Video Transcript
Current is how much of something is
moving in a particular direction. In this video, we will learn how to
calculate the electric current in a wire, which measures how much charge is moving
through the wire. Let’s start by describing a
different type of current, water flowing in a river or stream. Here we’ve drawn a stream flowing
down a river bed. And let’s just say that the
direction of the water flowing, that is, the direction of the current, is from left
to right. The actual value of the current is
the rate at which water is flowing.
To actually measure the current, we
measure how much water passes this line across the stream every second. Let’s say that we measure this to
be five liters passing the line every one second. Physically, this means that if we
placed an empty five-liter container across the stream, it would fill up in one
second. Similarly, a 10-liter container
would take two seconds to fill up. A 15-liter container would take
three seconds to fill up, and so on. This quantity, five liters every
one second, is exactly the current in the stream because it tells us the rate that
water is moving. Here we’ve measured the amount of
water in terms of its volume with units of liters. So the current in this stream is an
amount of water per second.
Let’s now consider the electric
current in a wire. The idea will be very similar to
the current in a stream. But instead of considering how much
water passes a point in the stream every second, we will consider how much electric
charge passes a point in the wire every second. Here we’ve drawn a simple circuit
with a cell connected to a bulb by two wires. When connected like this, the bulb
will light up because there is electric current in the circuit. Recall that the direction for the
electric current will be out of the positive terminal of the cell and into the
negative terminal of the cell.
Now, let’s recall that the electric
current gives us a measure of how much charge is moving through the circuit. So, just like we did for the water
moving down the stream, let’s pick a point in the wire, say, right here, and see how
much charge moves past this wire every second. However, in order to do this, we
need to know how to describe an amount of charge. Before, we described the amount of
water in terms of its volume using the units liters. We could have also described the
amount of water in terms of its mass using the units of kilograms. But electric current is about how
much charge is moving, not how much volume or how much mass is moving. So what we need is a unit for
charge that we can use to describe how much charge we have. The unit we use for charge is
called a coulomb, and its symbol is the uppercase letter C.
So just like we know that five
liters is an amount of volume and five kilograms is an amount of mass, five coulombs
is an amount of charge. So when we go back to the point we
were looking at in our wire, the current will be some number of coulombs passing by
this point every second. So with a total charge of five
coulombs passed by this point every one second, the current in the wire would be
five coulombs per second. Let’s consider the units for this
current in a little bit more detail. First, let’s abbreviate our units
of coulombs and seconds with their unit symbols. For charge, whose unit is coulombs,
this symbol is the uppercase letter C. And for time with units of seconds,
the symbol is the lowercase letter s. So we can rewrite this statement as
this statement.
Note that even though we’ve
abbreviated the units, we read it exactly the same way: five coulombs passing every
one second. Even though we can express the
current with units of charge and time, we would still like a single unit that
describes the current so that instead of talking about five coulombs passing every
one second for the current in the circuit, we can just say that the current in the
circuit is five units of current. We call this unit of current the
ampere, and its symbol is the uppercase letter A. The ampere is defined as a current
of one coulomb every one second. So the current in our circuit, five
coulombs passing every one second, is a current of five amperes.
There is another more mathematical
way to express the definition of one ampere. One ampere is one coulomb per one
second. And the word per is a word we often
use when we think about division. So we can write one coulomb per one
second as a single symbol with the unit symbol for coulombs divided by the unit
symbol for seconds. And we read this the same way:
coulomb per second. In other words, our definition of
an ampere is that one ampere is one coulomb per second. So a current of five coulombs
passing a point in the wire every one second is an electric current of five coulombs
per second, which is by definition the same thing as five amperes.
Now that we know the proper units
for charge and current, we can use the relationship between amperes and coulombs to
calculate the current in a wire. We start with our definition that
one ampere is one coulomb per second. Amperes are the unit for current,
coulombs are the units for charge, and the seconds are the units for time. Now, remember, the slash represents
division. So what this equation looks like is
current is equal to charge divided by time. And in fact, this is true. The electric current in a wire is
exactly equal to the total charge passing a point in the wire divided by the total
time it took that charge to pass that point. Using symbols, we write 𝐼 equals
𝑄 divided by 𝑡, where 𝐼 is the current, 𝑄 is the total charge, and 𝑡 is the
total time.
Let’s demonstrate how to use this
formula with a few calculations. If two coulombs of charge pass a
point in a wire in one second, what is the current? To do this calculation, we
substitute two coulombs for 𝑄 and one second for 𝑡 in our formula. So we have two coulombs divided by
one second. To do this calculation, we first
divide the numbers and then combine the units. Two divided by one is just two, so
two coulombs divided by one second is two. And then we have coulombs in the
numerator and seconds in the denominator, so we have two coulombs per second. But remember that one coulomb per
second is one ampere, so the current is two amperes.
Let’s do another calculation. A charge of four coulombs passes a
point in a wire in two seconds. Again, we substitute into our
formula: four coulombs for 𝑄 and two seconds for 𝑡. So the current is four coulombs
divided by two seconds. We again see units of coulombs in
the numerator and seconds in the denominator, so we know that our answer will have
units of coulombs per second. For the number, we take four
divided by two. Four divided by two is two. So the current is two coulombs per
second, which, as we know, is the same thing as two amperes.
