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So, this is for example, if I call this if I write the C-Rates here ok. So, this would be a 1 C-Rate if I draw 2 amps and it is going to get consumed in half an hour. So, we will call it; so, 1 C-Rate this will become 1 by 2 C-Rate and if I consume it in the 0.25 amperes 0.25 I am sorry this is 2 C-Rate two C-Rate. It’s an inverted relationship. So, if I draw 2 amps of current for a point 0.5 hours’ it is twice the capacity twice of the capacity of the battery. So, it will last only half an hour; so, that’s a 2 C-Rate and if I draw 0.25 amps; so, that is you are drawing much less than the capacity in terms of ampere-hours. So, it will last longer; so you will get 4 hours out of it. So, we call it 1 by 4 C-Rate ok. So, it is an inverse of this value this time or it is an inverse of what you are seeing here concerning the 1 hour of usage ok. So, a 1-ampere hour concerning 1 ampere-hour, if you can finish it in 1 hour it is a C-Rate, if you finish it in half an hour you are consuming; consuming the charge twice the rate; so, that’s called 2 C-Rate. If you take 4 hours to consume it consume the charge; that means, you are drawing the charge at one fourth the rate. So, that is 1: 4 1 by 4 C-Rate. (Refer Slide Time: 19:12) So, just to sum the same information I am summing up here. So, 1 C-Rate is discharged or charged in 1 hour, 2 C-Rate is discharged or charged in half an hour and 5 C-Rate for example, is discharged or charged in 12 minutes; 5 C-Rate means so, 1 by 5 of an hour that is 12 minutes. So, 60 by 5 that is 12 12 minutes is what it will take to do this in when; if you do the discharge or charge in 5 C-Rate. Similarly, you can go down in scale you can do 0.1 C-Rate very slowly you are drawing current out of that battery ok; in which case? Because it is 0.1 if you do 1 by 0.1 you will get 10 hours; it will the battery will now last you for 10 hours. So, the same battery can be tested under various conditions, you can test it at point 1 C-Rate, 0.2 C-Rate, 0.3 C-Rate etcetera C-Rate, 2 C-Rate, 3 C-Rate, 5 C-Rate etcetera. So, normally in battery testing, they do that; they do that to understand what is this battery capable of if I draw if I try to draw a lot of current from it; can it still sustain itself will it last how will it last, how will it perform? That is the reason why we do it in different C-Rates and then on that basis. And we always compare the C-Rate with the original capacity rated for the battery ok. So, it may perform a lot worse than that ok. So, for example, I am telling you here that if I do 2 C-Rate, it will consume the charge will get consumed in half an hour. But that is only under ideal conditions right. So, supposing the battery was not ideal; so, the 2 C-Rate may consume the charge in let’s say instead of 30 minutes, it may consume the charge in 20 minutes itself; which means you did not consume the charge completely, there was some unused charge. And that is the reason why even though you said 2 C-Rate and you normally expect you to finish in half an hour; it is not finishing in half an hour; in 20 minutes itself it is out of it it has hit you know boundary that you have set; you set 1.3 volts as the boundary, it has already hit the boundary beyond which you don’t want the voltage to drop; so, you have stopped the test. So, many batteries; so, that is why the C-Rate is always concerning the original capacity. Because you may not be drawing the original capacity, when you draw high C-Rates and; so, you cannot keep on changing this you know the meaning of the C-Rate. So, it is concerning the original capacity of the battery, the rated capacity of the battery which you which we know from the number of chemicals that we have put in. And then correspondingly we set the C-Rate and see how long does it last; it may not last half an hour, it may lose less than that. If you go to slow current densities it may last the whole distance. So, that is how you have to think about it. So, that’s the idea of the C-Rate. (Refer Slide Time: 21:44) So, now we will look at some incidentally since we talked about the charge and discharge a couple of few small terms here that we have to keep in mind. One is the state of charge which is the percentage of the maximum capacity that is remaining unused. So, if you have said you have completed you know 20 per cent of the batteries capacity has been used. So, the state of charge is 80 per cent is remaining 80 per cent remains in the battery that you can still use. So, if you were using 1 C-Rate. So, you know every 6 minutes is 10 per cent. So, you have consumed 20 per cent charge means 12 minutes of battery usage you have completed and the remaining 48 minutes remain in that battery which you can still use so; that means, that’s the that is the way you compare the state of charge; assuming a particular C-Rate to how long the battery will last. Depth of discharge means the percentage of