Resistors in series are successive resistors in which the same current cannot simply go through one resistor. We can add resistors, but it increases the resistance of the whole network. If one resistor goes out, all of the resistors go out. To add currents and determine the resistor series, we add resistor 1 + resistor 2 + resistor 3, etc.
Alright so let's talk about resistor combinations in series. Well first what does series mean? series means no choice, the current does not have a choice it goes through one of the resistors it got to go through the next one that's what I mean when I say series. So a series combination will look like this, you've got 1 resistor then the other one right there in series so that the current if it's going to go through r1 got to go through r2. Alright the current has to be the same, whenever I have any number of resistors connected in series all of them have the same current. Alright so what does that mean? Well what we're going to try to do is we're going to try to find an effective resistance that plays the role of this whole network both of these guys together. And we're going to say alright instead of writing 2 separate resistors I want to write just 1 and I want to know what should that resistance be in order that the potential difference across this combination is the same as the potential difference across this effective resistor.
Alright so what is the potential difference here? Well it's going to be the potential difference across r1 plus the potential difference across r2. Ohms law tells us that, that minus ir1 minus ir2 so that's across the series network. But what about across the effective resistor, well it's just going to be minus ir series so then all we need to do is say I want the potential differences to be the same. So minus ir1 minus ir2 needs to equal minus ir series. We'll cancel out all the minus i's and we get r series is just r1 plus r2 so to add resistors and series is the easiest thing there can possible be you just add the 2 resistances. Alright so if I've got a 2 amp current flowing through a 3 ohm resistor connected in series to a 4 ohm that's the same thing as a 2 amp current going through an effective combination of 7 ohms. So the potential difference is negative 14 volts ir.
Alright the important thing to remember about series is that whenever you add resistors in series it increases the resistance of the whole network. One way to think about series combinations is like Christmas lights, if one goes out they all go out because if one goes out then that means that the current going through that guy is 0. But current has to be the same in series so that means all of the currents go to 0. You've got just kind of this open circuit that's not working. So anyway that's connections of resistance in series.