Lesson Video: Calculating the Electric Current in a Wire | Nagwa Lesson Video: Calculating the Electric Current in a Wire | Nagwa

# Lesson Video: Calculating the Electric Current in a Wire Science • Third Year of Preparatory School

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In this video, we will learn how to calculate the electric current in a simple circuit.

15:29

### 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.

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