maximum capacity that has been discharged. So, sometimes you know when we use a rechargeable battery typical rechargeable batteries, let’s say you use it for some particular purpose often what will happen is we will not use it for till the complete end before you recharge it right. So, you are using in an in your camera, you have a rechargeable battery you are taking photos etcetera and then at some point you know evening you are back at your home or your hotel room and you want to recharge your battery. So, at that point the battery may not have completely discharged; it might have you know completed only three-quarters of its discharged and that point you recharge it. The same is true with our mobile phones you know whenever we get the time we reach we recharge it, we don’t necessarily wait till the battery completely you know winds up. So, this extent to which it has been discharged before; you recharge it is the depth of discharge ok. So, the depth of discharge is the percentage of the maximum capacity that has been discharged. So, it is sort of the inverse of the state of charge. So, what remains is the state of charge, what has been completed is the depth of discharge. Cycle life is relevant from the perspective of rechargeable batteries from the perspective rechargeable battery cycle life is important. Because it is the number of cycles before the battery fails to meet some performance specification ok. So, it means. So, let’s say typically recharge batteries rechargeable batteries; you may want it to run 1000 cycles, people try to advertise like that it runs 500 cycles, it runs 1000 cycles etcetera. So, why does it not run 2000 cycles when it is stopped why are they saying only 1000 cycles or why not say 1100 cycles? The reason being they have set some minimum performance limits. So, they say that you know it should at least last you if I am drawing say 1 amp; it should at least we are usually not drawing one amp, but let’s say we are drawing 1 amp it should last you at least 7 hours. Let’s say some idea like that they have; so, when they keep on doing the cycling, you know of charging, discharging, charging, discharging the chemicals slowly in some way deteriorate. So, some deterioration happens in all the chemicals that are present there or even the structure inside the battery deteriorates in some way. And then the capacity which was perhaps originally the battery was originally able to last 10 hours, slowly starts decreasing with progressive cycling; it draws drops to you know 9 and half hours, 9 hours, 8 and a half hours, 8 hours and so, on it keeps on dropping. So, by the time it reaches the 1000th cycle; it has probably reached 7 hours of discharge and that is all it's able to discharge before it stops it has already hit the cutoff and then it starts to have to recharge. So, and we set the standard we say that you know at least 7 hours it should last or some such thing we decide the number 7 is just an example I am giving you. So, at 1000 cycles it has already we hit that 7 boundary of 7 hours; if you cross 1000 cycles it starts decreasing in capability below 7 hours; it becomes 6 and a half hours or whatever you know 6 hours 50 minutes something like that and we decided that it is not acceptable to us. So, once you set that acceptability limit saying you know at least this much longer it should last; this point of performance it should give. Then you can give a define a cycle life. Because technically, if you don’t define that performance you know guarantee. So, to speak what is the minimum performance if you don’t define that; you can keep on charging and discharging a battery in indefinitely you can do it; it may not last you 10 minutes and then after 10 minutes you will have to recharge it, again 10 minutes that is going to be very annoying if you put that kind of a battery in your mobile phone right. So, you don’t want to keep on charging 10 minutes to use it for 10 minutes; you want to be in a situation where you can charge it for maybe an hour or half an hour on an hour and then you want this battery to last for you for the day right. So, something like that is what we are used to. So, we are expecting at least about 10 hours of service from the battery; I at least 10 I mean ideally you may be on 24-hour service, but at least 10 hours 10 to 12 hours is what we are looking for; for us to feel comfortable. So, 7 hours is actually on the lower side. So, so some criteria you have to set and concerning that we decided as cycle life because you can figure out how long it how many cycles it will do before it hits that performance limit. So, again this is something that the battery test station will do for you. We cannot do this on an actual you know you cannot distribute battery to 100 users and figure out when they start feeling uncomfortable about it. In a battery tester, you can set the current, you can set the voltage boundary and you can ask you to keep cycling and you