Electrical Energy and Capacitance (Summarized)

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[00:00:00]In this video um I'll be summarizing the last chapter of this semester which was electrical energy and capacitors.

[00:00:13]Okay. So I'm going to be very brief because this chapter mainly only involves um formulas knowing the formula and being able to plug in the given values. Okay, this should be considered to be the simplest chapter.

[00:00:36]All right. So, electrical energy and capacitors. Here we have to talk about the potential difference and the electric potential.

[00:00:46]Okay. Now, these are just some of the definitions, the concepts, how the formulas are coming to be. Okay. And which formulas you must know. So if you have a charge moving between two plates, okay, how do you find the work done by the electric field uh in moving the charge from point A to B? So this is how you find the work done. That's what the formula is saying.

[00:01:17]And then using the work energy theorem, we know that this being the work this being the work done. So we're saying work done is equal to the charge that you're moving multiplied by the electric field. Okay.

[00:01:33]Doing that work multiplied by the displacement. Okay. From the uh so this is change in the position. So it is coming from A to B. So it will be the position of B minus A. So this work done is nothing but the change in kinetic energy. Okay. And the same theorem says that the change in potential energy is equal to the change the negative work done. So what are they trying to say there? If there is an electric field.

[00:02:10]Okay. So we have an electric field.

[00:02:14]Okay. So we have this.

[00:02:19]These are the field lines. So there's an electric field and then we have point A.

[00:02:25]and point B there. So the work that should be done onto this charge in order for it to move from this point to that point that work from A to B will be given by the charge multiplied by the electric field and then multiplied by the displacement. Okay. So this same work the work from A to B.

[00:02:51]So the work from A to B is equal to the change in kinetic energy.

[00:03:00]So this charge if you're dealing with an electron it is charged and it has a mass and since it's moving it will have the initial velocity. So this is final velocity minus initial velocity that is the change in kinetic energy. Okay. So that is what they're trying to say. Then what is the change in potential energy?

[00:03:24]The change in potential energy is equal to the negative work done. Okay. So you just get that value and you multiply it by a negative. That is what they're trying to say. Okay. So here it's just a matter of understanding the formulas.

[00:03:41]Like I've said there are so many formulas that you have to know. And probably the concept what happens to the potential energy if let's say uh in this scenario okay let me use first cell so what we have here is we have a positive charge in a downward uh electric electric field so what should happen to the potential energy in this case and if let's say it was negative what should happen to the uh potential ial energy should it increase or decrease? Okay, so these formulas if you understand them you should be able to answer that question. Let's say we have a positive charge. This is a positive charge which is moving from A to B. So should the potential energy this potential energy increase or decrease?

[00:04:36]Okay, so you can answer that question if you just understand what this formula is saying.

[00:04:42]Perfect. Now what else must you know about this? What else must you know? So these are just calculations. You can maybe go through this example uh example 16.1.

[00:04:58]Go through that example. Okay. Example 16.1 to just appreciate what uh you are going to understand from what is on the top there. Then um what else? What else must you know?

[00:05:17]Okay. So here that's the example and then dynamics of charges. Well uh okay now the the other part here is the electric potential. So there is the potential energy and there is the electric potential. Okay. So this electric potential they are saying it is nothing but this is the change okay the change in the potential difference. So this is a potential difference the change in the electric potential is VB minus VA. So meaning the potential this point is going to have a certain potential which we are calling VB and that point will have a potential which you are calling VA. So the potential difference is just that.

[00:06:05]Okay, that is what they're trying to tell you there. And then that can be related to the uh potential energy, the change in the potential energy. So this electric potential, think of it um in this way.

[00:06:21]We have an electric force and the charge. Then there is something that is relating the electric force and the charge which is the electric field. And then we have the potential uh the potential energy and the charge.

[00:06:37]So something that relates the potential energy and the charge is the electric potential. So as you can see the electric potential this potential difference is also given by the change in the potential energy divided by charge.

