Voltage | Physics | Khan Academy

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." We hear about this all the time in our day-to-day life, but what exactly is it? That's what we're going to 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 are already familiar with: gravity. So here's a question: I have a ramp, and I'm going to drop a ball from some height over here. The ball is going to 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. We 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. That potential energy would have been converted into kinetic energy, and so if I know the kinetic energy, I can figure out the speed of the ball. So you would say, "Hey Mahesh, just give me the values of the potential energy of the system over here and when the ball is over here, and then you can just subtract those values, figure out the kinetic energy, and boom, you’re done."

In fact, while we're at it, you might as well ask me the values of the potential energy of the systems at every location over here because 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. When the ball is over here, it has zero Joules of potential energy, and so on and so forth.

Now just by looking at this, you can say that hey, when the ball comes from here to here, boom, see it would have lost 160 Joules of potential energy, and therefore the ball must have gained 160 Joules of kinetic energy. And 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 2 kg mass. But what if you're dealing with, let's say, a 4 kg mass over here?

Then you understand hey, no big deal. If you're dealing with a 4 kg object, if you had kept a 4 kg object over here, the potential energy would be just double. Because you remember that gravitational potential energy of the Earth-ball system is proportional to the mass of the ball and, of course, the mass of the Earth as well. But since it's proportional to the mass of the ball, if it's, 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 energy over here will be 200 Joules if you're dealing with a 2 kg mass, right? But what if you kept a 1 kg 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 wrote it per kilogram, this automatically means that if I kept 2 kg over here, it would be 200 Joules. If I kept 10 kg over here, it would be, 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. If you’re buying 2 kg, you just pay twice the amount.

So by writing per kilogram, it's a great indicator of how much price you have to pay based on how much, you know, kg of tomatoes you're buying. Same is the case over here. So 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: they 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 assigned at different points in space. Like over here, what do these numbers tell us? The 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. Now 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 positively charged. Let’s say it has a 2 Coulombs of charge. If we ignore gravity completely, okay, even then if I let go of this charge, because of the repulsive force, it will accelerate down. It'll speed up as it goes down and therefore, as it goes further down, it will gain some kinetic energy.

If 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." Because 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.

But then you would 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 potential energy of the electric potential energy of the system would be 100 Joules. Over here, it would be 80 Joules; and 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. Just like how these numbers are called gravitational potential, these numbers are called electric potential. And because electric potential is such an important concept, we actually give a separate unit for this: Joules per Coulomb is called volts. So we’ll say this is 100 volts; this point is at an electric potential of 80 volts, and so on and so forth. These numbers are called electric potential; they're identical and analogous to gravitational potential.

So finally, you may ask, well, is this what voltage is? Close enough! Voltage is basically the difference between the electric potential or electric potential difference. Why do we care about the 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—I only care about 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 volts. But what does it mean now? Can you answer what it means to say the voltage between these two is 60 volts? 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 would be three times that number and so much. But think about this way: what if a Coulomb went from here to here? Then it would gain 60 Joules of potential energy. It's 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.

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—it's just a way to tell which is higher and which 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, and this is lower.

And if I consider these two, then I would say this is this is positive, this is negative. So 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 defined voltages, we could have a ton of questions. Our 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, you 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.

I 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 want to design good bulbs that give out a good amount of light.

Okay, 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 can create a potential difference. Okay, when 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 said that voltage is always defined between two points. It'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.

So when we say that the wires are at a very high voltage, say 10,000 volts, what we really mean is that the electric potential difference between the wire and the ground, the Earth, 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? First 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 any 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. But 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 the ground. Therefore, if this is at 10,000 volts with respect to the ground, this is at 10,000 volts compared to the ground. Then if you subtract them, it should be zero, right? Because they are the same potential. Since they are the same potential, the potential difference between any two points in the bird is zero, and therefore no charges flow 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). This point is also at a high potential (100 Joules per kilogram), but what is the potential difference between them? Zero. They're both at 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.

What if, for example, 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 connected to, let’s say, this pole, which is at the ground level? So it is at the same potential as the ground and the other part is 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. 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 a high voltage, causing a potential difference across our bodies. But wait, when there is a potential difference, charges flow—we said, but which direction do the charges flow and how do we quantify that? We'll talk about all of that stuff in the next video.