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Series resistors

Resistors connected head-to-tail are in series. The equivalent overall resistance is the sum of the individual resistance values. Created by Willy McAllister.

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  • blobby green style avatar for user EricBNYC
    But didn't we just agree in the previous tutorials that electrons, and current, flow FROM the negative to the positive? Why did this video demonstrate current flowing FROM positive TO negative??
    (3 votes)
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    • purple pi purple style avatar for user APDahlen
      Hi Eric,

      Not exactly. By convention we say that current flows from positive to negative as shown in this video. At the same time we acknowledge that the electrons are the things that flow. The electrons flow from negative to positive.

      This is an unfortunate situation. Regrettable, this is one of the first roadblock in electronics. My suggestion is follow the convention – flow of current is from positive to negative.

      Regards,

      APD
      (47 votes)
  • leafers seed style avatar for user TeslaEE
    Hang on a second: Isn't the battery symbol actually just a symbol for a voltage source? I searched it online, and a lot of people say that it's a voltage source. Can someone explain this?
    (5 votes)
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  • leaf green style avatar for user dgdosen
    On the diagram - the passive components (resistors) have the +/- lined/chained together. Then why isn't the +/- on the battery running in that same direction? Is it because the battery isn't a passive component? It's the one thing I leave this video, and the one question I had from the last section of videos. I think the videos would be more effective if you mentioned and reconciled that :)
    (6 votes)
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    • purple pi purple style avatar for user APDahlen
      Hello Dgdosen,

      Correct, the battery is an active component.

      It may help to visualize the voltage measurement of the circuit at . Recall that a voltmeter is connected to two points in the circuit. We say that a voltmeter measures the potential difference between two points.

      For any component in this circuit the voltmeter would register a positive voltage when the “red” wire is connected to a “+” and the “black” wire is connected to a “-”

      Regards,

      APD
      (4 votes)
  • male robot johnny style avatar for user Mike Musarra
    Has the idea of the total voltage of the resistor components equalling the voltage of the battery been taught in an earlier module?
    (5 votes)
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  • hopper jumping style avatar for user Sam D
    But if both the voltage and the resistance is different for all the three resistors then how can the current be same in all three? I understand that charge can't pile up because of conservation of charge but I'm confused here.
    (2 votes)
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    • spunky sam orange style avatar for user Willy McAllister
      You rightly suspect that the current is the same in all three resistors (because charge doesn't pile up). You also know about Ohm's Law, which says v = iR, or solving for current: i = v/R.

      So what do the three different resistors "do" to make their currents all the same? What they "do" is adjust their voltage until v/R is the same for all three. That is the only condition that equalizes the current through all three resistors.

      This is a good example of how a collection of resistors team up when they are formed into a circuit. Each resistor brings its own version of Ohm's Law (depending on the resistor's value). When they get joined together in a circuit, it seems like they team up to solve their equations together. That's exactly what happens.
      (9 votes)
  • mr pink red style avatar for user jerdaouihicham8
    since the electrical current is the amount of charge that passes through a point per unit time,so increasing the resistance will decrease the voltage and these charges are going to spend more time passing through a point (because they have now less potential energy) so the current will change,but that's not the case here! you say that the current remains the same
    (2 votes)
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    • spunky sam orange style avatar for user Willy McAllister
      Be careful, we don't talk about the speed of current, we talk about amount of current. Current is amount of charge per second past a point. It is a "flow rate", not a measure of speed. If Speed was involved we would have units of meters per second. But meters/sec is not involved in quantitating current. Seems like it should be, but it's not. This is a really common bump beginners have to get over.

      In a series circuit the electrons come out of the negative battery terminal all jazzed up with V_bat volts (electric potential difference). By the time they reach the + terminal of the battery their voltage is zero. All that potential energy has been surrendered to the resistors in the series circuit.

      Suppose the battery is 9V and there are 3 resistors in series, all the same value, R. The battery voltage will be split evenly across the R's, each one experiencing 1/3 of the supplied voltage, or 3 volts each. The top resistor's top terminal is at 9V; its bottom terminal is at 6V (3 volt difference). Ohm's Law says the current in the top resistor is I = 3/R.

      The bottom resistor has 3V on its top terminal and 0 volts on its bottom terminal. Ohm's Law works out the same, I = 3/R. You can work out the resistor in the middle, and get the same I.

