Video: Electric Current

In this lesson, we will learn how to use the formula 𝐼 = 𝑄/𝑡 to calculate the current through a point in simple circuits given the charge moving past that point in a given time.


Video Transcript

In this video, we’re talking about the somewhat shocking concept of electric current. Electric current is something we’re able to witness in the natural world, for example, strikes of lightning. And it’s also something we experience up close. We probably all know what it’s like to get a mild electric shock when we put our hand near a metal object on a very dry day. That shock comes from the discharge of electric current.

And of course, in addition to these examples, there are many more examples of controlled applications of electric current. We use it to turn on lights, operate appliances, and heat and cool our homes. Though electric current may seem to be a very mysterious phenomenon, understanding it really comes down to understanding how electric charges, both positive and negative charges, interact with one another. But before we talk about electric charges, let’s talk for a bit about a different type of current.

We’re all familiar with currents of water. This is what flows in a river or in a stream. The way that water flows can help us understand how electricity flows, what electric current is. Think about the current in this river. We might describe it as fast moving or slow moving or somewhere in between. When we talk this way, we’re really referring to the speed of the water as it moves along, whether that’s fast or slow. But really when it comes to current, that’s not quite the whole story.

To see why, let’s consider a cross section of this stream. Let’s say that our cross section looked like this. It had this particular width to the stream and this particular depth. And we’ll say that all the water in the stream is moving along at the same speed in the same direction. Okay, that’s one scenario.

Now let’s imagine a second one with a different cross section to our stream. Now imagine that our stream cross section looked like this, same width as before, and all the water in the stream is moving at the same speed as before. But now the stream is much deeper. We can see that, in this case, there’s a much larger overall volume of water that passes by our observation point standing by the stream. Here’s the point.

Current of any type, whether a current of water or a current of electricity, is a description of the amount of flowing material that passes by a point over some time span. And we can write that down over here. This is our definition of what current in general is.

So now that we understand that, let’s get back to those electric charges we saw earlier, the positive and the negative charges. Here we have those electric charges, and we know that they have opposite signs. And what does this mean? Well, it means that they attract one another. That is, there’s an attractive force that draws the positive charge towards the negative and the negative charge towards the positive. These charges want to attract one another. And we know that the opposite is true. That is, we know that if we had two positive charges, then they would push one another away. The force on them will be like this. And likewise, if we had two negative charges, again the charges are the same and so they repel one another. There’s a force to push them away from each other.

This simple fact that unlike electric charges attract one another and like electric charges repel one another is the reason for electric current. In other words, it’s the thing that makes electric charges move through a circuit or through a loop. To see why that’s so, let’s consider an object called a conductor, which is made up of many many positive as well as negative charges.

Now in this little sketch here, we show our conductor with just a few represented charges but understand there are many many more than we’ve shown here. In any case, if we counted up all the negative charges that we see in the conductor and then we counted up all the positive charges, we will get the same number in each case. Overall, this conductor has the same number of positive as negative charges.

But here’s why it’s called a conductor. We call this a conductor because the negative charges shown here on our sketch, the charges in gold, are fairly mobile charges. It’s easy to pull them off of the atom they’re attached to and have them move around the conductor. In other words, if we bring other electric charges near this material, then this conductor is able to respond to that. Charge actually flows within it.

That said, if we just leave the conductor there, say sitting on a tabletop, then no charge will flow across it because we’re not providing any sort of electrical push. We’re not giving the charges in it any reason to move. But we can do that. We can provide that push by connecting our conductor up to a battery.

A simple way to think of what a battery does is it sends positive charges out in one direction and negative charges out in the other direction. Here our battery sends positive charge in a clockwise direction and negative charge in a counterclockwise direction. When the positive charge reaches the left side of our conductor, we can see what will happen by recalling our attraction and repulsion of electric charges that we learned over here. The positive charge in our circuit will exert an attractive force on these negative charges on the left side of our conductor. As a result, these negative charges will start to move to the left.

Remember, they’re able to because this is a conductor. As these negative charges leave the conductor, that will open up a region in the conductor which is depleted of negative charges. The other negative charges in the conductor will be drawn to that region. And they’ll all move to the left themselves. This process carries on through the whole length of the conductor, minus charges, negative charges, moving along to the left.

If this was the only part of the process, then very quickly our conductor would run out of mobile electric charges to contribute. But that’s where the negative charges that are sent out by the battery in the other direction come into play. These charges are able to replenish the supply of mobile and negative charges in the conductor by moving in from the right side.

All of these interactions between the positive and negative charges we have here are governed by these simple rules. Opposite charges attract, and like charges repel. The overall effect of all this is that negative charges, the minus signs, are able to move counterclockwise continuously through this circuit. We have a flow of electric charge, in other words, an electric current.