[00:06:54]Okay. So this implies that the change in the potential energy can also be given by that So it is just a matter of understanding the formulas. When you multiply throughout by Q, you're going to have that. And what if you want to find the work done using the electric potential?

[00:07:12]Well, where there is potential energy, you put that. So meaning work done which will be negative will be equal to Q change the potential difference meaning the work done is equal to Q then V B minus V A this is another formula. So this part only contains formulas that you should be able to understand. So here they are trying to tell you that if you have been given a charge let's say of plus 2 kum and this charge is moving from a point where the potential difference is let's say two to the point where the potential difference is 8 what is going to be the work done so the work done here is going to be two negative in the formula 2 is positive then 8 final which is VB minus 2 okay and And this is going to be six. So that will be minus 12 as your work done. Okay. Now basically this is what you you should be having uh unless otherwise but like I said this topic is easy. It's just a matter of you knowing um the formula to use. So we can also relate the potential difference to the electric field. We can relate the potential difference to the electric field. So here this is the work done. We know this relationship the relationship between the um work. So the relationship between what the work and okay this should be okay. So work done is equal to Q the change or the potential difference. So we also know that work done is equal to so here we said the charge that is moving the electric field and the distance. Okay. So where there is work you can put that. Okay. You can put this. So you're going to have Q E change in X Q change in V. So this Q and that Q cancels meaning the potential difference is equal to E changing X. You can just play around those same equations. So it's just a matter of knowing the equations because in questions usually most of the questions you are going to be given almost everything and uh you just have to know which formulas to combine to get what they're asking of you.

[00:10:00]All right. So basically that should be that should be it about that. So the other important aspect of this chapter is the electric potential which we are we at least we know something about. So that was the potential difference the change in V and then we know we have to know the potential energy due to the point charges. Okay. So the potential that is coming from a charge. So the electric potential coming from one charge. So let's say we have a positive charge here which is charge one Q1. And then we are looking for the potential at this point due to this charge. What is going to be that potential? So the potential will be K Q1 over R.

[00:10:57]So now what's the difference between the two? If you look at these two formulas don't uh mess them up. the formula for the electric field as um r squar this one only as r. Okay. So if you are following you can clearly see that according to this according to this this uh is error. Okay this should be error in principle.

[00:11:31]Okay. So if that is arrow meaning it will cancel with one ar there and where is this negative going? Where is it going? So you are it's like there is a charge that is at infinity then you are bringing it to a distance which is r. Okay. So meaning the the final the final which is vb= zero then you remain with VA. Okay. So those are just some derivation of the way of looking at it.

[00:12:05]But in principle what you have to know is the takeaway here is that the potential at this point due to that charge will be given by this. Now take note of one thing. This charge is going to be the charge as it is not the magnitude. I'm not putting Q1 in absolute. I'm just putting charge. Meaning if you've been given a positive value, you substitute a positive value as it is. If you've been given a negative value, you substitute a negative value as it is. That is the implication. Okay? So this one is capable of having a positive answer or a negative answer. The electric potential because the charge is going to be as it is. We are not just using the magnitude of the charge.

[00:13:02]Perfect. Now, uh you can be asked to find the potential due to other charges.

[00:13:10]Okay. You can be asked to find the potential due to other charges. So what we know is we have the electric potential which is this. And then what about the potential energy U or P? the potential energy due to two charges. So let's say there's Q1 here and we have another charge there which is Q2. So the potential energy between these two charges will be equal to P q1 Q2 over R. So again here we are substituting the values as they are.

[00:13:50]Okay. That's why this potential energy is we know it is related to work. So how can you define this in terms of the work like the example that I gave you? We are going to have a charge a charge that is at infinity.

