Lesson Video: Cells in Series Science

In this video, we will learn how to calculate the total emf of a set of cells that are connected in series.

13:51

Video Transcript

Cells are one source of the potential difference needed to make a circuit work. In this lesson, we will learn about the potential difference provided when several cells are connected in series.

Here is perhaps one of the simplest circuits that we could construct. It is an incandescent light bulb connected to a wire. Although this circuit is easy to construct, it is almost completely useless. There is no source of potential difference, so there is no current in the circuit and the bulb will never light up. However, if we use the wire to connect the bulb to a cell, the potential difference from the cell will cause charge to move in the circuit, which will cause the bulb to light up.

When we include this nine-volt cell in the circuit, the bulb lights up. This is because there is now current in the circuit. That is, charge is moving from the cell to the light and then back to the cell. Because the potential difference of the cell causes current and current is moving charges, we often call the potential difference of a cell electromotive force. Usually, though, instead of saying the long phrase electromotive force, we take the E, M, and F and abbreviate electromotive force as emf. So we would say in our circuit that the cell provides an emf of nine volts.

Now, remember, our primary goal is to learn about circuits with multiple cells. To think about such circuits, we’ll want a way to represent those circuits that is more general than the very realistic diagram we’ve already drawn. This is because there are many other real situations, like a flashlight or the light in a car where light is produced by a bulb connected to a cell by two wires. The examples we just mentioned all look very different, but the physics of the circuits is the same.

To allow us to focus only on the electronic structure of these circuits rather than their particular sizes or shapes, we will use standard symbols to represent each component. This symbol, a circle with an X through it, represents a bulb. The wires in the circuit will be represented by lines. And for neatness, we will almost always draw these lines straight or turning at right angles. Finally, the symbol for a cell is one long line and one short line separated from each other by a small gap.

The long line represents the positive terminal of the battery, and the short line represents the negative terminal. Usually, we also label the cells in a circuit diagram with the emf that they provide. So if we label this cell nine volts, it could be the nine-volt cell that provides the emf to our original circuit. Note, though, that the orientation of the cell in our original diagram and the orientation of the cell in our circuit diagram are reversed. In our original diagram, the positive terminal is on the right. And in the circuit diagram, the positive terminal is on the left.

In this particular case, though, the physics is the same because the cell is the only component in the circuit that has a positive and a negative terminal. We will need to pay careful attention to the orientation of cells in a moment when we consider multiple cells connected together. Let’s say we have a fancy new speaker system that requires 10 volts to operate. However, we don’t have a 10-volt cell. We only have two five-volt cells. So we need to figure out how to use these two cells to power the speakers and listen to our favorite tunes. We can get an idea for what to do by drawing a simple circuit diagram that shows a cell connected to a single component like, say, a buzzer, which is another object that makes noise.

We know that the direction of the current in this circuit will follow the wires from the positive terminal of the battery back to the negative terminal. Now, this is a particularly simple circuit because there is only a single cell. And the current is only along a single path from the positive terminal to the negative terminal. However, in more complicated circuits, we can have many cells and many different paths that the current follows from the positive terminals of the cells to their negative terminals.

So how do we figure out how much emf is driving current along a particular path? Well, we simply start at one point in the circuit and draw the path of the current all the way around until we get back to where we started. Then, to find the emf driving current along this path, we look at all the sources of emf along this path. Here, it’s just the one cell. Therefore, the total emf driving current along this path is just the emf of this single cell. But remember that we need more emf driving current along the path in our circuit than can be provided by a single cell. So let’s redraw our circuit with two cells and see what happens.

We’ve connected two cells to our buzzer here, one after another. When we now follow the current around this circuit, we see that it passes through both of the cells before returning to where it started. This means that there are two cells providing emf to drive the current in this circuit. Because these cells appear in the same path, one after another, and in particular with the positive terminal of one next to the negative terminal of the other, we say that they are connected in series.

Cells in series are all driving current in the same direction. So the resulting current is stronger than each individual cell would produce from its own emf. Therefore, cells in series act as one larger unit, providing a larger emf than the individual cells do on their own. This resulting emf is just the sum of the emf from each individual cell. Using this, we can power our speaker system. We need 10 volts, and we have two cells of five volts each. So if we connect these cells in series, the resulting emf will be five volts plus five volts, which is the 10 volts that we need. Note, again, that we’ve been very careful to connect the positive terminal of one cell to the negative terminal of the other cell. Orienting the cells the same way ensures that their emfs all add up to the required value.

So far, we’ve only talked about connecting two cells in series. But in fact, we can connect any number of cells in series, and the rules stay the same. In this diagram, we have a three-volt cell, a five-volt cell, a one-volt cell, and a six-volt cell. If we follow the path of the wire, we see that it passes through each of the four cells, one after another. Moreover, the cells are all oriented the same way, with their positive terminal on the right and their negative terminal on the left.

