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# Introduction to circuits and Ohm's law

## Video transcript

what we will introduce ourselves to in this video is the notion of electric circuits and Ohm's law which you can view as the most fundamental law or the most basic law or simplest law when we are dealing with circuits and it connects the ideas of voltage which we will get more of a intuitive idea for in a second and current which is denoted by capital letter I I guess to avoid confusion if they used a capital C with the Coulomb and what connects these two is the notion of a resistance resistance that is denoted with the capital letter R and just to cut to the chase the relationship between these is a pretty simple mathematical one it is that voltage is equal to current times resistance or another way to view it if you divide both sides by resistance you get that current is equal to voltage divided by resistance voltage divided by resistance but intuitively what is voltage what is current and what is resistance and what are the units for them so that we can make sense of this so to get an intuition for what these things are and how they relate let's build a metaphor using the flow of water which isn't a perfect metaphor but it helps me at least understand the relationship between voltage current and resistance so let's say I have this vertical pipe of water it's closed at the bottom right now and it's all full of water there's a water above here as well so the water in the pipe so let's say the water right over here it's going to have some potential energy and this potential energy as we will see it is analogous to a voltage voltage is electric potential electric potential now it isn't straight up potential energy it's actually potential energy per unit charge so let me write that potential energy per unit unit charge you could think of it as joules which is potential energy or units of energy per Coulomb that is our unit charge and the units for voltage in general is volts now let's think about what would happen if we now open the bottom of this pipe so we open this up what's going to happen well the water is immediately just going to drop straight down that potential energy is going to be converted to kinetic energy and you could look at a certain part of the pipe right over here right over here and you could say well how much water is flowing per unit time and that amount of water that is flowing through the pipe at that point in a specific amount of time that is analogous to current current is the amount of charge so we could say charge per unit time Q for charge and T for time and intuitively you could say how much how much charge flowing flowing past a point in a circuit a point in circuit in a let's say a unit of time we could use to think of it as a second and so you could also think about it as coulombs per second charge per unit time and the idea of resistance is something could just keep that charge from flowing at an arbitrarily high rate and if we want to go back to our water metaphor what we could do is we could introduce something that would impede the water and that could be a narrowing of the pipe and that narrowing of the pipe would be analogous to resistance so in this situation once again I have my vertical water pipe I've opened it up and you still would have that potential energy which is analogous to voltage and it would be converted to kinetic energy and you would have a flow of water through that pipe but now every point in this pipe the amount of water that's flowing past at a given moment of time is going to be lower because you have literally this bottleneck right over here so this narrowing is analogous to resistance how much charge flow impeded and peated and the unit here is the ohm is the ohm which is denoted with the Greek letter Omega so now that we've defined these things and we have our metaphor let's actually look at an electric circuit so first let me hat construct a battery so this is my battery and the convention is my negative terminal has is the shorter line here so I could say that's the negative terminal that is the positive terminal associated with that battery I could have some voltage and just to make this tangible let's say the voltage is equal to 16 volts across this battery and so one way to think about it is the potential energy per unit charge let's say we have electrons here at the negative terminal the potential energy per Coulomb here is 16 volts these electrons if they have a path would go to the positive terminal and so we can provide a path so let me draw it like this and at first I'm gonna not make the path available to the electrons I'm gonna have an open circuit here but I'm gonna make this path for the electrons and so as long as our circuit is open like this this is actually analogous to the closed pipe the electrons there's no way for them to get to the positive terminal but if we were to close the circuit right over here if we were to close it then all of a sudden the electrons could begin to flow through this circuit in an analogous way to the way that the water would flow down this pipe now when you see a schematic diagram like this when you just see these lines those usually denote something that has no resist but that's very theoretical in practice even a very simple wire that's a good conductor would have some resistance and the way that we denote resistance is with a jagged line and so let me draw resistance here so that is how we denote it in a circuit diagram and let's say the resistance here is 8 ohms so my question to you is given the voltage and given the resistance what will be the current through this circuit what is the rate at which charge will flow past a point in this circuit pause this video and try to figure it out well to answer that question you just have to go to Ohm's law we want to solve for current we know the voltage we know the resistance so the current in this example is going to be our voltage which is 16 volts divided by our resistance which is 8 ohms and so this is going to be 16 divided by 8 is equal to 2 and the units for our current which is charge per unit time coulombs per second you could say 2 coulombs per second or you could say amperes and we can denote amperes with a capital a we talked about these electrons flowing and you're gonna have 2 coulombs worth of electrons flowing per second past any point on this circuit and it's true at any point same reason that we saw over here even though it's wider up here and it's narrower here because of this bottleneck the same amount of water that flows through this part of the pipe in a second it would have to be the same amount that flows through that part of the pipe in a second and that's why for this circuit for this very simple circuit the current that you would measure at that point this point and this point would all be the same but there's a quirk pause this video and think about what do you think would be the direction for the current well if you knew about electrons and what was going on you would say well the electrons are flowing in this direction and so for this electric current I would say that it was flowing in I would denote the current going like that well it turns out that the convention we use is the opposite of that and that's really a historical quirk when Benjamin Franklin was first studying circuits he did not know about electrons they would be discovered roughly 150 years later he just knew that what he was labeling as charge and he arbitrarily labeled positive and negative he just knew they were opposites he knew something like charge was flowing and so in his studies of electricity he denoted current as going from the positive to the negative terminal and so we still use that convention today even though that is the opposite of the direction of the flow of electrons and as we will see later on current doesn't always involve electrons and so this current here is going to be a 2 ampere current