[00:14:11]the charge that is at infinity bringing it to a distance that is r away from uh a given charge. Okay. So the potential energy between the two charges or the potential energy for a point charge is simply the work done or the work that is required in bringing a certain charge from infinity to a distance r. That's how you can define the potential energy which is given by that. So what happens if you have a positive charge here Q1 you have maybe another positive charge there Q2 and another negative charge there Q3. How do you find the potential energy? So that is R1 and then that is okay let me just say R. So R and that is also R. How do you find the potential energy for this system? The potential energy for this system will be the sum of the potential energies. So the potential energy for the entire system this system will be the potential energy. So let me use u okay you can say yeah u of one and two. So the potential energy between these two charges plus the potential energy between one and three between these two. then plus the potential energy between two and three that is uh that is it. Okay. So one and two you're going to use this distance.

[00:15:46]Then one and three you use this plus that which is two r as the distance to put there. But the charges you're getting them as they are. You're not getting the magnitudes. Okay. Then 2 three you get that distance together with the charges. That's it. So this can be in any configuration. We can say okay we have a square or we have a rectangle where we have Q1 positive Q2 Q3 and Q4.

[00:16:20]What is going to be the total potential energy? So you add one two. So here the potential energy between these two those two those two and those two. So it would be one two uh two three uh three two and sorry. So one two two three then 3 4 and then 4 1 okay you add them that's it. So this can be positive or a negative value because when does it become positive? Well, if these are unlike terms because if this is positive that is negative the total the the multiplication here gives you a negative answer. But the moment they are like terms you're going to end up with a positive value. Okay. So basically that is it. I'm sure there is an example that you can solve in way. So um okay. So make sure you go through this example.

[00:17:21]Example 16.4.

[00:17:24]this example, let me highlight it. So go through this. It will help you practice on how to find the field, the electric field at a given point. You do not need to resolve the field. Okay, this example will tell you that. So the field at this point due to this charge is going to be in that direction. But the electric field is a scalar quantity. So you just add whether it is at an angle or where you just add as a normal value. Okay.

[00:17:58]Now what example can you do? Okay. This is what I was talking about. This is example 16.5 also go through it. It will expose you on how to apply the formula for the potential energy.

[00:18:17]All right. Then there's a part where you need to read. So we've already talked about this formula. How the work done is related to the change in the uh potential electric potential. Okay, that formula and then there is a part where this part. So this I I I think there was a question in the test which was saying what do you know about the equipotential surface? So equip potential surface we know that the charges are going to be in the inner shell. Okay, they are going to lean against the wall and these equipotential surfaces the electric field lines are perpendicular to the surface at any given point. Okay.

[00:19:11]And what we know is that just from the name potential surface, the electric potential the electric potential is the same for the surface. Meaning the potential at A will be equal to the potential at B. And if the potential is the same, if the potential is the same, let's see if the potential. So here we are saying work done in moving a charge is given by this that is the work done. Okay. Now for the potential surfaces, we're saying VB is equal to VA. The potentials are the same meaning the work done here will be equal to zero. There will be no work done by the electric field in moving the charge across the equipotential surface. That is another thing that you should know.

[00:20:08]Okay. So this electric field won't do any work in moving the charge across the equipotential surface. Why? because the potential at any given point is the same.

[00:20:21]Okay. So, uh these things that are in board they are points you can just uh note them make sure you go through them.

[00:20:31]Okay. And this is about the potential surfaces and I'm sure everything is uh described. Okay. So yeah that should be it.

[00:20:46]Now I think this is the last part which is the capacitors. So that is uh the last part of this chapter capacitors. So a capacitor this is just a device that is used to store energy. Okay. And just like I've said even here you just need to know the formulas. Okay. You just need to know the formulas. Now what formulas are we talking about?

[00:21:18]Well, there is the first formula that is the general formula. The one we are seeing here.

[00:21:25]Capacitors is equal to this one, the one I've highlighted. Capacitance is equal to charge over the electric uh the potential difference. Okay. So, and the units it's kum per volt. Then there's another formula when you are dealing with parallel plate capacitor.

