Hi everyone. In this video, we are going to review some of the basic electricity definitions and units that we covered in physics. The first definition that we have is the charge is a fundamental electrical quantity, and we denote it by symbol Q. The smallest charge that we have is the charge of the electron, and it is equal to -1.6×10^-19 coulombs. So the unit of the charge is coulombs.

Coulomb was named after the scientist Coulomb who described or characterized the charge. When those charges move from one location to another, we have electrical current. Electrical current is measured in amp or ampere, and by definition, it is the rate of change of the charge over time. So we can write that I is equal to dQ over dt.

Whenever we have a wire or a conductor, the amount of charge passing through an area determines the current that goes through this conductor. As we mentioned, current is measured in units called amps, after the scientist André-Marie Ampère, but also can be defined as coulombs per second, which is the rate of change of charge over time t. Okay. Nonetheless, we use amps in all of our practical considerations.

Now let's do this simple example. Assume that I have an inductor through which there are 10 electrons passing every second, and we'd like to compute the current passing through this inductor. If we know the number of electrons and the time period, I can get the current because we know that the current I is equal to dQ/dt. Okay.

How many charges per second do we have? 10. And those are 10. The charge of an electron is -1.6×10^-19 coulombs. So this is the total charge moving. I have 10 electrons multiplied by the charge of an electron over what time period? It is 1 second. So as a result, substituting into that equation, we have I equal to -1.6×10^-18 amps.

Where did this minus come from? It actually comes from the charge of the electron. Here I ignored adding this negative sign for the electron charge. Okay.

Now, in order for those charges to move from one location to another, we need some potential difference like voltage difference. This actually happens when we place a conductor in an electric field. The electric field will exert work on that charge. We have so this work is defined as energy. So the energy by definition is your ability to perform work to move a charge from one location to another. We measure the energy in joules and we give it a symbol as W, and sometimes we give it the symbol as E.

When we have this setup in the electric field, we have a voltage developed, like potential difference voltage potential. The voltage by definition would be the amount of work needed to move one charge. So by definition, V is equal to dW over dQ. Units of W are joules. The units of the charge are coulombs. Together they make the unit for the voltage, which are volts. Okay. So volt you can think of it as the amount of energy that you need to move a charge to another area.

Another related definition that we are not going to focus on in this course is the magnetic flux. If I have a magnet moving, it will make a magnetic flux, and if this magnet is moving within a wire, we are going to induce current into that wire. The magnetic flux in general is the measurement of the total magnetic field which passes through a given area. We denote it as Φ and measure it in webers.

In magnetism, the flux is the equivalent to charge in electricity. We know in electricity now that flow of charge gives current. In magnetism, flow of flux actually gives the voltage. So the voltage is equivalent to the rate of change of the magnetic flux. As I mentioned, in this course we are not going to focus on the magnetic flux, but we are going to use this equation when we talk about inductors midway through the semester.

Another definition that we have is power. Power is the rate of work over time. So by definition, it is the change of work over time, dW/dt. Taking this mathematical derivative, I can write it as (dW/dQ) × (dQ/dt). Now this first term here is the rate of work per unit of charge. This is the amount of work or amount of energy you need per unit of charge. This is actually the voltage. And dQ/dt is the rate of change of charge over time, so this is actually the current.

The power of an electric circuit or an electric element is the voltage across this element times the current going through this element. So this is a universal equation that we can use to compute the power for any electric device. The units for the power are watts, and we give it a symbol W. But please do not confuse the W we have for watts versus the W we have for energy.

Let's do a couple of problems together to practice those definitions.

Problem number one: We are asked about the amount of energy that is imparted to one electron as it flows through a 6V battery. Here we have a 6V battery and I have an electron moving, and we would like to know how much energy is needed to move this electron.

We are given V is equal to 6 volts, and we have a relationship between voltage and energy. We know that V is equal to dW/dQ. Voltage is the amount of work required to move one electron. Okay. So from this equation here, we can write that dW is equal to V dQ.

We have V = 6 volts, but what is dQ? In the problem, we are asked only to move an electron, so dQ here is one electron, which is -1.6×10^-19 coulombs. This gives us a solution for the work for one electron is equal to -9.6×10^-19 joules. Don't forget the unit. The units are joules for energy.

Another example we have introduces another definition, which is an amp-hour. Amp-hour is the time integral of the current. Let's consider this problem: Over 8 hours, we measure 4500 amp-hours. So we integrated the current over time, we had 4500 amp-hours through our measurement unit, and we want to know the total charge that flowed through this device.

Here we have time, we have current, and we are asked about the charge. Do we have a relationship between those three quantities? Yes. We are given current and time and we are asked about Q, and we know that the current is the rate of change of charge over time. So far, so good.

We are being asked about the charge, so we can write that dQ equals to I dt. If I integrate both sides of this equation, I get Q equals to the integral of I dt. Now what is the integral of I over time? This is the amp-hour.

So far, so good. Here we have our Q equals to 4500, but that was measured in terms of hours. If you consider the units, we define amps and charge in coulombs and the time is in seconds. So now we need to convert from this hour unit to seconds.

First of all, when we measured those 4500 amp-hours, that was measured over eight hours. Within an hour, we have 60 minutes, and within the minute, we have 60 seconds. So now this should be our total charge there, and the units are coulombs.

Within this example, we practiced the definition of the current as being the rate of change of charge over time, and given the current and time period, we were able to obtain that charge.

Within this video, we introduced the definition of charge, current, energy, voltage, and power.

Thank you.