So since these cells are all on the same path, one after another, and oriented the same way, they must be four cells in series. And the total emf of these four cells would just be the sum of the emfs from each individual cell, three volts plus five volts plus one volt plus six volts. Three plus five is eight, eight plus one is nine, and nine plus six is 15. So the total emf of this series combination of four cells is 15 volts.

We actually have a special name for cells connected in series. Several cells connected in series are called a battery. In fact, the batteries that we use in everyday electronics are called batteries because inside they’re a collection of multiple cells. In fact, batteries play exactly the same role as cells in electronic circuits. They’re both sources of emf. When connected to a circuit, an ideal battery actually behaves exactly like a single cell with the same emf as the battery. That is to say, the physics of a circuit connected to this 15-volt battery would be exactly the same if that same circuit were connected to this 15-volt cell.

In fact, the main reason why we use batteries instead of single cells is because of the chemistry used to produce the emf in an individual cell. There are several different chemical reactions that produce emf in individual cells. But each chemical reaction produces only a single value for the emf, which is the same for all cells using that type of reaction. So we can’t make individual cells with any emf that we want. But what we can do is connect those individual cells in series to produce a battery with the emf that we need. Now that we’ve learned a little bit about cells in series, let’s work through some examples.

Which of the following diagrams shows three cells connected in series?

Recall that in series means that the cells are connected one after another. So if we draw a path through a circuit with three cells connected in series, all three cells will be along that one path. Now, these diagrams don’t show complete circuits, only parts of circuits. But that’s okay. The idea is the same. We’re going to draw a path from one end of the diagram to the other. In the diagram on the right, there are three possible paths going from left to right across the diagram. One path goes up, across, back down, and out. One path goes straight across the middle of the diagram. And the last path goes down, across, back up, and out.

We can see that there is exactly one cell on each of these three possible paths. Since each path only has one cell, we know that this diagram doesn’t show three cells in series. Because if there were three cells in series, all three cells would be on the same path. In the diagram on the left, there’s only one path, and that path passes through all three cells. And three cells on one path is exactly what we would expect for three cells connected in series. So the diagram with three cells connected in series is the diagram on the left. Several cells connected in series are sometimes called a battery.

In our next example, we will identify the special circuit symbol that represents a battery.

Which of the following is the correct circuit symbol for a battery?

Recall that a battery is several cells connected in series. Looking at the symbols we are given, the one on the far right shows a single cell. This single cell is not a battery because a battery, by definition, consists of multiple cells. But we do expect that the circuit symbol for a battery will be similar to the circuit symbol for a single cell. Looking at the other three symbols, the symbol second from the right shows two cells with a dotted line between them. This dotted line represents the possibility that there may be other cells connected between these two cells.

But either way, all of the cells represented by this symbol are connected one after another. That is, they are connected in series. And indeed, this is the circuit symbol of a battery, cells connected in series. It’s worth mentioning the names of the other two symbols we see here. To the left of the battery is a resistor, and all the way on the left is a bulb. It’s worth knowing these symbols, in part because if we recognize these symbols as a bulb and a resistor, we could immediately identify them as incorrect answers.

Now that we’ve worked through two examples identifying cells in series, let’s find the total emf of a series combination of three cells.

The diagram shows three cells connected in series. What is the total emf provided by the cells?

First, let’s recall that emf is another name for potential difference. And it’s given in volts, specifically the voltage listed by each cell. So the emf provided by the first cell is three volts, by the second cell is six volts, and by the third cell is two volts. Now, we are looking for a total emf, and it is a total emf from cells connected in series. We can do this by recalling that to find the total emf provided by a series combination of cells, we simply add up all of the emfs from each cell. So the total emf in the diagram we are given is three volts plus six volts plus two volts.

Remember that when we add quantities with the same units, we add the numbers and keep the units. So three volts plus six volts is three plus six, which is nine volts. Using the same idea, nine volts plus two volts has units of volts. And the number is nine plus two, which is 11. So the series combination of cells in the diagram provides a total emf of 11 volts.

Alright, now that we’ve worked through several examples, let’s review what we’ve learned in this lesson.

In this lesson, we learned that when cells are connected one after another in a circuit all with the same orientation, they are connected in series. We also learned that we can call several cells connected in series a battery. This is the same word as the batteries we use in everyday electronics because the batteries in everyday electronics are actually several cells connected in series. Finally, we drew diagrams representing cells connected in series and learned that the total emf or electromotive force of this series combination is the sum of the individual emfs provided by each cell.

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