[00:21:49]So for the parallel plate capacitors the capacitor is given by that the highlighted one here. So it is given by epsylon okay multiplied by area the area of the plate divided by the distance. So this is the permitivity permitivity in free space the epsylon. So the epsylon not there is the permitivity in free space and then I think there was a question in the test which was saying what should happen how do you increase the capacitors? How do you increase the capacitors for the parallel plate capacitor? So here we know that the capacitance is proportional to the area and inversely proportional to the separation distance of the plates. Okay.

[00:22:46]So these are the two plates that we have. We going to have a positive and a negative plate. Okay. So there will be an electric field there. So the capacitance is proportional to the area.

[00:23:00]Meaning when you increase this you're increasing that. when you reduce that you're still increasing that. Okay. So how do you reduce? You reduce by reducing that this is going to reduce and by increasing that that is going to reduce. Okay. That is what the formula means. All right. Now what else must you know about capacitors?

[00:23:27]Okay. So apart from that well this is just an example that you can go through let's go to the combinations of capacitors I think this is where maybe I can do one or two calculations but uh let's say so if we say combination of capacitors we've got two configurations here we can say the capacitors are arranged in parallel or they are arranged in series.

[00:24:06]Okay. So this is going to be the battery and then we are going to have that.

[00:24:14]Okay.

[00:24:16]Then we have that.

[00:24:20]Perfect. So we have C1 and C2. So these two capacitors are arranged in parallel.

[00:24:30]And how do you find the effective?

[00:24:33]How do you find the equivalent? The equivalent capacitors is going to be just the sum of the two.

[00:24:41]This is going to be the case all the time. By the way, if you've been given the parallel arrangement, you always sum the individual uh capacitors in order to find the equivalent. Okay? And then for series, you have a battery there and then you have this and you have that.

[00:25:05]Okay? So this is C1, that is C2. How do you find the equivalent? Well, you say 1 / C equivalent is equal to 1 / C1 + 1 / C2. Okay? And then when you do your math here, you're going to have C1 C2.

[00:25:24]And then you're going to have C1 + C2.

[00:25:27]Meaning the C equivalent is just going to give you the reciprocal of that, which is C1 C2 over C1 + C2. That is how you find the equivalent. Okay. Now there's um there's a concept that you should know about these two arrangements. Okay. What concept is that? So this battery is going to have some voltage V for the parallel arrangement.

[00:26:01]These two capacitors, these two capacitors C1 and C2, these two are going to have the same voltage.

[00:26:14]Okay, the two capacitors are going to have the same what voltage. So this voltage that is coming from the battery will be the voltage for C1 and also the voltage for C2. That is the implication.

[00:26:28]Okay. Then for the series arrangement C1 and C2 are going to have the same charge. They are going to have the same what charge.

[00:26:43]So that concept is very important. So the charge of the entire circuit will be equal to the charge on C1 and the charge on C2. The voltage of the entire circuit should be equal to the voltage on C1 and the voltage on C2. Okay, how important is that information?

[00:27:04]How important is that information? So here if I say we have um we have this case, let's say there's a battery of 10 volts and then we have a parallel arrangement.

[00:27:25]Okay, we have that parallel arrangement. Then uh let's say we have um what values can I use here? Okay, for simplicity, let's say we have one uh one and two.

[00:27:42]Okay, I won't put micro farids. I'll just put farads like that. Okay. Now, if they say find the charge on one F.

[00:28:03]How do you find the charge on this um capacitor?

[00:28:08]How do you find the charge on that capacitor? Well, the first thing we have to do what? We have to combine the two.

[00:28:17]So if you combine the two what are you finding? So maybe that would would be the first question. Find the equivalent.

