Voltage (electric potential difference)

0:00- [Mahesh] You probably know that power lines are very dangerous, because they have very high voltage, right? So, we should stay away from them. But then what about these birds? Why don't they get electrocuted? To answer that question, we need to dig deeper into this word voltage.

0:12We hear about this all the time in our day-to-day life, but what exactly is it? That's what we're gonna find out in this video. So let's begin. I think the best way to gain a deep intuition of voltage is by looking at something that we already familiar with, gravity.

0:27So, here's a question. I have a ramp and I'm gonna drop a ball from some height over here. The ball's gonna roll down and when it comes over here, it'll have some speed. How do I figure out that speed? Well, we know one of the cool ways of doing that is by using energy conservation.

0:42We say that, "Hey, the ball over here has zero kinetic energy, but the ball-Earth system has some potential energy over here. And when that ball rolls down and comes all the way here, notice because it's closer to the Earth now it would have lost some potential energy and that potential energy would have been converted into kinetic energy."

1:03And so, if I know the kinetic energy, I can figure out this speed of the ball. So you would say, "Hey, Mahesh, just gimme the values of the potential energy of the system over here and then the ball is over here." And then you can just subtract those values, figure out the kinetic energy and boom, you're done.

1:17In fact, while we are at it, you might as well ask me the values of the potential energy of the system at every location over here, 'cause then you can do this for any two points, right? So, you might expect something like this. This means that when the ball is over here, the system has 200 joules of potential energy.

1:34When the ball is over here, it has zero joules of potential energy and so on and so forth. And now, just by looking at this, you can say that, "Hey, when the ball comes from here to here, boom. See, it would've lost 160 joules of potential energy and therefore the ball must have gained 160 joules of kinetic energy."

1:49And since you know the mass of the ball, you can now calculate the speed of the ball. So easy, right? But wait a second you say. You quickly realize that these numbers only work as long as you're dealing with a two kilogram mass. But what if you're dealing with let's say a four kilogram mass over here, then you understand, hey, no big deal.

2:08If you're dealing with a four kilogram object, if you had kept a four kilogram object over here, the potential energy would be just double, because you remember the gravitational potential energy of the Earth-ball system is proportional to mass of the ball and of course, mass of the Earth as well.

2:20But since it's proportional to the mass of the ball, if you're dealing with twice the mass, the numbers would just be twice. If you're dealing with half the mass, then the numbers would over here would be just half of it. So, you get now an incredible idea. You say, "Hey, hey, hey, the potential here will be 200 joules, if you're dealing with a two, if you kept a two kilogram mass, right?"

2:38But what if you kept a one kilogram mass? Then the number over here would be 100 joules. So, you say, "Let's write this down as 100 joules per kilogram." By writing it this way. We are now indicating that if I kept a kilogram over here, the gravitational potential energy of the system would be 100 joules, but because I written per kilogram, this automatically means that if I kept two kilograms over here, it would be 200 joules.

3:04If I kept 10 kilograms over here, it would be a, you know, 10 times that 1,000 joules and so on and so forth. So, by writing it as per kilogram, you are now indicating what the potential energy would be for any mass that you keep. Just like this is just like how in grocery stores, you know, they have an indicator of how much price you have to pay per kilogram of tomatoes.

3:25If you have two kilograms, if you're buying two kilograms, you just pay twice the amount. So, by writing per kilogram, it's a great indicator of how much price you have to pay regard based on how much, you know, kilograms of tomatoes you're buying. Same as the case over here.

3:37So, let's do that everywhere you say. So over here it would be 60 joules per kilogram. This would be half of it, 20 joules per kilogram. And so now, we have indicators of what the potential energy would be for any kilogram that you keep over here. These indicators are given a name.

3:54They are called gravitational potential. I know we could have done better. We could have come up with better names, because it could be confusing. What is gravitational potential and what is gravitational potential energy? Subtle difference. Gravitational potential is a number that we assign at different points in space.

4:12Like over here. What do this number tell us? Number tells us what the gravitational potential energy would be if you had kept a kilogram of mass over there. So for example, the gravitational potential energy here would be 20 joules, if you kept a kilogram, but if you kept three kilograms, the gravitational potential energy would be three times that much, 60 joules and so on and so forth.

4:34Now, guess what? We do something very similar with electric potential energy and define something called electric potential, okay? So, let's look at that. We have a charged balloon fixed to a ceiling and close to it we have a tiny styrofoam, which is also a positively charged.

4:48And let's say it has a two coulomb of charge, if we ignore gravity completely, okay? Even then, if I let go of this charge, because of the repulsive force, it'll accelerate down, it'll speed up as it goes down, and therefore as it goes further down, it'll gain some kinetic energy.

5:02If I asked you how much kinetic energy it has gained, how would you calculate that? You would again say, "Hey, Mahesh, give me the values of the electric potential energy of the system over here. And when that object is over and the styrofoam is over here, 'cause then if you subtract the two, you can find how much the potential energy has decreased and you can calculate how much the kinetic energy has increased."

5:24But then you do something very similar. You would say, "Hey, hey, hey, instead, just give me the electric potential energy value per coulomb everywhere," because if I give you that, then you can do this for any charge moving from any one point to another. This means if you had a coulomb over here, then the electric potential energy of the system would be 100 joules, or here it would be 80 joules.

5:50And so, when a coulomb goes from here to here, it would have lost 20 joules of potential energy gaining 20 joules of kinetic energy. But if it was three coulombs instead, it would just be three times that number. And just like how these numbers are called gravitational potential, these numbers are called electric potential.