can also say a cycle till you get the 7-hour mark and tell me when that happens. So, once you set this up; it will continue to do that I mean it will continue to do the testing for you know 100 cycles, 200 cycles etcetera and then at some point it will stop and then you can take the data, and you can plot it and you can see what is happened ok. So, this is the meaning of this cycle life ok. (Refer Slide Time: 26:58) So, I keep talking of charge curves and discharge curves. So, now, we will briefly look at what is this charge-discharge curve; how does it look what is it that we can understand from it. So, for that we will make a plot; so, on our y-axis, we will have the voltage we always talk of voltage concerning a battery. So, we will put voltage here ok; so, and let’s say you know the most common value that we keep hearing is you know you go and buy batteries in a shop, you will see the 1.5-volt battery. So, just, for example, we will take a 1.5-volt battery; so, I will put 1.5 here. So, let me say this is 0 have the x-axis here. So, this is 0; so, I will say this is 1 and this is 0.5. So, this is 0 volt 0 I mean 0.5 volts 1 volt, 1.5 volts. On our x-axis, we will plot time in hours ok. So, that’s what we have plotted on time; this is the voltage in volts that’s sitting up there right; so, voltage. So, this is what we have plotted; so, normally what would happen is. So, we will just put some time here I will just put some numbers here. So, I will just say let’s say this is 10 hours and this is 20 hours roughly. So, this is 15, this is 5 ok. So, some sometimes it is some such numbers we have. So, now, if you start taking this battery and you discharge it and let’s say we have a 1-ampere hour battery and I do 0.1 C 0.1 C-Rate discharge charge-discharge, but that’s what I have put into the system. So, this means this battery will now last 10 hours or it’s you can expect it to last 10 hours ok. 1 divided by 0.1 the capacity divided by the C-Rate will give you how long it last ok. So, that is how we are getting this value; so, so roughly I can expect that it last about 10 hours and I set some limit I say you know 1.3 volts somewhere here 1.3 I say it should not go below 1.3. So, that’s one value as I set here. So, what you will see is that what you will see is basically a curve that starts around 1.5 and then decreases little bit in voltage and then sort of stays stable more or less stable and then begins to fall like this. This is roughly the kind of performance that the battery will show; it will start, at some voltage the open-circuit voltage that you measure then the voltage will drop a little bit as soon as you start drawing current from it. Then it stays at that lower value for a steady distance of time I mean period and then as you get close to the end of its capacity; it voltage will start dropping again and you have said this cut off at 1.3. So, your test the battery tester will stop testing it at that point; then we will say that we are you know recharging it. So, at this point you have finished the charge; so, you want to recharge it. So, when you recharge it you reverse the direction of the current. So, usually what it will do is suddenly the voltage or climb up. So, I will say again I will set another value here 1.7 volts ok. So, we will set that also just a moment; I have just seen that there. So, we have let’s say 1.7 volts there; so, that’s the value we have and I have set that value that is a guideline I have there. So, if I now do the recharge what will normally happen is it will suddenly shoot in voltage it will cross the 1.5 and then it will start recharging and this is how the curve looks recharge curve. It will again stay flat more or less for the whole period; till we are getting close to this 20 hours and at that point, it will do that. A voltage will start climbing up kind of steeply and you will see at that point know it will hit the 1.7-volt boundary and it ill stop. So, generally by the way; so, if you look at this curve what we see is that the recharge will happen at typical voltages; if I draw a guideline here this is the guideline that I will draw here for 1.5 volts. So, what you will typically see is that the discharge is happening even though you rated the battery at 1.5 volts; discharge happens at values just below the 1.5 volts 1.2, 1.3 I mean I mean not 1.3 we are keeping above 1.3 say 1.4 volts; most of the discharge happens at 1.4 volts one and then when you do the recharge most of the recharge is probably happening at 1.6 volts. So, this is because of you know various inefficiencies that are present in the system including IR resistances and so, on. So, you end up having to draw put more voltage when you are trying to recharge the battery, you get a little less voltage when you discharge the battery. So, that is always a gap there that represents the inefficiency that is what this curve shows you ok. So, this is how this curve would look and I can also