Series and parallel circuits

0:00- [Narrator] If we have a simple circuit with a battery and a resistor and we close the switch, a current runs in the circuit and the potential along this wire is always the same. The potential along this wire is always the same. And so look, the voltage across the battery or the potential difference across the battery is the same as that across the resistor and that's pretty much the circuit analysis.

0:19But what happens if we have more than one resistor connected in a circuit? What are the different ways to connect them and what happens to the currents and the voltages across them? Let's find out. The first way we can connect the two resistors in a circuit looks somewhat like this, and we call that a series connection.

0:37Think of series connection as resistors connected in a single chain. So let's close the switch. What happens? Well, just like before a current runs in the circuit and to measure that current, we can attach an ammeter and let's say the ammeter reads 0.1 ampere, just you know, to take some numbers.

0:56Remember that adding the ammeter itself does not affect the current, it does not affect the circuit, mainly because ammeters have very low resistance. So we have not added any extra resistance to the circuit, and so they don't affect the circuit. But here's the question.

1:13What about the current here, here, here. Will it be the same or different? Well, notice that whatever current's flowing here, all of that has to flow here because there is no alternate paths available. Similarly, all the current from here has to flow here and from here to here and here.

1:28So the current everywhere must be the same, which means the exact same current flows through both these resistors. And that is a defining feature of series connection. The same current flows through them always. Now of course we could have confirmed that by adding more ammeters and they would all show 0.1 amperes, but that's unnecessary.

1:50Okay, so in series connection, the same current flows through the resistors, right? But what about the voltage? Would that be the same as well? Let's see. I always like to be a little bit more careful about the voltage. So let's do it a little bit more slowly.

2:02Let's say that the battery voltage is five volts. What does it mean? Well, it means that as I go from here to here, the electric potential energy increases by five joules per coulomb, right? That's the meaning of voltage. So if I say at this point the electric potential is zero, then at this point the electric potential will be five volt.

2:22The potential difference is five volt, okay? But what's important is what about the electric potential here, here and here? Remember, we always model our wires to be ideal, meaning no resistances. And of course, we are also modeling our ammeter to have no resistance.

2:37And so when charges move through ammeters or wires, they don't lose any energy. And so the potential stays the same. So the potential everywhere along this wire is fire walled. And the potential everywhere along this wire is zero volt, which means, look, as I go from here to here, the potential drops from five to zero.

2:58So the potential difference across these two points is five volt. But what is the potential difference across this resistor? Well, I don't know. To answer that, I need to know the exact value of the resistors, but let's not worry about that. Let's just attach a voltmeter and see what it reads.

3:15Let's say the world meter reads two volts, then the potential difference across this resistor is two volts. That means the potential goes down from here to here from five to. Five minus two, three volts. So over here, now the potential is three volt, and that means the potential from here to here goes down by three volts.

3:37The potential difference between these two points is three volts. So if I were to attach a voltmeter here, it would read three volts. And so we have now finished our analysis and we can now answer our question. Does the voltage across the resistors stay the same?

3:52No, need not be. Look, the potential difference is not the same across the resistors. And so in series connection, the same current runs through them, but they could have different voltages. In fact, notice the voltage gets divided among them, right? The five volt got divided among them as two and three.

4:10And that's why sometimes resistors connected in series are also called voltage dividers because they literally divide the voltage. And finally, wouldn't adding voltmeters like this create additional paths for the current to flow? So wouldn't it change how much current flows through these resistors?

4:28No, because voltmeters have very high resistances. So pretty much no current flows over here. And so all the current flows just through these resistors, which means they do not affect the circuit. Okay, here's another question. What if I have two resistors connected this way?

4:48Are they still in series? Well, now it looks different compared to this circuit, but they are still connected as a single chain and more importantly, look, the same current flows through them. That is the defining feature of series connection. And therefore, these two resistors are still connected in series.

5:08In fact, if I had a third resistor over here, look, now all three are connected in single chain. And again, the same current flows through all three resistors, which means all three resistors are now in series. So you can have more than two resistors connected in series.

5:25But what if I had a fourth resistor connected like this? Ooh, things are getting more interesting now. Let me get rid of the direction of the current. We don't need to know that. Let me just add some names to these resistors. Okay, now are these two resistors, R1 and R2, still in series?

5:44What do you think? Pause the video and think about it. Well, now notice it's not a single chain. There is an alternate path available. And again, more importantly, think about the current through those resistors. Will the current through R1 be always equal to the current through R2?

6:04Need not because of this additional path, the current at the top could split over here and so they could recombine, which means it's possible for the current through R2 to be greater than the current through R1. So the same current need not flow through them so R1 and R2 are no longer in series.

6:22But what about R2 and R3? Are they in series? Yes, they're still connected in a chain, but more importantly, look, the same current will always flow through them because there are no alternate paths in between. And therefore R2 and R3 are still in series. All right, that's the story of series connection.

6:43Now, there's another way to connect these two resistors, somewhat like this, across the same points. This is called a parallel connection. Parallel connection is where resistors are connected across same points. Look, these two resistors are connected together with nothing in between, no components in between, and these two points are connected together with no components in between.