Once we have an electric current set up in this circuit, our next step is we wanna quantify it. We wanna know just how much current is flowing. That brings us back to our definition of current. It’s the amount of flowing material, in this case electric charge, that passes by a particular point in some amount of time.

In line with this definition for current, let’s go ahead and pick a particular point in this circuit. It could be anywhere. But it’s the point where we’ll watch for the flow of electric charge. Let’s say that point is right here in the top left corner of our circuit. So say we stand here and we watch that particular point. And as we watch, we count every single negative charge that passes by that point. And more than that, say we have a stopwatch with us so that we’re able to count the number of charges that pass by that green point in our circuit over some particular time interval.

Let’s say that, using our stopwatch, we count off one second of time passed and that, in that one second, we count 27 negative charges flowing past that particular point in our circuit. So we had 27 negative charges pass by a point in our circuit in one second. And what our definition for current says is if we divide that amount of flowing material by the time interval of one second, then that is a measure of the current in our circuit.

What we found then is that the current in our circuit, which we symbolize using the letter capital 𝐼, is equal to 27 negative charges passing by a point in the circuit every one second. This brings up the question though, how much charge is in 27 negative charges? We’d like to quantify that somehow.

Well, it turns out that all of the negative charges we’ve been talking about that are in our conductor have a particular electric charge to them. This amount of charge, which we often abbreviate using letter 𝑄, is equal to negative 1.6 times 10 to the negative 19th coulombs, where coulomb is the unit of electric charge. Just like meters is the unit of distance or seconds is the unit of time, coulombs is the unit of electric charge. Knowing this number is great because we can substitute it in for the symbol we’ve had here of negative electric charge.

Now we actually know how much charge that is. With that substitution in, now look at our expression for the current 𝐼. We have some amount of flowing material, charge, divided by some amount of time. If we went ahead and calculated this fraction, that would give us the current running through this circuit. But what would the units of that current be?

Well, we can see that they would be coulombs per second. But there’s another name for a coulomb per second. The official unit of electric current is called the ampere. And we symbolize it using a capital A. One ampere is defined in terms of coulombs and seconds. In fact, one ampere is equal to one coulomb of charge passing by a point in our circuit every one second.

If we take a look back at the amount of charge that each one of the negative charges in our circuit holds, we can see that we would need billions and billions of those single negative electric charges to make up one coulomb of total charge, far more charges than we could count. Nonetheless, that’s the definition of an ampere of current. It corresponds to one coulomb of charge passing by every second.

Let’s get some practice now with electric current through an example.

Which of the following is the correct formula for the amount of charge flowing through a point in a circuit in a given time? 𝑄 represents the amount of charge, 𝐼 represents the current, and 𝑡 represents time.

In this example, we’re looking for the correct formula out of the four choices we’re given, A, B, C, and D, that represents the amount of charge, 𝑄, flowing through a point in a circuit over a given time. In other words, we want to know mathematically how it is that charge 𝑄, current 𝐼, and time 𝑡 are related.

It will be helpful to us to recall the general definition of just what a current is. Current is a measure of the amount of flowing material passing by a point in some amount of time. When it comes to electric current, that flowing material is charge. We represent that using the letter 𝑄. And we can represent some amount of time using the letter 𝑡.

Since current has to do with the amount of charge passing a point per unit time, we can divide 𝑄 by 𝑡, and that will give us the current, which we symbolize with 𝐼. We now have a mathematical equation for current. Let’s see if we find this equation anywhere among our answer options.

Looking first at answer option A, we see that that claims that current is equal to charge times time. But our equation shows that current is equal to charge divided by time. This means that option A is not the correct formula. All the remaining options after this one have 𝑄 isolated by itself on one side of the equation. In order to see how our equation compares, let’s algebraically rearrange it so that 𝑄 is on one side by itself.

To do this, we can take our equation and multiply both sides of it by the time passed 𝑡. When we do this, 𝑡 on the right-hand side of the equation cancels out since it’s in both numerator and denominator. Our equation now reads 𝑄, the charge, is equal to 𝐼 times 𝑡. And we see that, of the three choices B, C, and D, it’s D that matches up with this expression. So the correct formula for the amount of charge flowing through a point in a circuit over a given time is 𝑄 is equal to 𝐼 times 𝑡.

Let’s summarize what we’ve learned so far about electric current. We saw in this lesson that electric current is the amount of charge flowing past a point in some amount of time. If we write that as an equation, we can express it as 𝐼, electric current, is equal to charge, 𝑄, divided by time, 𝑡. We also saw that the flow of charge happens thanks to interactions between positive and negative electric charges.

We saw that these opposite charges attract one another, while on the other hand if we have a pair of like or similar electric charges, they repel one another. And we also saw that the unit of electric charge is the coulomb, while the unit of current is the ampere. And we saw they’re related to one another this way, that one ampere is defined as one coulomb of charge passing a point in one second. So then electric current is the flow of electric charge over time.

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