tell you that you know this is one way. So, normally when you do a charge-discharge curve; so, it will continue to do this. Supposing I say do this for you know 100 cycles; so, this is like 20 hours. So, beyond 20 hours again you are you know this blue curve will repeat after that. So, for example, it will continue doing this; so, from here if you do the discharge, it will come down and it will fall back like this and then you will continue this. So, this continues indefinitely; so, you can keep doing this many times and then do it. Of course, this means you will have an indefinitely long graph because you were 100 of cycles you will have. So, that gets a little messy to look at; so, another way in which they represent this is the instead of you know continuously keeping it as a linear scale that’s continuously going on endlessly on our right-hand side, we keep since we know that we are doing a point 1 C-Rate; you know that this test can you know any cycle whether it is a charge cycle or a discharge cycle, it is only going to last about 10 hours it may last even less than that, but typically it will going to only last 10 hours. So, we can just stick to this part of the curve. So, we can just stick to this 10 hour part of the curve and plot everything within this 10 hours. So, we can have all these charge curves as well as the discharge curves within the same 10 hour period; repeatedly is resetting this to 0. So, all; so, whatever you see here between 10 and 20 hours, you should simply shift it back by 10 hours and you can plot it between the 0 and 10 hours. So, that’s another way in which you can plot. So, that your entire plot stays between 0 and 10 hours you see multiple curves; each representing 1 cycle of charge and now one cycle of discharge; so, this is how we have plotted. The other point we have to keep remembering is that I have we have just seen here that we have used a particular C-Rate. So, what happens if you use a different C-Rate. So, this is the point one C-Rate it took us 10 hours to do the charge or discharge and this is what we saw right. So, we can also plot this in terms of capacity this is the time that I have plotted I can also plot this as to capacity. So, I will have on the x-axis capacity in that case. So, in so, the point is that if I plot it as time then clearly the C-Rate will simply keep on changing the time dramatically just because the C-Rate is different. So, if I instead of you know 0.1 C; if I use 0.2 C; that means, I am doubling the current; that means, then the battery will last only half as long in terms of time. So, automatically that itself means that the test will end in 5 hours if even if everything were idea. So, by simply going from 0.1 C to 0.2 C to 0.3 C etcetera you will keep on changing the time anyway, but the original capacity of the battery is the same. So, therefore, it may make sense to plot multiple different C-Rate information concerning the capacity so, that you can see if there is a difference in terms of you know behaviour because of the C-Rate. So, for example, we can plot it like this. I will have again voltage here and I will have the capacity. So, I have a 1-ampere hour. So, this is 0 this is 1 ; so, this is 0.5 0.75, 0.25. So, this is a capacity this is in ampere-hours. So, the capacity is unaffected by what C-Rate you are doing right. So, the capacity of the battery is the same; the C-Rate simply tells you what how quickly or how slowly or withdrawing this capacity and using putting it to some use. So, here I will have a voltage of 1.5 volts. So, this is 1, this is 0.5 ok. So, now, based on the C-Rate we will have you know the different-different capacity. So, let’s say my the first I draw it at some particular C-Rate I get this capacity; then I draw at some other C-Rate a higher C-Rate higher C-Rate will usually mean it will perform a little worse because you're drawing current much faster and you may not even reach the full 1 C; you may even before the one C is reached you may hit some boundary. I have kept a much lower boundary here let’s say I am setting a 1-volt boundary here as the test condition; I can do some other C-Rate which may be even higher performance higher rate. So, you will see that the higher the C-Rate you do you may never completely reach the full capacity because inefficiencies are such that you will hit a hit your cutoff boundary before you even reach the complete capacity of the battery. So, this means for like for example, let’s say this is 60 per cent let me just say that this is 0.6 it means only 60 per cent of the battery I used; I already hit the boundary for that whatever I set as the cutoff limit for the voltage and saying I don’t want to go below this voltage. So, because it may damage the battery or it may not be useful for the end activity that is in putting it to use for. So, for those two reasons I may set a cut off voltage and so, it hit this 1-volt cutoff voltage in this case I set it at 1 