7:06They're connected across the same points, that is a parallel connection. Now let's close the switch. Just like before, a current runs in the circuit and you can clearly see, this time the current gets divided between these two. And that's why parallel connections are also called sometimes current dividers.

7:25So would the current through the resistors be the same? They not be because the current can be divided anyhow, so they can have different currents flowing through them. And again, to measure that current, we can attach ammeters. Look, there are two separate paths, and the two ammeter readings could be very different from each other.

7:42Again, just taking some numbers over here. The current can be different in parallel connection, but what about the voltage across them? Would that be the same or that would be different as well? Pause the video and think about this. Well, just like before, if I call this point to have zero potential, then look all these points along the wire should have zero potential including these two points.

8:06And then the potential at this point would be five volts and all of these points would be at five volts including these two. So you can clearly see, right in front of our eyes, the voltage across this resistor is exactly the same as across this resistor. So that's the defining feature of parallel connection.

8:23When two resistors, or any two circuit elements for that matter, are connected in parallel, they will always have the same voltage. It makes sense because they're directly connected across the same points, right? That's the defining feature of parallel connection.

8:35Again, we could have attached voltmeters and they would've confirmed that they indeed have the same voltage of five volts, but we don't need to do that. And just like before, I can draw the same circuit differently. This circuit looks different, but it's the same circuit.

8:49These two resistors are still in parallel. These two ends are connected directly. These two ends are connected directly. They're connected across each other, they're in parallel. They have the same voltage across them. But what if I had some resistor in between like this?

9:05Now look, these two ends are no longer directly connected. There is an element in between. So they're not connected across the same points anymore. They're not in parallel. These two points need not be at the same potential now. Therefore, the voltage across them could be different.

9:22But what if I had another resistor connected this way? This alternate path does matter for the current purposes, but it doesn't change the fact that these two points are still connected directly. So they have the same potential and these two points have the same potential so they have the same voltage across them.

9:41They're still in parallel. Beautiful, right? And I could have also drawn this same circuit this way. Again, looks quite different from this one or this one. But notice, these two ends are connected directly with no circuit elements in between. These two ends are connected directly with no circuit elements in between.

10:01They are the same potentials and therefore the same voltage. They're in parallel. What about these two? Well, these two ends, look, are they connected directly? Yes, they are. What about these two ends? Are they connected directly? Oh no, there's a battery in between.

10:18So they are not directly connected. They may not have the same potential, therefore, they're not in parallel. In fact, if you look carefully, this resistor is connected in a single chain with this resistor. Look, all the current from here would flow through this resistor, meaning these two resistors are in series, so they look like they're in parallel, but they're not.

10:45So we have to be very careful, looks can be deceiving. For parallel connection, always check if both the ends are connected across the same points. Over here, they're not. Let's bring back our earlier circuit. Can you pause the video and see whether any two resistors are in parallel?

11:04Pause and try. All right, what about R1 and R3? Let's look at their ends. Hey, they're not directly connected. There's a battery in between, they're not in parallel. What about R1 and R2? These two ends are directly connected. Okay, but what about these two ends?

11:20Hey, they're not directly connected. No, they're not in parallel. Hey, what about R1 and R4? These two ends are connected directly. No circular elements in between. And these two ends are directly connected. So they are connected across the same points. They are in parallel.

11:36The voltage across them will always be the same. And R2 and R3, look, they are connected in series. So in this circuit, we have a combination of series and parallel connection. And look at how far we've come. We started with a circuit with just one resistor and now we are analyzing combinations of series and parallel connections, which is awesome, right?

11:57But guess what? We can have even more fun by adding more switches. What happens if I close this switch, but I keep both these switches off? Well notice no current runs in this circuit. Because these two are no longer connected over here, this has become an open circuit.

12:18Okay, what if I close this switch, but I still keep this open? Well, now notice a current only runs in this part of the circuit. There's still no current over here. And now if you look carefully, notice that all the three are connected in a single chain, the same current flows through them.

12:39So R3, R4 and R2 are now in series. You might say, hey, there is this alternate path over here, but that's not connected. So by keeping this switch open, I have made these three in series with each other. Okay, the last thing we can do with this circuit to have more fun is we can add short circuits.

13:00What if I directly connect a wire from here to here? Now whatever current enters over here, almost all the current flows here because there is no resistance over here, right? And so now I have short circuited this point. And so now this, there's no current flowing through this resistor, so it's effectively not there.

13:21So if this was, for example, a light bulb, if I short circuit it, then no current flows through the bulb. And since the resistor, R4 is also connected in parallel with R1, no current flows through it as well. But as we saw earlier, short circuiting can be very dangerous.

13:38So please never ever attempt to do that at your homes. Anyways, similarly, I can short circuit this two points over here and no current flows through R2 now. So putting it all together. When resistors are connected in a single chain like this we call them the series connection and the defining feature is that the same current flows through them.

14:01And when resistors are connected this way across the same points, that's called a parallel connection. And the defining feature is that the same voltage appears across them.