      One way to think about this is to imagine water flowing in a garden hose. One end is connected to a faucet on the wall. One end is open and laying on the ground. If you know the flow rate at the faucet is 10 gallons per minute, you would expect the flow rate at the open end to also be 10 gallons per minute. Why is that? Well imagine what would happen if it wasn't true. If the flow rate at the open end was 9 gallons/min where did the other 1 gallon/min go? Did it leak out of the hose? Did it vanish into an invisible hidey hole in the hose? No! All the water that comes into the hose has to go out the far end of the hose, and it has to do it at the same flow rate (same amperage).
      (7 votes)
  • leaf green style avatar for user Ayman
    at why is the current same everywhere
    (2 votes)
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    • spunky sam orange style avatar for user Willy McAllister
      You can answer this by thinking about the opposite question. What if the current was different in different parts of the circuit?

      If that was the case, that means that moving charge in one part of the circuit is not flowing in another part. That means the charge has to find some place to hide and pile up in a corner of the circuit somewhere. If that happened you would end up with a big concentration of electrons. Those electrons repel each other and will refuse to hang out together. You get either a big boom, or those electrons find a way to flow through the rest of the circuit.

      A good analogy: Connect together garden hoses with different diameters, all in series. Turn on the water. All the water that comes out of the faucet eventually comes out of the last hose. It has to, there's no place else for it to go (assuming there are no leaks). If you measure the current in every section of the hose, fat or thin, the flow rate will be the same, the same value for gallons or liters per second in every section of the hose.
      (6 votes)
  • blobby green style avatar for user Anushka Jha
    When charges flow through a resistor the energy gained by the charges decreases i.e the Potential difference decreases therefore by ohm's law (i.e V directly proportional to the current flowing in the circuit)the rate of flow of charges i.e current would also decrease,then how can be the current same even after coming out of the resistor?
    (2 votes)
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    • spunky sam orange style avatar for user Willy McAllister
      Yes, V is directly proportional to current in Ohm's Law, V = R i. That means if the voltage goes down then the current goes down, too. BUT! that is true only if R is constant. As charge flows through a resistor the remaining resistance gets smaller.

      Picture a big R made of a series of six little rrrrrr's. Apply a voltage V across R. Ohm's Law says the current is i = V/R = V/6r.

      After a charge passes the first little r there are five r's left. The charge has given up 1/6 of its potential energy (its voltage) so it has a voltage of 5V/6.

      If you apply a voltage of 5V/6 to 5/6ths of R you get i = 5V/6 / 5R/6 = V/R. The current after passing one little r is the same as at the beginning. And so forth all the way to the end of the resistor.
      (4 votes)
  • female robot grace style avatar for user sirona1010
    please tell me. what's the different from a series has R1 = 100ohms, R2 = 50ohms, R3= 150ohms vs Rs=300 ohms. why don't we use Rs instead of R1, R2 and R3? The current is the same but the Voltages are different. When the Voltage goes through the R1, R2 and R3 it will have V1 = 0.5V, V2 = 0.25V and V3 = 0.75V is there any effect, any useful or helpful from seperate the resistors?
    (1 vote)
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    • spunky sam orange style avatar for user Willy McAllister
      The circuit with three resistors in series isn't particularly useful, but it does demonstrate how series resistors work. A real-world example when knowing about series resistors can get you out of a bind is if you want to achieve a certain resistance value but you don't own that exact resistor. You can get the value you want by combining resistors in series. Another example is if the resistance you want falls between the standard values you can buy. If you need 400 ohms (not a standard value for 5% resistors), you can get it by combining 300 ohms plus 100 ohms in series (both standard values).
      (5 votes)
  • blobby green style avatar for user sa9504793957
    How can you say that the same amount of charges flow through all three resistors?.. If there is higher resistance then there must be lower charge passing through and vice versa and so other resistor after it will get lower charge.. Please help me.
    (1 vote)
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    • duskpin ultimate style avatar for user Katya
      Charge never changes since the current has no where to go except the next resistor. The resistor can't keep some of that charge in it to change the amount of flow going out, meaning the same amount of charge HAS to keep flowing regardless of how many different resistors it has.

      The short answer is charge can't leave a circuit or build up anywhere, so the total charge going out of anywhere (including a bunch or resistors) is always equal to the value it started at.
      (4 votes)