volt let’s say and it is hitting this one more cutoff voltage at only 60 per cent of capacity. So, it is not helping us. So, so the point is you can draw it I you have to understand. So, that therefore, different C-Rates, the performance can be different you may not completely get the full capacity out of it. And you need to understand this for your battery so, that you can tell clearly whether or not this battery can be put to use for some purpose or not. Or if you get a new battery that you want to put it for some experiment, for some end-use you know what usage that induces how much current it will draw. You can test and check whether your battery can handle that activity right. So, this is the way you do that test. (Refer Slide Time: 38:01) So, the same information I am just showing you in these plots here; this is a discharge curve here and this is a charge or recharge this is what we just discussed. And then the same thing as I said you know instead of you can just take this part of the curve and push it back into this part of the plot; so that the whole plot stays within 10 hours and so, that is exactly what we have done here. (Refer Slide Time: 38:27) So, I have just plotted it all within 10 hours, I have shifted the charging curve also within this 10-hour window. So, there everything now shows up between this 0 and 10 hours. (Refer Slide Time: 38:38) And then as I said you know we can have the capacity here if you want to look at the effect of different C-Rates on discharge possibility. So, I have a C by 2, I have C, I have 2 C and 5 C; as you can see the rate at which I am discharging the battery is getting higher and higher and higher. So, the speed with which I am pulling something out of it is higher; usually, this is what happens the closer you are to you know doing it, the more slowly you do it the more completely you can extract the charge out of the battery. The faster you do it before the full charge comes out of the battery; it starts showing you bad performance and then you stop the test. So, that is why C by 2 gives you much better performance than C and which performs better than 2 C, which performs better than 5 C. And as I said it makes sense to keep capacity here because only then you can you know at a glance; at a glance, you can compare these C-Rates. If you put time here it is very misleading because anyway, the C-Rate guarantees you that the time is not going to be the same. It is only the capacity that’s the same across the batteries across the; I mean across the various tests even though you are drawing different currents, the capacity is the same. So, an ideal battery would be something there where even at 5 C-Rate you will get the full capacity that is that you are getting from C by 2 rates; that would be a beautiful battery. You make a battery where you start at C by 2 rates, you go up to 5 C-Rate or even 10 C-Rate, you will still keep getting the full capacity of the battery out that would be a very nice battery to make; usually, that is not the case the higher the rate at which you draw the current, lower is the capacity that you can extract from the battery. So, this is the effect of the C-Rate on the charge or discharge. (Refer Slide Time: 40:10) Also, I pointed out that please remember we keep on having voltage on the y axis, but there is will have different things on the x-axis; we already saw time as one parameter we can put on the x-axis, we saw capacity as another parameter that you can put on the x-axis. Now, I am going to show you something called a polarization curve where on the x-axis we have current density ok. So, please keep in mind the curves look similar, but the meaning or the significance is very different. So, this and so, whereas, the previous curve that we saw here this kind of a curve is taking 10 hours to complete because you are completely extracting all you know chemicals out of that system. A polarization curve happens in a matter of minutes; so, you may take 1 minute to record this curve. So, this is a sort of an instantaneous snapshot of the state of your battery. So, what happens is you stop the test, you measure what is the open-circuit voltage ok. So, that is 1.5 volts then you draw let me just say this is 1. So, I will just put some values here. So, I will say let’s say 1, 2, 3. So, let me say this is 10 amps ok. So, that’s 1 current densities 1. So, let’s say this is 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1 amp per square centimeter. So, you change the current to point 1 amp per square centimetre; you measure the voltage and this will take you just about say 10 seconds to do. So, then you immediately change the current to 0.2 amps current amps per square centimetre, measure the voltage like that you continue. You set the current, measure the voltage and do this only for about 10 seconds then you get all these points. So, you are not even actually able to reach 1 amp per square centimetre well before that