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Course: Class 12 Physics (India) > Unit 3
Lesson 6: Combination of cellsCells connected in parallel
Let's explore how to calculate the effective EMF and internal resistance when cells are connected in parallel. In a parallel connection, the maximum currents provided by cells add up. Created by Mahesh Shenoy.
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In the practice quesitons given ahead, when we consider parallel combinations the net voltage does not take into account the internal resistance. The question ahead asks for the resistance in the circuit (& I is given) and for that, I first calculated the equivalent emf of the cells and then used ohm's law but by using terminal voltage as V i.e, eq. Emf - ir(where r = r1.r2/(r1+r2)). But in the solution, it tells me to directly use the emf (i.e Eq. emf/I) . Why is my solution incorrect?(4 votes)
This is because the internal resistance of a cell is nothing more than another resistor. So the voltage across the unknown resistor is calculated with the EMF without the internal resistance factored in. We just find the total EMF of the two cells and use that.
If you can't wrap your head around that, think about the fact if we used the terminal voltage (i.e., V = Emf - Ir) in calculating the voltage across the unknown resistor, we would have subtract voltage for every resistor in the circuit as well, which is obviously wrong and doesn't make much sense.(1 vote)
So to be clear, if 2 cells of the same capacity(same voltage and amperes) are connected in parallel, the total voltage output would stay the same, but the number of charges per second would increase, and therefore the amperes would increase? Correct?(3 votes)- If two cells different EMF is connected in parallel without having any internal resistance what would be the effective EMF of this two cells?(2 votes)
- cells will always have some internal resistance(1 vote)
- I don't get it. Suppose there is a 12 V and a 14 V battery(Each with 4 ohm internal resistance) . If they are connected in parallel and there is a 15 ohm external resistor then the current found out due to equivalent 13 V and 2 ohm would be I= E(R+r)= 0.76 A. But when we connect the batteries in series the emf becomes (12+14)=26 V right? Then the r also becomes (4+4)= 8 ohm. So current flow is 26/(15+8) = 1.13 A.(I=E/R+r) . So in any way we can see that the current we get is more for the series combination of cells rather than parallel ,so what di u mean(1 vote)
- In this video, at 2.18 it is said that an another resistor might come. How will the coming of an external resistor in the circuit effect the effective EMF of cells in parallel and what will be the new formula?(1 vote)
Video transcript
let's talk about what happens to our batteries when they are connected in parallel in previous videos we saw what happens when they're connected in series we saw that their emfs get added up and as a result we end up with more voltage so for more voltage you connect them in series and we also saw their internal resistance is also getting added up if you need a refresher feel free to go back and watch that video now let's focus on what happens when you connect them in parallel we will see in this video that when you connect them in parallel you end up getting more current and will clarify what this means and compare with this all right so let's uh dim this part and focus on the parallel connection so the question we're going to try and answer is if i know the emf and the internal resistance of each of these batteries what's the effective emf and what's the effective internal resistance meaning if i were to replace these comp this combination with just one single cell what would be the emf of this cells so it has the same effect as these two so let's call that effective m f e p p for parallel and uh let me let me just write that a little bit to the top so e p p for parallel and what would be the effective internal resistance over here how do i calculate that and i don't want to do a lot of equations i want to do this logically so the key thing for parallel connection as you may remember from studying other parallel connections like that of resistors or maybe capacitors is that in parallel the current gets added up so what i mean is if this were to be connected to some external circuit then we'll see that whatever current we get from this battery and whatever current we get from this battery notice that they get added up over here so the current that you get from the effective battery is the sum of the currents that you get from the individual batteries and i can use that to build an equation over here all right so how do i know what is the current here what is the current here and what's the current here because i know that this equals this plus this this is the same thing as this one okay this equals this plus this so how do i calculate the current for that i need to attach it to some um external you know i need to attach a circle i need to close this circuit that's what i mean that means another resistor might come but you know what i like to think of to keep things simple i like to just short circuit it so just hear me out what if i were to just connect the ends like this and short them there is the same thing as shorting this circuit as well right so notice that i have shorted short circuited this battery so this battery also has short circuited meaning no external resistance