Class 12 Physics (India)
Cells in series
Let's explore how to calculate the emf and internal resistance of an effective cell when cells are connected in series. Both the emf and the internal resistances add up. Created by Mahesh Shenoy.
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- Okay so I understood the video but I have a question-
What about the current ? Is it greater as compared to using a single cell, or less ?(2 votes)
- At2:06, shouldn't the current be taken from positive to negative point of the cell(2 votes)
- So is the summed battery in series on the right -2V volts or +2V volts. If it comes down to an exam question are we suppose to reverse the positive and negative, is the Positive end allowed to be on the left?
Or is it always Mod, always positive?(1 vote)
let's look at what happens when you connect batteries in different ways so just like when it comes to resistors we have two kinds of connection we have series connections when batteries are connected end to end this way and we have parallel connection when your batteries are connected across each other this way and what we will see and we will discuss this throughout the video is that in series connection we will find that the batteries end up giving you more voltage all right and in parallel connection we'll see we end up getting more current and we'll clarify what that means so in this video let's focus on the series connection and see how we get more voltage and in the next video we'll focus on the parallel connection see what it means to have more current and we'll compare them all right so let's start by focusing on the series connection in this video all right so why is it that in series when you connect batteries in series you get more voltage well let's think about this let's start with something that we already know and we've seen before that batteries have something called an emf and let's say for example this battery has an emf e1 which is 5 volt and this one has an emf of let's say e2 which is i don't know seven words so let's try and answering this question what would now be the effective emf of these two cells in other words what i'm asking is if i were to replace these two these two batteries with one single battery what would its effective emfp what would the emf of this battery be so that it's equivalent to two batteries does that make sense just like how we do it for resistors so how do we figure this out logically without having to do too many derivations logically how do we figure this out for this we need to recall what's the meaning of emf and we've talked about that in previous video but let me just let's just jog our memories okay the idea behind emf or the way i like to think about it is batteries what do they do what's their job their job is to push charges push think of positive charges in reality it's electrons negative but it's easier to think in terms of positive charges so their job is to push positive charges from negative to positive so let me bring in a positive charge over here so the battery's job is to act like a pump and push them from positive from negative to positive push them from negative to positive and the emf represents how much energy the battery delivers to the charge per coulomb for example five volt means when the battery pushes it from its negative to positive it delivers five joules of energy per coulomb if this was one coulomb it transfers five joules of energy and similarly what does this battery do when it pushes it from negative to positive it transfers seven joules of energy per coulomb so this is one coulomb this battery would transfer seven joules of energy and if this concept of emf is not clear to you or you need a refresher feel free to go back and watch our videos on ef's internal resistances terminal voltage and then you can come back over here again all right so now the question we are asking is what is the effective emf so what would be the if emf of this effective battery so let's call it as es what would that be so what we're asking is what would that if i were to take it a charge one coulomb from here to here how much energy would get transferred to it because of these two batteries together that would be the effective emf does that make sense so can you pause the video and think about based on what we just said what would be the effective amf all right hopefully you've tried so we know that when a coupon goes from here to here it gets five joules and then when it goes from here to here it gets another seven joules so what is the total energy transferred per coulomb that's five plus seven that is 12 joules and so the effective emf is 12 volt and as a result you can now hopefully see that the effective emf in general so s stands for series effective emf is just the sum of these two e1 plus e2 and if there were more cells connected in series i hope you agree they'll be just e1 plus c2 plus e3 and e4 and this is why i said in series connection you get more voltage out of it so whenever you require more voltage from a battery or multiple batteries you just put them in series now one thing to be careful about is notice to get more voltage look at the connection the positive needs to be connected to negative that's how the connection needs to be all right now my question to you is and i want you to think about this what if we didn't connect it that way what if we connected it this way what if we connected positive to positive or negative to negative can you now think a little bit about what would the effective emf of this be use the same idea think think logically and then think about what that you know effective mf is yeah so can you pause the video and think about this all right let's see so i'm going to bring this charge and now i know that when this charge goes from here to here the battery pushes it and provides five joules of energy per coulomb if this was one column it transfers five joules but what happens when the charge goes from here to here now notice it's going in the opposite direction it's going from positive to negative and when that happens it loses energy now you can imagine the battery sucks energy out of it so how much energy is being sucked out of this charge now not uh sucked out seven joules so think about it when it goes from here to here it gains five goes from here to here it loses seven so by the time it comes here it has a negative two volt so we can say the emf the effective emf of this is negative two volt and at this point you might be a little comfortable like what does it mean to be negative well it basically is talking about the direction of the battery so here's what i mean so since i know that this side i'm getting less than zero you can imagine that this oops one second this is the positive side of this effective battery and this is the negative side and that makes sense this battery is dominating so the terminals will have the polarity of this battery and so that basically means now your effective battery should have a positive here negative here so your effective battery would look like this and its net emf is going to be es is going to be two words so i've already taken care of the negative negative basically means flip the battery so two words and so um it's not going to be always more voltage it will get more voltage if you connect in right main and then when i say right way you connect positive to the negative positive to the negative and we have seen that batteries have something called internal resistance and what's the idea behind that that basically means when the battery is pushing the charge and transferring say in this case five joules of energy per coulomb not all the five joules get transferred to the charge some of it gets wasted as heat and that's due to the internal resistance a lot of internal resistance means a lot of heat gets generated and so that's also an important factor and so the question now we have is let's keep the charge aside okay so the question now is if i know the internal resistance of this cell let's call that as r1 and if this has an internal resistance r two what's the internal resistance of this effective cell what's the total internal resistance again can you pause and think about this i'm going to give you a clue you already know what happens to resistances when they're connected in series so it's going to be the same thing so pause and think about this all right we've seen that when resistances are in series they just get added up that makes sense again right when the charge goes from here to here it encounters this resistance and this resistance so the total resistance becomes r1 plus r2 and as a result the total resistance oops the total resistance or the effective resistance is going to be r1 plus r2 what about over here what do you think will happen to the effective resistance over here will it be subtraction or will it add up well it doesn't matter how you orient the batteries the resistance will always add up resistance don't have a polarity so regardless of how you connect the batteries the resistances will always add up so long story short if you want more voltage from your batteries you connect them in series their emfs get added up connect provided you connect them the right way but their internal resistances also get added up in the next video we'll look at what happens in parallel connection