Video Transcript
Cells are one source of the
electromotive force required for electronic circuits to function. When there are multiple cells in a
circuit, the total emf provided by all of those cells depends on how the cells are
arranged. In this lesson, we will learn about
the emf provided by multiple cells when they are arranged in parallel.
First, let’s recall that real cells
have a variety of shapes, sizes, and emfs. When drawing diagrams of electric
circuits, we represent all cells with the same symbol. The long line represents the
positive terminal of the cell, and the short line represents the negative terminal
of the cell. Recall also that when there is
current in the circuit, electrons are moving from the negative terminal of the cell,
around the circuit, and back to the positive terminal. Finally, we also labeled the
potential difference, that is, the electromotive force provided by the cell near the
cell symbol. Here, we’ve written five volts near
the cell, which tells us that the emf of this particular cell is five volts. In the context of cells, emf and
potential difference are two ways to describe the same thing.
Alright, now that we remember how
to represent cells in a diagram, let’s see a diagram showing cells connected in
parallel. In this diagram, there is a
resistor and also three cells. And these three cells are connected
in parallel. To see how we identify that these
cells are in parallel, let’s draw the path of current through this circuit. Since the positive terminal of all
of the cells is on the left and the negative terminal is on the right, the direction
of the current will be counterclockwise through the circuit. It’s worth mentioning that the
direction in which the electrons actually move is clockwise. The reason for this is because of
the way current was historically studied. And the result is that the
direction that we define as the direction of the current is opposite to the
direction in which the electrons in the circuit actually move.
Let’s draw the path of this
current, starting from this point. The path of the current continues
counterclockwise along the wires and through the resistor and then back toward the
cells. At this point, however, there are
actually three different paths for the current. One possible path goes up and
through the top cell, back down, and completes the circuit. Another possible path goes straight
through the middle cell and completes the circuit. And the last possible path goes
down through the bottom-most cell, back up, and completes the circuit. So there are actually three
possible paths for the current. And each of those three paths has
exactly one cell. This is how we know that the three
cells are in parallel.
There are multiple valid paths for
the current, and each of those paths passes through a different cell. As an example of cells not in
parallel, we have these three cells here. These cells are not in parallel
because there is only one path from one side of the cells to the other side. And it passes through all three
cells. So because all of the cells lie on
a single path rather than on multiple paths, these cells are not in parallel. Okay, so we can identify cells in
parallel by finding multiple paths for the current that pass through different
cells. Let’s now learn what the total emf
is from a parallel combination of cells.
The rule giving the total emf is
quite simple. If all the cells have the same
orientation and all of the cells have the same emf, if both of these conditions are
met, then the emf of the parallel combination of cells is exactly the same as the
emf of one of the individual cells. Let’s make sure we know how to
check these two conditions. Checking that all of the cells have
the same emf is straightforward. We just look at the emf labeled for
each cell. After adding an emf label to each
cell in the diagram on the left, we see that the topmost cell has an emf of three
volts, the middle cell has an emf of three volts, and the bottom-most cell also has
an emf of three volts. So all three of these cells have
the same emf.
To check that the cells have the
same orientation, we need to look at where the positive and negative terminals are
located. In the diagram on the left, all
three cells have their positive terminals facing left and their negative terminals
facing right. Because these positive terminals
all face in the same direction as the current in the rest of the circuit, all three
cells have the same orientation. What we have found then is that all
of the cells in our diagram have the same orientation and the same emf and are also
connected in parallel. So the total emf of this
combination of cells is the same as the emf of one of the cells, which is three
volts.
Before we work through some
examples about cells in parallel, it’s worth understanding what can go wrong if two
cells connected in parallel don’t have the same orientation. In this diagram, the cells have
opposite orientations. The cell above has its positive
terminal on the left, while the cell below has its positive terminal on the
right. Remember that current leaves the
positive terminal of a cell and enters the negative terminal. This means that there is now an
allowed path for current that starts at the upper cell, goes through the lower cell,
and returns back through the upper cell. The current along this path never
moves through the rest of the circuit.
Since there are no other components
that this current must pass through, the result will be an uncontrolled current that
will eventually, in a real circuit, melt the wires and destroy the cells. This is why it is always important
when connecting cells in parallel to connect them with the same orientation. Alright, now that we’ve learned
about cells in parallel, let’s work through some examples.
The diagram shows three cells
connected in parallel. What is the total emf provided by
the cells?
Looking at the diagram, we see that
each of the cells has the same emf, specifically four volts. We next notice that moving from
left to right, all of the cells have their negative terminal on the left and their
positive terminal on the right. So all of the cells have the same
orientation along the path of current. We now recall that when all of the
cells in a parallel combination have the same emf and the same orientation, the
total emf is the same as the emf of one of the individual cells. Since each of these cells has an
emf of four volts, the total emf of this parallel combination is also four
volts.
In this example, we used the emf of
individual cells to find the total emf. In our next example, we will use
the total emf to find the emf of the individual cells.
The diagram shows three identical
cells connected in parallel. The total emf provided by the cells
is six volts. What is the emf provided by each
cell?
Whenever we need to relate the
total emf provided by a parallel combination of cells to the emf provided by each
cell individually, there is one relationship we should think of immediately. If cells in parallel have the same
orientation and the same emf, then the total emf of the parallel combination is the
same as the emf of each cell individually. From the question, we know that the
three cells are identical, which means by definition they have the same emf.
Looking at the diagram, we see that
all three cells have the positive terminal on the right and the negative terminal on
the left, which means they have the same orientation relative to the direction that
current would have if these cells were connected to a circuit. So all of the cells have the same
orientation and the same emf, which means that the total emf of this combination
must be the same as the emf of each individual cell. We already know from the question
that the total emf is six volts. And since the total emf is the same
as the emf of each cell, the emf of each individual cell in this parallel
combination is six volts.
Alright, now that we’ve worked
through some examples, let’s review what we’ve learned in this lesson. In this lesson, we learned to
identify when cells are connected in parallel by looking for circuits where there
are multiple paths for the current but each path has only one cell. We also learned that the total emf
of a parallel combination of cells is equal to the emf of an individual cell if all
of the cells have the same orientation and the same emf. Finally, we learned how to
distinguish between the circuit diagram for a safe combination of two cells in
parallel, where both cells have the same orientation, from the unsafe combination of
two cells in parallel, where the cells have opposite orientation. This second combination is unsafe
because there will be uncontrolled current that will heat up the circuit and
components until the wires melt or the circuit is otherwise destroyed.
