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### Course: Electrical engineering > Unit 2

Lesson 2: Resistor circuits- Series resistors
- Series resistors
- Parallel resistors (derivation)
- Parallel resistors (derivation continued)
- Parallel resistors
- Parallel resistors
- Parallel conductance
- Series and parallel resistors
- Simplifying resistor networks
- Simplifying resistor networks
- Delta-Wye resistor networks
- Voltage divider
- Voltage divider
- Analyzing a resistor circuit with two batteries

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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.

## Want to join the conversation?

- 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??(8 votes)
- 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(55 votes)

- 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)
- Hello MysteriousCharacter,

They are two different things. A voltage source is a mathematical construct - something imaginary that helps us model our circuits. A battery on the other hand is real BUT it can be modeled as a DC source and a resistor.

I made a few videos on this topic see:

https://www.youtube.com/watch?v=cYGHibYmzb0

https://www.youtube.com/watch?v=rWYgoL-wzNE

Regards,

APD(8 votes)

- 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)
- Hello Dgdosen,

Correct, the battery is an active component.

It may help to visualize the voltage measurement of the circuit at10:15. 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)

- 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)
- Hello Mike,

You are describing Kirchhoff's Voltage Law (KVL). It is included here on Khan Academy as:

https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-dc-circuit-analysis/v/ee-kirchhoffs-voltage-law

See also:

https://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws

Regards,

APD(6 votes)

- 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)
- 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)

- at11:20onwards, how can wires just be 'zero-current'? Won't current flow through any conductive wire it finds?(2 votes)
- Current only flows if there is a complete path back to the power source (a complete "circuit"). So you can have a conductive wire, but if it is not part of a path back to the battery it won't have any current in it.

Imagine those two horizontal wire stubs are just stubs going nowhere. The current in them is 0.(6 votes)

- 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)
- 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).(6 votes)

- at3:40why is the current same everywhere(2 votes)
- 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)

- is the total potential drop across a series configuration of resistors is equal to the sum of the potential drops across each resistor?(2 votes)
- Yes. That is exactly right. When you do a problem with series resistors it is a good final check of your answer if you confirm this. Find the voltages across individual resistors, add them up, confirm the total is the voltage across the ends of the series chain.(4 votes)

- what are the advantages of connecting electrical devices in parallel with the battery instead of connecting them in series?(2 votes)
- There are no advantages of parallel over series connection. It's just two possible ways to connect circuit elements.

A very simple example of how to chose... Suppose you are building a circuit and you need a certain value resistor, say 500 ohms. What if you don't have that value resistor in your stock, and you don't have time to order from Digikey? If you have two 250 ohm resistors you could connect them in series to get what you want. If you have two 1000 ohm resistors you could connect them in parallel to achieve your goal.(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.