 Let's talk about what happens to our batteries when they are connected in parallel. In previous videos we saw what happens when they are 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 we'll clarify what this means and compare with this. Alright so let's 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? If I were to replace this combination with just one single cell what would be the EMF of this cell? So it has the same effect as these two. So let's call that effective EMFEP, P for parallel and let me just write that to the top. So EP, 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 way do we connect it to some external circuit then we will 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. Alright 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. This equals this plus this. So how do I calculate the current? For that I need to attach it to some external, you know I need to attach a circuit, 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. 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. Alright 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 figure that out? You may ask. So if you 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? Alright so the current due to just this battery, if you only 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 whatever short, 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 ever generate. Alright 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? Alright 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. And so do you now understand the meaning of this equation? We derived it logically but do 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. 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? So then you will not get added up. So you need to attach them in the right way meaning positive connected to positives negative connected to negatives. 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 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 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 one over RP equals one over R1 plus one 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. 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 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 a lot of such series combos in parallel until you get whatever maximum current you want. So it's going to be always some series and parallel mixed combination.