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### Course: AP®︎/College Physics 2>Unit 3

Lesson 2: Compound circuits

# 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??
• 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
• 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?
• 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:

Regards,

APD
• 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 :)
• 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
• Has the idea of the total voltage of the resistor components equalling the voltage of the battery been taught in an earlier module?
• 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.
• 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.
• at onwards, how can wires just be 'zero-current'? Won't current flow through any conductive wire it finds?
• 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.
• 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
• 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).
• at why is the current same everywhere
• 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.
• is the total potential drop across a series configuration of resistors is equal to the sum of the potential drops across each resistor?