[00:28:26]So the C equivalent is equal to 1 + 2 which is just three currents. What does that mean? This means that we have compressed this diagram to this. We just have one. Okay, which is the equivalent there. So if you have the capacitor here, if you have the capacitor there and you have the voltage according to this formula, the capacitor is equal to charge over the voltage. So if you're looking for the charge that is passing through this equivalent, what are you going to say? This charge is equal to C change in V. So the C which is the equivalent is three. The charge is 10.

[00:29:14]So that gives you 30 kum. Okay. So this is the charge on the equivalent. That is the charge on the equivalent. How do you find the charge on these separate um capacitors? How do you find the charge on these separate capacitors? So the charge on 1 F will be equal to C for one. So let me call this one one and that one two. So C1 then change in uh V which is the potential difference. So C1 is 1 multip by this which is 10. So that will just be um 10. Then the other one you say this multip by 10. Why am I using 10? Because I know the voltage on this is just equal to the voltage of the entire circuit which is what? 10. Okay.

[00:30:14]So in an event where they say find the equivalent, you should find find also the charge for the equivalent and then find the charge for the independent uh capacitors. So here you're going to see that this is going to be 10 kum that is 20 kum when you add the two you're still getting 30 kum which was the charge on the equivalent and it makes sense. Okay now uh how do you practice that? So you can practice that with the this example.

[00:30:51]Example 16.7.

[00:30:55]You can practice that with that example.

[00:30:57]Example 16.7. There are even other follow-up questions that you should do.

[00:31:03]Okay. Perfect. Now let's go to the series arrangement. You see? So we are going to just get the same uh setup but we same values but we just change the configuration. So here we have a battery and then we have C1 which is one then we have C2 which is two. Okay. And then we do that. So this is 10 volts. We cannot say in this case we cannot say the voltage is the same.

[00:31:42]The voltage is um different. What is the same is the charge of the system. But how do you find the charge of the circuit? So in order for you to find the charge of the circuit you need to find the equivalent uh capacitor. So the equivalent capacitor in this case will be equal to C1 C2 over C1 + C2 which is going to be 1 * 2 / 1 + 2 and that gives you 2 / 3. Okay, that is going to be the equivalent. Now what you've done is you have reduced this to that just one where this is equivalent and that is still 10. So if you find the charge here that is going to be the charge of the entire circuit. So how do you find the charge? Well charge is equal to so we say charge is equal to capacitors and then the voltage change the potential difference. So this is 2 over 3 * by 10 which is going to be 20 / 3 kum that is the charge. Okay. So if this is the charge of the entire system, if that is the charge of the entire system, it implies that this is the charge on that and that is the charge on that.

[00:33:11]The same value because we said the in series connection the charge is the same for series connection the charge is the same. Where do you find that in say well I'm sure it should be stated somewhere.

[00:33:29]Perfect. So here this statement in board the one I'm highlighting capacitors in parallel both have the same potential difference across them. Okay. So even for the other part I'm sure they have stated so so the charge is the same. So the charge being the same it implies that if we want to know the voltage this voltage that is passing through uh C1 what do we do? We just say the charge divided by C1 capacitors when you make this subject of the formula. So the charge there is 20 / 3 then it will be multiplied by 1 / C1 right uh which is going to be so sorry so this is C1 C1 is one yes so that is going to give you 20 over 3 uh volt then the other one what do you do the other one you say the charge which is 20 over 3 then you multiply by that so this is going to give half of that is what 10 over uh 3 that is what you have. Okay. So in principle in in principle we are saying when you add this potential difference and that you should get the one for the battery the total one for the circuit. So 20 + 30 uh 20 / 3 + 10 / 3 this is uh 30 / 3 which is 10 and it makes sense.

[00:35:10]Okay. So for this case ensure to go through example 16.8.

[00:35:18]You can go through example 16.8 to gain the understanding on the uh capacitors. Okay. which are arranged in series.

[00:35:30]Perfect. So what about the energy stored by the capacitor? So the energy that is stored by the capacitor also we just know the formula. The formula is uh so these are the formulas that we have here. These are the formulas you have to know them. What are these formulas saying? Okay, what are the formulas saying? So the formulas are saying that the energy that that is going to be stored by the capacitor is half CV².