Video transcript

- [Voiceover] Now that we have our collection of components, our favorite batteries and resistors, we can start to assemble these into some circuits. And here's a circuit shown here. It has a battery and it has three resistors, and a configuration that's called a series resistor configuration. Series resistors is a familiar pattern, and what you're looking for is resistors that are connected head to tail, to head to tail. So these three resistors are in series because their succession of nodes are all connected, one after the other. So that's the pattern that tells you this is a series resistor connection. So we're gonna label these our resistors here. We'll call this R1, R2, and R3. And we'll label this as v. And the unknown in this is what is the current that's flowing here, that's what we want to know. We know v, we want to know i. Now one thing we know about i is i flows down into resistor R1, all of the current goes out of the other end of resistor R1 because it has to, it can't pile up inside there. All that goes into here, and all that comes out of R3. And i returns to the place it came from, which is the battery. So that's a characteristic of series resistors, is in a series configuration is they are head to tail, and that means that all the components, all the resistors share the same current. Current. That's the key thing. The thing that we don't know that's different between each resistors, is the voltage here, and the voltage here, let's call that v1, this is v2, plus, minus, and this is v3, plus, minus. So in general, if these resistors are different values because they have the same current going through them, Ohm's Law tells us these voltages will all be different. So the question I want to answer with series resistors is could I replace all three of these with a single resistor that cause the same current to flow? That's the question we have on the table right now. So we make some observations, we have Ohm's Law, our friend, Ohm's Law. And we know that means v equals i times R, for any resistor. That sets the ratio of voltage to current. And this is another thing we know about this, which is that v3, plus v2, plus v1, those are the voltages across each resistor, those three voltages have to add up to this voltage because of the way the wires are connected. So the main voltage from the battery equals v1, plus v2, plus v3. We know that's for sure, and now what we're gonna do is we're gonna write Ohm's Law for each of these individual resistors. v1 equals i, and i is the same for everybody, times R1. v2, this voltage here, equals i times R2. And v3 equals i times R3. Now you can see, if I had four, or five, or six resistors, I would have four, or five, or six equations just like this for each resistor that was in series. So now what I'm gonna do is substitute these voltages into here, and then we'll make an observation. So let's do that substitution. I can say v equals i, R1, plus i, R2, plus i, R3. And because it's the same i on every resistor, I can write v equals i, I'm gonna factor out the i. R1, plus R2, plus R3. Now what I want to do is take a moment here and compare this expression to this one here, the original Ohm's Law. Alright, there's Ohm's Law. So we have v equals i, some current, times some resistor. I can come up with a resistor value, a single resistor that would give me the same Ohm's Law. And that is gonna be called, let's draw it over here. Here's our battery. And I'm gonna say there's a resistor that I can draw here, R series, that's equivalent to the three resistors here. And it's equivalent in the sense that it makes i flow here, that's what we mean by equivalent. So in our case, to get the same current to flow there I would say v equals i times R series, in which case, what I've done is I've said that R series is what, is the sum of these three things, R1 plus R2, plus R3. This is how we think about series resistors. We can replace a set of series resistors with a single resistor that's equivalent to it if we add the resistors up. Let's just do a really fast example to see how this works. I'm gonna move this screen. Here's an example with three resistors. I have labeled them 100 ohms, 50 ohms, and 150 ohms. And what I want to know is the current here. And we'll put in a voltage, let's say it's 1.5 volts, just a single small battery. So what is the equivalent resistance here? One way to figure this out and to simplify the circuit is to replace all three of those resistors with a series resistor, RS, and that is, as we said here, is the sum, so it's 100, plus 50, plus 150. And that adds up to 300 ohms. So that's the value of the equivalent series resistor right here. And if I want to calculate the current, i, i equals v over R, and this case, it's R series, and that equals 1.5 divided by 300. And if I do my calculations right, that comes out to .005 amperes. Or an easier way to say it is five milliamps, milliamperes. So that's i. And now that I know i, I can go ahead and I can calculate the voltage at each point across each resistor because I know i, I know R, I can calculate v. So v1, v1, which is the voltage across that resistor, v1 equals i, R1, as we said before. So it's five milliamps times 100 ohms, 0.5 volts. Let's do it for the other one, v2, equals i, same i, this time times R2, five milliamps times 50 ohms, and that equals 0.25 volts. And finally, we do v3. This is plus, minus v3. And that equals the same current again times 150 ohms, which is equal to 0.75 volts. So we've solved the voltage and the current on every resistor, so this circuit is completely solved. And let's do one final check. Let's add this up. Five, five (mumbles) is zero. Carry the one, six, seven eight. 15, 1.5 volts, and that's very handy because that is the same as that. So indeed, the voltages across the resistors did add up to the full battery that was applied. There's one more thing I want to point out. Here's an example of some series resistors. And that's a familiar pattern. And you'll say, "Oh, those are series resistors." Now, be careful because if there's a wire here going off and there's, doing this, or there's a wire here, connected to this node here, this still looks like they're in series, but there might be current flowing in these branches here. If there's current flowing out anywhere along a series branch, anywhere along what looks like a series branch, then this i may or may not be the same as this i. And it might not be the same as this. So you gotta be careful here. If you see branches going off your series resistors, these are not in series unless these are zero current. If that's zero current, and if that is zero current, then you can consider these in series. So that's just something to be careful of when you are looking at a circuit and you see things that look like they're in series, but they have little branches coming off. So a little warning there. So that's our series resistors. If you have resistors and series, you add them up to get an equivalent resistance.