6:08And because electric potential is such an important concept, we actually give a separate unit for this. Joules per coulomb is called volts. And so, we'll say this is 100 volts. This point is at an electric potential of 80 volts and so on and so forth. And so, these numbers are called electric potential.

6:27They're identical, analogous to gravitational potential. So finally, you may ask, "Well, is this what voltage is?" close enough. Voltage is basically difference between the electric potential or electric potential difference. Why we care about difference? Because remember, when a charge moves from one point to another, if I want to know how much it gains kinetic energy, I don't really care about what the value of electric potential here is and what the value of electric potential here is.

6:51All I care about is what the difference is, right? And that difference is what we call voltage. So for example, the voltage between this point and this point is basically the electric potential difference between those two points, which is 60 volt. But what does it mean now?

7:06Can you answer what does it mean to say the voltage between these two points is 60 volt? It means if a coulomb goes from here to here, it would lose 60 joules of electric potential energy. That's all that it means. And of course, if you're dealing with three coulombs of charge, it'll be three times that number and so much.

7:23But think about this way, what if a coulomb went from here to here, then it would gain 60 joules of potential energy, which is the opposite, right? So in general, if I have electric potential difference between any two points, some number is given, it could mean that it could either lose or gain that depends upon which is at a higher potential value and which is at a lower potential value.

7:43And to indicate that, we often use positive and negative signs. The higher potential value is always given a positive sign and the lower potential value, let's say consider this lower potential value, we'll give it a negative sign. But remember, it doesn't mean that there's something positive here and something negative over here.

8:00It's just a way to tell which is a higher, and this is lower. For example, if I were to consider these two, then I would say, this is positive and this is negative, because this is higher, this is lower. And if I consider these two, then I would say this is positive and this is negative.

8:17So positive just means high, negative just means low. So, that I would understand which direction a coulomb would lose potential energy and in which direction it would gain potential energy. That's it. Okay, now that we've defined what voltage is, we could have a ton of questions.

8:31Our first question should be, why should we care? Sure, every coulomb going from here to here, loses 60 joules of energy, but what can I do with that information practically? Well, where do you think that energy goes? Well, we might think it goes into kinetic energy as we've been discussing so far, but if you are considering circuits and real wires, well, charges will bump into atoms and all of that, their kinetic energy would be converted into heat energy, which means that 60 joules of energy gets converted into heat.

8:57I now have a method to calculate how much heat energy is generated in a wire. Isn't that incredible? That's incredible because that means I can now predict things like how much heat energy would be generated in a bulb, for example, which is required if you wanna design good bulbs that give out good amount of light.

9:16Okay, another question we could now have is what generates this potential difference in the first place? Well, in general, whenever there is an electric field, like for example, the charged balloon created an electric field, whenever you create an electric field, you'll create a potential difference, okay?

9:32When it comes to circuits, that electric field is created by, no surprise, batteries. Batteries are the ones that create electric fields and create potential differences. Okay, another question we could be having is, we say that voltage is always defined between two points.

9:47It's an electric potential difference between two points, right? But we say things like, "Hey, that wire is at very high voltage, it's at 10,000 volts." What does that mean? Ah, again, when it comes to electric circuits, which is where this is useful, our second point is often considered the ground.

10:05So, when we say that the wires are at a very high voltage at 10,000 volts, what we really mean is that the electric potential difference between the wire and the ground, the Earth, that is 10,000 volts. Finally, this brings us to our original question. Why don't birds get electrocuted when they sit on high voltage wires?

10:25First of all, what does it mean for wires to be at a high voltage? Well, it basically means the potential difference between the wire and the ground. This is the symbol that we use for ground is very high, say 10,000 volts. Now, if you consider only one bird, say this bird over here, then because it is sitting on the wire, it has the same voltage, meaning again, it also has a very high potential difference compared to the ground.

10:48But here's a question. What is the potential difference between any two points inside the bird? That's the big question. What do you think? Well, the answer is zero, because both the points are at the same potential with respect to ground. And therefore, if this is at 10,000 volts with respect to ground, this is a 10,000 volt compared to ground, then if you subtract them, it should be zero, right?

11:11Because they're the same potential, and since they're the same potential, the potential difference between any two points in the bird is zero and therefore no charges for from one point to another. This is very similar to how, if you were to keep a ramp horizontally over here, then notice this point over here is at a high gravitational potential, 100 joules per kilogram.

11:29This point is also at a high potential, 100 joules per kilogram. But what is the potential difference between them? Zero. They're both the same potential, so there's no potential difference, and therefore the ball will not roll. The ball would only roll, if there was some potential difference.

11:43What if, for example, if you know, if it was inclined like this? Similarly, since there is no potential difference, charges will not flow from one part of the body to another. But what if the bird somehow had one part of its body connect, you know, on let's say this pole, which is at the ground level.

12:00So, it is at the same potential as the ground and the other part touching the wire. Now, there will be a potential difference between the, you know, these two parts. There'll be potential difference between points in its body. Now, there will be charges flowing that could be lethal to the bird.

12:18And that's why we advise never to touch any live wire, any high voltage stuff, because a part of our body would be on the ground. And then the other part would be at the high voltage causing potential difference across our bodies. But wait, when there is a potential difference, charges flow we said, but which direction the charges flow?

12:35And how do we quantify that? We'll talk about all of that stuff in the next video.