationship you establish between resistance and any one of these three it would be the opposite relationship with current so if I here I can see that resistance is directly proportional to resistivity well then the electrical current would be inversely proportional to the resistivity resistance is directly proportional to the length of the wire current would be inversely proportional to the length of the wire so resistance is inversely proportional to the cross-sectional area of the wire uh your electrical current would be directly proportional to the cross-sectional area of the wire so kind of works that way so next question here we'll do some plugin and chugging a piece of copper wire has resistance of 8.00 ohms it is replaced with a new piece of copper wire that is three times longer and has a radius that is double the original what is the resistance of the new wire so a couple things I want to look at here so we want to look at that relationship between resistance and the length and they're directly proportional and then resistance in the cross-sectional area and they're inversely proportional uh and in this case the original wire was 8 ohms for resistance uh the new piece of crop wire is three times longer so and if we've got a wire that is three times longer [Applause] then that's going to increase the resistance by a factor of three as well now we're also told that the uh radius of the wire is doubled well we see cross-sectional area we don't see radius so don't just double it here so cross-sectional area typically a wire has a round cross-section it's a circle and that area is p r s and so in this case if you double that radius that's going to quadruple the cross-sectional area and if we quadruple that cross-sectional area that's going to cut the resistance by a factor of four it's going to be a fourth of the value all right so we can see that with what we did to the length we tripled the resistance with what we did to the radius and therefore cross-sectional area we reduce the resistance by a factor of four so in this case overall sum these two up and it's going to betimes 3 and * 1/4 and so the resistance is now going to be 3/4s of its original value well the original value was given as 8. ohms and 34 * 8. ohms probably do in your head is now 6. ohms now we want to briefly talk about the temperature dependence of the resistivity for a substance turns out that for conductors they tend to be more conductive at lower temperatures less conductive at higher temperatures and while it's the opposite for semiconductors we're going to kind of exclusively talk about conductors in this course and one of the reflections that they are more conductive at lower temperatures is they have a lower resistivity at lower temperatures as we'll be able to see in this equation a little bit but ultimately if you know the resistivity at one temperature and it might be a value you looked up in a table online somewhere or something like that but then you can calculate the resistivity at a second temperature provided you know what's called the temperature coefficient of the resistivity for that substance uh and from there it'll be plug and chug now one thing to note delta T here in chemistry we like to think of that you know involving like a process that's under going a temperature change and it's t final minus t initial well we're not doing a temperature change here we're just comparing two different temperatures but the final you kind of think of as the temperature corresponding to the new value of the uh uh resistivity you're trying to calculate and the initial temperature as being the temperature corresponding to the value of the resistivity you already know so some textbooks Define this with like row2 and Row one which would be then T2 minus T1 same diff but this is kind of the convention I'm going with all right now one thing to note resistance and resistivity are directly proportional and because they are there's a directly analogous equation that compares the resistance of a wire let's say at some new temperature compared to a value you already know at some other temperature but it's directly analogous so r = r * 1 + Alpha Delta T and the idea goes like this let's say you uh raise the temperature on a conducting metal uh and the resistivity goes up by 5% well if the resis ity goes up by 5% then the resistance will as well since they're directly proportional which is why the equation works out exactly the same all right let's do a calculation here the question says a piece of copper wire has a resistance of 8.00 ohms at 20.0 De C what would its resistance be at 50.0 De C and then the temperature dependence U sorry the temperature coefficient of resistivity is given in parenthesis as 0393 per de C from here we can do some plugin and chugging so we use the second these two equations to get the resistance directly so we want to solve for that resistance at some new temperature 50° C the resistance we know is 8.0 ohms I'll multiply that by 1 plus and that temperature coefficient it's given as 0393 per degre celsus and multiply that by the temperature change T minus t KN which is going to be 50.0 de C minus 20.0 de C cool and make sure you get your parentheses right here so we get a couple different sets of them uh one thing we should note is that because we're looking at a second temperature that is now higher we should expect a higher resistance corresponding to that lower conductivity for a conductor at a higher temperature let our calculator do the heavy lifting for us so 8 * parentheses 1 + 0393 * 30 and I'll close my parentheses and we're going to get 8.94 32 which in this case I want three sig figs so 8.94 ohms and that matches expectations that at a higher temperature 50° celius compared to 20° CSUS that the resistance should go up now I want to conclude this lesson by just briefly talking about superconductors no math no calculations just a conceptual understanding of what they are and the big key is this you need to understand that a superconducting material has effectively a zero resistance associated with it and the reason it has zero resistance is because it has a resistivity of zero as well now the problem is that is that superc conduct materials that we know of they're not always super superc conducting they're only superc conducting as you lower the temperature below some certain threshold temperature and unfortunately for every superc conducting material we know of those threshold temperatures are really really really low way lower than kind of any normal outside temperature you're likely to experience even in cold climate uh and so having a a superconduct material that operates in anything resembling ambient temperature anywhere on Earth it's not the most likely thing just yet but we're doing quite a bit of active research uh and it's kind of a big deal if we could find one that operated at something resembling more ambient temperatures if you think of like uh your power lines so there is a lot of energy dissipated just in the transmission of electricity along those power lines so your your power lines might stretch for M sometimes in length and that great length corresponds to a great resistance and that great resistance corresponds to not only to a great uh potential drop but a great power being dissipated across those power lines as well uh and so real increase in efficiency would be possible if we could replace all those power lines with super conducting power lines not presently possible but maybe just maybe in the future if you found this lesson helpful consider giving it a like happy studing