Video: Electric Current

In this video, 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, our topic is electric current. Electric current is the flow of electric charge. And here, we see three examples of this type of flow. A lightbulb lighting up in an electric circuit, our finger getting a small electric shock when it comes near a door knob, and even a bolt of lightning are all examples of electric charge in motion.

Before we talk about electric current though, let’s think about a current that we may be more familiar with. Say that we have a channel that carries water, and this water flows left to right as we’ve drawn it. Water flowing like this, all moving along in the same direction, is called a current. And beyond describing the current as fast or slow or somewhere in between, it’s actually possible to quantify it. We can say that current, which is some collection of objects flowing together like water is flowing in this channel, is equal to the amount of the flowing substance divided by an amount of time.

Say, for example, that we stood at the end of this trough and we counted off using a stopwatch some amount of time, say, one second. And say further that during that time interval, we were able to collect all of the water that flowed out of the channel. In that case, we would’ve measured the amount of flowing substance moving through this channel in some amount of time. By knowing those two quantities and taking their ratio like this, we could calculate the current flowing through this channel. And this method applies to any kind of current, whether it’s water flowing or some kind of gas or even electric charge.

Now, when we’re talking about water, we know that it’s gravity that causes this substance to flow. But when we talk about electric charges, negative and positive, it’s a different force entirely. Whenever there’s an object with a net electric charge, that object creates an electric field around itself. This field, which points inward for negative charges and outward for positive charges, has an effect on any other electrically charged objects nearby.

Now, let’s imagine that these two charged objects are fixed in place. They can’t move. But let’s say that we put an electric charge between them that is capable of moving, and that this is a positive electric charge. Because of the electric field that this charge is in, it experiences an electric force. If we recall the rule that like electric charges repel and unlike charges attract, we can see that this positive charge will be drawn to the negative charge, and it will be pushed away from the positive. Now, let’s think about what would happen if we increase the space between our two fixed charges, and we also put lots more positive charges in between them.

Now, every single one of these charges would again be drawn to the negative charge, and it would be repelled from the positive. The charges as a group would start to flow from right to left. We can see that as these charges are in motion, what we have is a current. This time, the current is made of electric charge. And what’s more, we could quantify this current according to this relationship. Let’s say that we put a dashed line across the path of our moving electric charge. And then, over some amount of time that we pick, say that it’s one second, we count just how many of these positive charges flow past our line.

Now, when our current consisted of flowing water like we saw a moment ago, we didn’t need to measure individual water molecules in order to measure the current overall. That’s because, in that instance, our flowing substance was simply water. But now, our flowing substance is electric charge, so it will be important to know just what is the electric charge of each one of these moving charges. Let’s say that each one has the charge of a proton. We’ll call it 𝑞 sub p.

Electric charge is measured in units of coulombs abbreviated with a capital 𝐶. And the charge of a proton is 1.6 times 10 to the negative 19th of these coulombs. So, each one of these positive charges has a net charge of 1.6 times 10 to the negative 19th coulombs, and these charges are moving past our line, and we’re counting them. And let’s imagine that after we let one second of time elapse, that’s the amount of time over which we’ll calculate our current, we count a number of positive charges that we’ll simply refer to as 𝑁. 𝑁 could be five or 10,000 or any other integer value. It’s the count of the number of positive charges that move past our dash line in one second.

Now, if we were to go ahead and divide 𝑁 by one second like this, then, in that case, our current would be calculated in terms of the number of positively charged moving objects. But what we really want, instead of this, is to calculate this electric current in terms of the total flow in charge. In other words, we would like our numerator to be the total electric charge that passes by our dashed line in one second of time.

And since each one of our moving charges has the net charge of a proton, that means we can multiply 𝑁 by 𝑞 sub 𝑝, and that will equal the total charge that has flowed past our line in one second. If we let 𝑁 times 𝑞 sub p equal the symbol capital 𝑄, then capital 𝑄 represents the total charge that has flowed past our point. So then, the total amount of flowing charge we have is capital 𝑄, and the total amount of elapsed time is one second. So, 𝑄 divided by one second is equal to the current of electric charge, that is, the charge that’s flowing between this fixed positive charge and this fixed negative one.

So, we’ve seen that when we’re talking about electric current, our amount of flowing substance is the electric charge. And we’ve seen further that this charge is measured in units called coulombs. Now, if we have one coulomb of electric charge passing a point every one second, then we have what is called one ampere of electric current, where ampere is symbolized with a capital 𝐴. Just as coulomb is the unit of electric charge and second is the SI base unit of time, ampere is the SI based unit of current.

In general though, when we’re talking about electric current, we won’t have exactly one coulomb of charge passing by every one second. Instead, we’ll have some general amount of charge we can call it 𝑄 and also some general amount of time we can call 𝑡. And it’s this ratio, 𝑄 divided by 𝑡, that’s equal to the electric current 𝐼. And from our units equation down below, we can write that current measured in units of amperes is equal to total charge measured in units of coulombs divided by the total time measured in units of seconds.

