[MUSIC] Welcome back to Linear Circuits, I'm Dr. Harris. In this lesson we will discuss Voltage, by the end of the lesson, you should be able to both describe and quantify voltage. This lesson builds upon charge flow, remember that charged particle exert a force on other charged particles. The charges that you see here, positive and negative, have electric field lines that point towards the negative charge, and away from the positive charge. So this force per unit charge is called an Electric Field and remember that charges flow because their electric fields exert forces that push each other. So these electric fields that are pushing the charge will help us to define voltage. Now what is voltage? When moving through an electronic field, a charge either gains energy of loses energy. Charges lose energy when they're moving in the same direction of the electric field lines. The charges that you see here, have an electric field line that points from top to bottom, and the charges are moving in the same direction, so they are losing energy. Charge gains energy when it's moving in the opposite direction of the electric field lines, so these charges would gain energy if they were moving from bottom to the top. Now voltage is the energy that is either gained or lost per coulomb of charge and because it's the energy gained or lost per coulomb of charge, we can use that definition to calculate voltage. So consider charging moving from A to B, Voltage is the change in energy per coulomb of charge so we can express it as a first derivative. DW, DQ. Or it can be expressed simply as energy joules over charge in coulombs. So voltage is simply energy over charge. We'll use a variable, V, and the units joules per coulomb, or volts. The first quiz says four coulombs of charge lose 20 joules of energy when moving form a to b, what is voltage, V-ab? And the second says 21 joules of energy are required to move 3 coulombs of charge from b to a, what is the voltage V-ba? Pause the video for a moment and try the quizzes on your own, and then play and we'll work through the quizzes together, so remember that voltage is energy over charge in both cases. So here we have 20 joules of energy and 4 coulombs of charge, so our voltage is 5 volts. In this case, we have 21 joules of energy and 3 coulombs of charge or seven volts. However, notice that the voltage or the charge is moving in this case from v to a, which is against the electric field line. So this voltage is negative, a negative voltage actually means that we gained energy. A positive voltage means that we have lost energy, so when the charge moved from A to B, it lost energy, we're moving the electric field lines and we get a positive five volts. When we move from B to A, we gained energy going against the electric fuel lines and we get a negative seven volts. Another important fact to realize about voltage, is that the measurements are always from a reference point. In other words, voltage measurements are relative, not the voltage itself, but the measurements. As an analogy, consider a mountain, in order to measure the height of point a, for instance on this mountain, we must define a reference point, because we could measure a from b or we could measure a from c, or we could even measure a from sea level. Now, a has an absolute height, but that height doesn't mean anything to us unless we actually define a reference point. And it's similar for voltage, in order to measure a voltage at point a, in a circuit we have to define a reference point. And this reference point only effects our measurement not the actual direction of the electric field, that causes the voltage to drop or increase. So in this cartoon, you see that the electric field lines are actually pointing from a to b but we can take a voltage measurement by measuring b as the plus end and a as the minus end, or we could measure a as the plus end and b as the minus end. In the case where we're measuring b as the plus end, then current going from b to a or voltage drop from b to a would be negative, a voltage drop from a to b would be positive. But it depends on the way that we take our measurement. So let's see how that is applied when we look at the voltage drop around a circle. Another important thing to remember about voltage potentials, is that they add from point to point. Now consider the mountain above just once more, if we travel from point a, to b, to c and then back to a, our height has not actually changed. Similarly, in a circuit if we travel from a to b, c, d, and then back to a, our voltage has not changed and that's because the voltages add from point to point. So, let's look at this circuit and consider, if we go from c to b. Now, when we go from C to B we go from plus to minus, which means we have dropped, we've gone down six volts going from minus to plus. Now, from b to a, we're going from minus to plus instead of from plus to minus. We're going from minus to plus, so we've actually increased, we've gone up four volts. So, we went down six, but we only went back up four. So at point a we've got a total of down 2 volts. Now we go from minus to plus, which means we're increasing. We go up 5 volts, when we travel from a to b, minus to plus is up five volts. Just like when we went minus to plus here we went up four volts. So at this point, we've gone down two but we've gone up three, so we have a total of up three volts. Now from d to c, we're going from plus to minus, so we've gone down three volts and our total voltage is zero. So you see the potentials, add as we go around the loop and back to our starting point. Just as if we were on the mountain and we went from A to B to C, and then back to A. So the key concepts that we've covered in this lesson are, one, voltage is the energy either gained or loss per coulomb of charge. And you can define that as the first derivative dw, dq of the voltage. Also, voltage measurements are relative, so you have to define a reference point. And finally, voltage potentials add as you travel from point to point. [MUSIC]