But let’s now compare our two
results. In our first case, with two
coulombs every one second, we found that the current was two amperes. In the second case, with four
coulombs every two seconds, the current was also two amperes. This shows why it is useful to
represent current in its own special unit of amperes. Although knowing that a charge of
two coulombs every one second is enough to know the current in the circuit, it is
not immediately obvious that this is the same current as four coulombs every two
seconds. But when we compare the values of
the current as given in amperes, we can see immediately that they are the same.
Although we won’t actually do these
calculations, it’s worth mentioning two other ways that this formula, 𝐼 equals 𝑄
over 𝑡, is useful. As we’ve written it, this formula
tells us how to calculate the current in a wire, knowing the total charge passing
through the wire in some amount of time. We can, however, use the same
formula to calculate the total charge moving through a wire if we know the current
in the wire and we also know the amount of time. Similarly, we can calculate the
amount of time the charge was moving through the wire if we know the total charge
and we also know the current. Alright, now that we’ve learned how
to calculate current, let’s work through some examples.
The diagram shows an electric
circuit containing a cell and a bulb. The current in the circuit is two
amperes. How much charge flows past point 𝑃
in the circuit in one second? The current in the circuit is two
amperes. How much charge flows past point 𝑃
in the circuit in one second?
The diagram shows the cell, the
bulb, and also the wires connecting these two components. The point 𝑃 is over here, and the
arrow shows us the direction of the current. And we are told that the value of
this current is two amperes. Recall that the unit symbol for the
ampere is the uppercase letter A. Now, the question asks us to
determine how much charge flows past point 𝑃 in the circuit in one second if the
current in the circuit is two amperes. To do this, we’ll need to recall
how current is related to charge and time. One ampere, the unit for current,
is defined as one coulomb of charge moving past a point in one second.
In our question, we’re also
interested in a time of one second. But instead of a current of a
single ampere, we have a current of two amperes. Luckily, the conversion is
easy. If one ampere is one coulomb per
second, then two amperes is two coulombs per second. And this is our answer. Two amperes is two coulombs of
charge passing a point every one second. So the answer is two coulombs.
We should pay careful attention to
the two statements we’ve written down. On the left, we defined one ampere
with a time of one second and two amperes also with a time of one second. This is because current is always
defined by how much charge moves past a point in exactly one second. So as the current changes, the
amount of charge changes, but not the amount of time it takes that charge to
move.
Alright, let’s now see another
example where we will calculate and compare the current in several circuits.
David sets up three circuits. He measures how much charge flows
through each circuit in the same amount of time. His results are shown in the
following table. Which circuit has the greatest
current?
We need to determine which of
circuits one, two, and three has the greatest current based on the information in
this table. To practice calculating the current
in a circuit, we will calculate the current in each circuit from the charge and time
in the table and then compare those results. Recall that we can calculate
current from the equation 𝐼 equals 𝑄 divided by 𝑡, where 𝐼 is the current
measured in amperes, 𝑄 is the charge measured in coulombs, and 𝑡 is the time
measured in seconds. All we need to do now is substitute
the values from each circuit into this equation.
In circuit number one, the charge
is 20 coulombs and the time is five seconds. So using 𝐼 equals 𝑄 divided by
𝑡, we have 20 divided by five, which is four. And since our units for charge are
coulombs and our units for time are seconds, the units for this current are coulombs
per second, or amperes. So the current in circuit one is
four amperes. In circuit number two, the charge
is 25 coulombs and the time is five seconds. Since the units for charge and time
are again coulombs and seconds, the current will again have units of amperes, and
its numerical value will be 25 divided by five. 25 divided by five is just
five. So the current in the second
circuit is five amperes.
Finally, in the third circuit, the
charge is 12 coulombs and the time is again five seconds. The units for charge and time are
again coulombs and seconds, so the units for the current will again be amperes. And the numerical value will this
time be 12 divided by five. Since 12 divided by five is 2.4,
the current in the third circuit is 2.4 amperes. Now that we have calculated the
current in each circuit, we can see immediately that the greatest current is five
amperes in circuit two. So the circuit with the greatest
current is circuit two.
Now that we’ve calculated some
currents, let’s review what we’ve learned in this lesson. In this lesson, we learned that
electric current is how much charge moves past some particular point, usually in a
circuit, in some amount of time. In order to think about particular
values of current, we need to know how much charge we have and also the amount of
time. Amounts of time are measured in
seconds. But for measuring how much charge,
we needed a new unit, so we introduced the coulomb as a unit of charge. Just like we sometimes abbreviate
seconds with s or meters with m or kilograms with kg, we abbreviate the coulomb with
the uppercase letter C. Now that we have a unit for charge,
we also want a unit for current. That unit is the ampere. Sometimes to represent the ampere,
we use the uppercase letter A.
We also defined the ampere in terms
of coulombs and seconds as one ampere equals one coulomb per second. We can also express this
relationship using only the unit symbols. As usual, uppercase A means the
ampere, and here uppercase C divided by lowercase s is the way we symbolically write
coulomb per second. Finally, we wrote down a formula
for calculating the current: 𝐼 equals 𝑄 divided by 𝑡, where 𝐼 is the current in
the circuit, 𝑄 is the total charge that flows past a point in the circuit, and 𝑡
is the amount of time that it takes for that charge to flow. Finally, it’s worth noticing that
this formula agrees exactly with our definition of current and also with the
definition of an ampere as a coulomb per second.