[00:36:08]Okay. So in an event where they they're talking about um parallel plate capacitors this C the C there is defined as that.

[00:36:24]So this equation can also change to so where they see we put that so we're going to have epsylon a v² over 2d in an event where they talking about parallel plate what capacitors that is going to be the c okay so it is just a matter of knowing the formula depending on what has been given to you so assess what is it that you have if you you have um if you have what if you have been given the area and the distance then they give you the voltage then this is the formula you're going to use to find the energy that is stored okay then there are there are some questions that I would like to bring to your attention so we talked about the potential energy between the two point charges so this is your test the test that you wrote And then there was this question question 19 this question here. Okay I can even highlight it. So what is the minimum work required by an external agent to separate the two charges um that that are so the charges are on those points okay to an infinite distance apart. So what they are saying here is we have charges let's say we have positive charges that are separated by a certain distance R. So this is Q1 that is Q2. So what work must you do or must an external agent do in order to separate these uh charges to a distance that is infinite apart. So infinite apart the work done this work done should be given by what?

[00:38:24]The change in the potential energy. Okay the change in the potential energy let me use that the change in the potential energy meaning there will be potential energy. Okay, where we are taking them which is at infinity minus the potential energy where they were the initial potential energy. Okay. So now this one should be the potential energy at infinity. If we know that between two charges potential energy is given by that two then r when r is infinity that goes to zero. So this is going to be zero.

[00:39:04]This term becomes zero. Hence you just remain with that. So in order for you to find the work done by the external agent you just have to get the initial potential energy and multiply it by negative. Meaning you just come here and say okay this work done will be K Q1 Q2 over R just this arrangement here. So in order to answer that question all you needed to do was to say okay this is at they separated by what? So if they at those points then what can we say? If this is the separation distance then you say the charges are the same you say K q1 Q2 divided by separation distance which should be in SI units. Okay, don't forget these are prefix. You can't say this is the SI unit. No, you have to substitute this by the value. So that is micro it's 6. Okay.

[00:40:12]So make sure you're using the SI unit and to answer that question you all you need to do is to do that. That is the work done by an external agent. So you need to have the spring con sorry the kums constant and then you need to have the charges you take them as they are.

[00:40:33]Okay you take them as they are. So according to this question that came in the test you add both these are positive charges. So if they are positive charges we expect the answer to be negative.

[00:40:47]Okay we expect the answer to be negative unless otherwise. Now um basically that should be that should be it. This is the summary of electric electrical energy and capacitors.

[00:41:06]uh the rest I think they are just applications and uh you know you just have to maybe you can also go through this example to just appreciate how to use and apply dialectrics and uh yeah so this is very easy for you to comprehend I believe you you got this okay and this should mark the end of the semester Okay. And unless otherwise so you were told that you need to do current and resistance. Okay. So for current and resistance well you can do them up to maybe this point not where you have to start talking about the circuit that is not necessary. Okay. So just the basics remember usually we examine you depending on the things that you've covered. So don't base your focus or your concentration on the things that you haven't done. Focus on the things that you have done and make sure you become a master of those things. Okay?

[00:42:21]Go through all the tests.

[00:42:23]Know them. Know the questions. I'm not expecting you to fail the same question twice.

[00:42:30]I'm expecting you to get the question.

[00:42:33]If they happen to repeat a question, you should be able to get it correctly.

[00:42:39]Okay. So, this is going to be the last video and I believe if you have watched all the videos, you have become a data girl or a data boy. Okay. So, this is just a declaration that you have to make. You have to believe in yourself and um you know for you to come here you've passed through secondary you've written your grade 12 so meaning you are capable of doing anything okay you've done this before it is not your first time and you just have to believe that you will do it again all the best and uh good luck thank