Now that we’ve talked about the flow of electric charge in general, let’s talk about it in a specific case, when this charge is moving through electrical wires. Here we have a loop of wire, and one segment of the wire, this part here, is expanded for an up-close view. Like all electrical wires, this one is made of conducting material, some kind of metal typically. This means that when we think about the atoms that make up the wire, these atoms are comprised of a nuclear core, the nucleus, some number of electrons that are fairly strongly bound to the nucleus.

But then, there’s at least one electron, which, even though it does orbit around the nucleus for now, it will be easy from an energy perspective to pull it away from this atom. That is, it wouldn’t take much energy to strip this electron away from the atom and have it move around freely. So that’s how these metal atoms are constructed. And if we take a zoomed-in view at how these atoms are arranged in the wire, the nuclei of these atoms, where all the positively charged protons reside, are arranged in a fairly stable grid pattern. To a large extent, these nuclei are fixed in place. They can’t move. But what can move easily throughout this wire are the loosely held electrons that each conducting atom contributes.

And remember, all the other segments of this wire are just like the one we’ve drawn a zoomed-in view of here. So all along this loop of wire, there are these positively charged atomic nuclei in a grid pattern and then these very loosely held electrons attached to those nuclei. Earlier, we saw that an electric field is something that can exert an electric force and create movement in electric charges. And that’s exactly the mechanism that’s used in order to create the flow of electric charge in an electric circuit.

Typically, what supplies that electric field is a cell or a battery that we put in the circuit. As we’ve drawn it, the left side of this cell is positively charged, and the right side is negatively charged. And the presence of this cell with these oppositely charged ends establishes an electric field that runs all throughout this wire. We saw earlier that electric fields point away from positive and toward negative charges. In other words, they show us the direction where positive charges are pushed. That’s the same way the electric field all throughout the circuit points. It points in a clockwise direction, so it’s away from positive and toward negative.

And just like we saw earlier, this field will have an effect on the motion of the free charges in our wire. Recall that those free charges are electrons because all the positively charged protons are bound up in the core of the atomic nuclei. They can’t move much, but the loosely held electrons can. And so, the free electrons do start to move, but in which direction? Well, since they have a negative electric charge, they’re attracted to a positive charge and repelled from another negative. This means that the average motion of these negative charges will be in the counterclockwise direction. And it’s these negative charges in motion that give this wire a current, that is, a continuous flow of electric charge.

Now, for historical reasons, it was thought that the charges that are in motion in an electric circuit are not negatively charged, but rather positively charged. If that were true, if positive charges were able to move along conducting wires, then we can see that in this circuit, they would move in a clockwise direction. And that’s because it’s that direction for a positive charge that would lead it to move towards the negative terminal of our cell and away from the positive terminal.

Even though we now know that it’s the negatively charged electrons that move and create current in a wire, because the earliest notions of charge flow in an electric circuit held that it was positive charges that moved, it’s charge flow in this direction that’s referred to, even today, as conventional current. We can say that the direction of conventional current is the direction that positive charges would flow in a wire if they did indeed flow. We can understand, though, that for a metal wire, the actual charge flow, the real current, consists of the movement of negative charges, electrons. And naturally, this flow is in the opposite direction of conventional current.

It’s important to understand this distinction because, oftentimes, we’ll be given an example scenario where we’ll simply be told the direction of the current. When we hear that, what’s being described is the flow of conventional current, the movement of positive charge. Now, in general, when we’re not constrained to talking about charge flow through wires, both positive and negative charges can move and be a part of electrical current. But the great majority of cases we’ll likely encounter do consist of charge flow in metal wires. And when this is the case, it will be helpful to recall that positive charges don’t move in these circuits. But negative charges, electrons, do.

And it’s worth noting that each one of these flowing electrons has an electric charge which is equal and opposite the charge of a proton. That is, if we call the charge of an electron 𝑞 sub 𝑒, then that charge is equal to negative 1.6 times 10 to the negative 19th coulombs. And each one of these flowing electrons adds up to contribute to a total amount of moving charge over some amount of time, which defines the current in the circuit.

Now, let’s summarize what we’ve learned about electric current. Starting off, considering current from a broader perspective, we saw that current can be defined as an amount of some substance flowing over an amount of time. We then considered that this flowing substance can be electric charge and that it’s electric fields that create an electric force on charged objects, which tends to make them move. We saw further that electric charge is measured in units called coulombs, and a coulomb per second is equal to the unit of electric current, the ampere. And ampere, then, represents some amount of electric charge flowing past some point every second.

Expanding on this, we saw that electric current 𝑖 in units of amperes is equal to a total amount of charge 𝑞 in units of coulombs divided by a total amount of time in units of seconds. And lastly, we saw that in a wired electrical circuit that’s powered by a cell or a battery, the direction that positive charges would flow, if they did flow in such a circuit, is called the direction of conventional current, while the direction of electron flow, the charges that actually move in such a circuit, is opposite this. This is a summary of electric current.

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