zero external resistance this battery has also been short-circuited notice and the effective battery has also been short-circuited all right so if i look at just this battery can you tell me how much current will come out from this battery just concentrate on this circuit how do you how do you figure that out you may ask well think about it in this circuit of the top battery the total voltage in the circuit is just e1 the emf of this cell the total resistance in this circuit is r1 in this entire circuit you don't have any external resistance so it's only r1 and so voltage we know resistance we know so what do you think will be the current in this circuit so can you pause and think about that all right so the current due to just this battery if you commonly consider this circuit the current that will come out from this battery that would be the voltage of this battery divided by the resistance and that current would be e1 divided by r1 so e1 divided by r1 that's the current that this battery will push and in fact if you remember from our previous videos when we looked at cells and emfs this is the maximum current this battery can ever give because notice even when i short-circuited it i have put zero resistance but you know whatever whatever shot even in even in a short circuit the minimum resistance the battery will provide is r1 you can't get even less resistance than that and therefore this is the maximum current this battery can never generate all right similarly what do you think is the maximum current this battery can generate well it's going to be e2 by r2 right what do you think the maximum current this battery will generate what is the current generated in this by this effective battery well same logic it's going to be ep divided by rp and now i know that this current should equal this current plus this current that's what it means to be effective so now i can write an equation so again can you pause the video and write an equation connecting the currents now all right so i know that this current which is ep by rp write that over here ep divided by rp that equals this current plus this current so it's going to be e1 by r1 plus e2 by r2 and there we go that's our equation for that's our equation for cells connected in parallel and if there are more cells connected i can just write e1 plus r1 plus e2 by r2 plus e3 by r3 and so on and so forth okay and so do you now understand the meaning of this equation we derived it logically but you understand this represents the total maximum current the effective battery can get and these are maximum currents the individual batteries can get and now do you understand why in parallel i said that you get more current because by connecting them in parallel i have increased the maximum current that you can ever get so if you want to increase the capacity of providing more current then you have to attach the batteries in parallel now again be aware that if you you need to attach them in the proper way um what if i flipped one of these batteries then the current would be in the opposite direction then the total current would be the difference between the two currents right um so then you will not get added up so you need to attach them in the right way meaning positive connected to positives and negative connected two negatives all right but if you look carefully you might say hey but i have two unknowns over here i don't know what ep is i don't know what rp is and i have only one equation how can i solve for this and you're right we can't solve this just by using this equation we have two unknowns so i need one more equation if i were to solve for ep effective emf and effective resistance so where do i get the second equation for well the second equation i can get just by looking at the resistances because i know just like how we did here before i know uh what happens when resistances are in parallel so can you pause and write down what would be the equation for the effective internal resistance these are in parallel all right hopefully you've tried so what is the formula when the resistance are in parallel we get 1 over rp equals 1 over r1 plus 1 over r2 and so notice i can first calculate what the effective resistance is by knowing r1 and r2 and then i can plug that over here and then i can calculate what the effective emf is and this is how you can calculate the values of ep and rp when you have batteries connected in parallel so when we compare these two what we see is if you want more voltage from your batteries you need to connect them in series um but since the internal resistance also increases this is not so good in getting more current if you want to get more current from your battery you need to attach them in parallel because remember when resistors are connected in parallel the net resistance decreases so when batteries are connected in parallel the effective internal resistance decreases and therefore gives you more current in practice however we always end up getting giving mixed combos so for example you want to build an electric car with a particular voltage and you want to be able to get a particular amount of current from that battery then what you do is you add batteries in series until you get the required emf and then you take such combos and you put them put a lot of such combos series compose in parallel until you get whatever maximum current you want so it's going to be always some series and parallel mixed combination