Solved example: Potential difference & work done

- [Teacher] The potential difference between the two terminals of a cell is three volts. Find the work done in moving five coulombs of charge across the cell. So we need to calculate how much work is being done in moving five coulombs of charge. So let's see what's given to us. We have a cell. Let's say this is our cell. And it's given that across the ends of the cell, across the terminals of the cell the potential difference is three volts. And to calculate work done from this number we need to first understand what this number really means. So we have seen in a previous video that volt really means joules per coulomb. And this is telling us that three joules of work is needed to move every coulomb of charge from one point to another, three joules per coulomb, that's what we mean by three volts. It's an indicator of how much work needs to be done to move a coulomb from one point to another. So now that we know what it means, what is the meaning of potential difference, let's see if we can answer the question. We need to calculate the work done in moving five coulombs of charge What we already know is to move one coulomb we need to do three joules of work. To move five coulombs, how much work do we need is the question. So, with this data, pause the video and see if you can try and answer this question yourself. Alright, now let's do it. So, one coulomb to move from one point to another, three joules of work. If you had two coulombs, it would be twice the amount. If you had three coulombs, it would be thrice the amount. So to move five coulombs, it would be five times the amount. So, work done would be three joules per coulomb, this is three joules for every coulomb, but since we are moving five coulombs we multiply it by five, and that would be, the coulomb cancels, that would be 15 joules. So we need to do 15 joules of work to move five coulombs across. So, notice that, if we understand what voltage is, or what potential difference is, if we understand the meaning of volts, we don't have to remember any formula, we can just logically solve problems like this. Let's try another one. It takes 20 joules of work to push four coulombs of charge across the filament of a bulb. Find the potential difference across the filament. So, great idea to pause the video and see if you can try this problem yourself first. Alright. In this question we are asked to find what the potential difference is And what we are given is the work done to push four coulombs of charge across the filament of your bulb. So let's say here is the filament of a bulb. We know to push four coulombs of charge, to push four coulombs of charge across the filament it takes 20 joules of work. 20 joules of work. So given this, we are asked, What is the potential difference across the filament? Well again, if we go back over the definition of what potential difference is, it's a measure of how much work needs to be done per coulomb. Now, we know to push four coulombs of charge we have to do 20 joules of work. So to move one coulomb how many, how much work should we do? Well, the amount of work that we need to do would be 20 joules per four coulomb, because that's what voltage is. Voltage is a measure of how many joules per coulomb. And that would be five joules per coulomb. Let's use the same color. So four goes five times, so that'll be five joules per coulomb, and joules per coulomb is what we call as volt. And so, the potential difference across the filament of the bulb is five volts. Again notice, we didn't have to use any formula. All we did is use the definition of voltage or potential difference.