you see this curve; so this at any given point in time; if you continued at this point’ if you continued at this particular 0.5 amps per square centimetre and did a long test in that would correspond to a C-Rate. So, each of these points corresponds to different C-Rates right. So, these are different C-Rates that are being momentarily tested you switch on the battery, you are sitting at 0. you raise the C-Rate to point 1 C-Rate and then you check what is the voltage and current relationship’ immediately change it to 0.2 C-Rate, 0.3 C-Rate like this you continue till some C-Rate which is high enough and that the battery is unable to support it and then you get this curve. So, this tells you at a given instant in time what is the current you can get a different C-Rates then. So, that is called the polarization curve, and it is usually an excellent indicator of what is possible in the battery ok. So, you can take the nice idea the nice thing about a polarization curve is that as I said it only takes about a minute to record to measure minute or 2; it will take only that much. So, if you have about 10 points here and each point is going to take 10 seconds so that’s only about 100 seconds. So, less than 2 minutes is you; you can record this curve. So, as opposed to curves such as this is going to take 10 hours right 10 hours to completely charge a battery and another 10 hours to completely discharge the battery. And if you are going to do 10 cycles; so, that is each charge-discharge cycle together is 20 hours, you are going to do 10 such cycles that are going to be 200 hours. So, that is a very long test right. So, that’s 8 days of testing right 24 hours a day; so, about 8 days of testing you are looking at. This testing on the other hand is 2 minutes; so, 1 minute to 2 minutes ok. So, this is a very useful test that way the charge-discharge test is more representative of what it will do long term, but this gives you a very good snapshot of it, it tells you what is possible it may not fully capture all the details at the charge-discharge curve gives you, but it does tell you what’s possible with the battery, what is the state of health of the battery even after what after about you know you have used the battery for you know 10 hours. You just want to check what is the state of health of the battery you can do a polarization curve and you can compare it with the polarization curve that was there at the start of the batteries life. So, you can also use this to compare multiple batteries because you can also do the full charge-discharge curve and say you know this battery lasts at 100 cycles, another battery lasts 150 cycles and then you can say this, therefore, the second batteries better than the first battery, but in the process you have consumed a huge amount of time to figure that out a polarization curve as I said only it takes about a minute or 2. (Refer Slide Time: 44:49) So, for example, if you look at this you have two different cells here cell A and cell B and I have done a polarization curve for both those cells. You can see here clearly that cell B is giving you much lower voltages for any given current density compared to cell
A. And we use current density because then you can you know compare even cells of different sizes. So that is the reason you can you know to normalize for the size larger; so, if you have one electrode which has some area and another electrode which is twice the area; then clearly you know it one electrode the first electrode has some chemicals, the second electrode has twice as many chemicals. So, if you draw 1 amp from here it is the same as drawing 2 amps from the second battery. So, that is why you have to divide the area by 1 amp this divide this area by 2 amps you will be sitting at the same current density that way you can compare them that’s the idea. So, now, you can see here that cell B has a polarization curve that is lower than cell A; so, you can say that cell A is better than cell B.
his may also be that for the same cell at different points and time you can see that you know it is deteriorating, how it is deteriorating etcetera. So, therefore, this is a very useful curve to have a polarization curve for any electrochemical device and certainly, for batteries this is useful. (Refer Slide Time: 45:55) And from the same curve, you can also find out the power curve; power as a function of current density. Because for example; when you are at the open-circuit voltage the current density is 0. So, therefore, the power is 0 V power is equal to V into I. So, you can multiply by the area if you want or you can just do power density here power per unit area in that sense and then you can get. So, for every value of voltage, you find out what’s the value of current and then you get this product. So, similarly, you do various points on this curve and then you will get this curve. So, it tells you; what is the point at which you are getting the maximum power.