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Capacitors & Capacitance | 9 mins | 0 completed | Learn |

Parallel Plate Capacitors | 15 mins | 0 completed | Learn Summary |

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Capacitance Using Calculus | 8 mins | 0 completed | Learn |

Combining Capacitors in Series & Parallel | 14 mins | 0 completed | Learn |

Solving Capacitor Circuits | 28 mins | 0 completed | Learn |

Intro To Dielectrics | 15 mins | 0 completed | Learn Summary |

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Concept #1: Combining Capacitors in Series & Parallel

**Transcript**

Hey guys. In a previous video, we addressed, what a single capacitor connected to a single battery circuit looked like. Now, for the next couple videos we're going to move on to what circuits look like that have multiple capacitors, okay? So, in this particular video, we're going to tackle probably what would be considered the first half of that problem, which is how to identify different connections between these capacitors, okay? And how to combine them into what's known as an equivalent capacitor, let's get started.

In circuit problems, meaning problems with multiple capacitors because we already looked at problems with single capacitors and those are very easy in circuit problems we need to collapse or combine capacitors into a single equivalent capacitor, what this means is, that even those you could have a random array of capacitors connected to a battery, that battery would effectively see a single equivalent capacitor, alright? that's the idea behind this concept of equivalent capacitance, it's just the capacitance that all these random capacitors are equivalent to, is what it represents, okay? We have two different types of connections between capacitors when we're talking about multiple capacitors, we have a series connection, which is a direct connection between two capacitors. So, that's a direct connection, we could also have a third capacitor and a fourth capacitor etc, etc, okay? This is absolutely equivalent to a single capacitor, the question is, what is its capacitance? Well, if this is C1 and this is C2, this is C3, this is going to have some equivalent capacitance and we want to know what that is, well, it turns out that not the equivalent capacitance but one over the equivalent capacitance equals 1 over C1 plus 1 over C2 plus 1 over C3 etc, because you could have as many capacitors in series as you want as long as they're all directly connected to one, one after the other, okay? And those would be exactly equivalent to a single capacitor that had this equivalent capacitance, the second type of connection is a parallel connection, what a parallel connection is, is it's formed by two capacitors that are on opposite branches of a loop, alone, okay? What I mean is, imagine that some sort of loop and on opposite sides you had capacitors that were there alone, okay? That is an example of a parallel connection, you can however have multiple capacitors in parallel, you would just have to have multiple loops, okay? For instance, if I added another one down here, this would still be in parallel, okay? Because, this is one loop right here, where you have two capacitors that are alone and this is another loop right here where you have two capacitors that are alone. So, basically, if the first ones in parallel, the second one and the second ones in parallel the third, the first has to also be in parallel with the third, okay? We'll call this C1, C2, C3, this is absolutely equivalent to a single capacitor with some capacitance C equivalent, the question is, what is that equivalent capacitance? Well, it's just the sum of the individual capacitances. So, for capacitors in parallel the reciprocal is the sum of the reciprocals for capacitive, sorry, for capacitors in series it's the sum of the reciprocals, for capacitors in parallel it's just the sum, okay? Now, we want to do two examples to illustrate how to do this process. This is extremely important because as you're going to see in the next video, this is the first half to solving these complicated circuit problems with multiple capacitors, okay? So, imagine. So, this question is, what is the equivalent capacitance of the following capacitors? Imagine that this was connected to a battery like so, you don't need to write this down, this is just for your benefit, then the battery would effectively see only one capacitor so with the equivalent capacitance, that's what we're getting at here, okay? Now, what we need to do is we need to identify which capacitors are in either series or parallel connections, something that I didn't address, that's important to recognize, is that capacitors can also be neither series nor parallel, you don't want to do that, which capacitors do you think are in either series or parallel connections, if you look at this above figure, okay? The two, two farad capacitors are in parallel and the 1 and 4 farad capacitor are also in parallel, but there is no connection between any of the other ones, okay? Those four connections right there, those are neither series nor parallel, the 2 and the 2 are in parallel, to 1 of the 4 are in parallel, so this is absolutely equivalent to this, the question is, what's the capacitance of both of those? Since they're in parallel you just sum them, so the equivalent capacitance of this is the sum, right? 2 plus 2 is 4 and the equivalent capacitance of this is the sum, 1 plus 4 is 5. So, we have a 4 farad capacitor and a 5 farad capacitor. Now, both of those are in series, right? There's a direct connection between them so this is absolutely equivalent to a single capacitor, the question is, what's its capacitance? Since they're in series we need to do the reciprocals. So, 1 over C equivalent is going to be 1 over 4 plus 1 over 5, the least common denominator is going to be 20, so this is 5 over 20 plus 4 over 20 which is 9 over 20 and now we have to take the reciprocal of this. So, C equivalence is going to be 20 over 9 which is about 2.2 farads, so the equivalent capacitor is a 2.2 farad capacitor and if you connected a battery to this arrangement here, it would see a single 2.2 farad capacitor, okay?

Let's do the last example. What is the equivalent capacitance of the following capacitors? So, once again, we want to look for series or parallel connections, this is a loop. So, your first instinct might be to see parallel connections, the problem is that part of being parallel is you have to be alone on the opposite branches of the parallel. there are two here and two here. So, they're clearly not alone, but the two upper capacitors are in series and the two lower capacitors are in series. So, we didn't combine those first, right? As long as we can identify series and parallel connections we're good, so this is absolutely equivalent to a single capacitor on top and a single capacitor on the bottom. Now, there's a little shortcut equation that you guys might find useful, this only applies for two capacitors, okay? Only for two, you can say that the equivalent capacitance is C1 and C2 over the sum, a little bit of technical difficulty there, that was weird, C1 plus C2, okay? This only works for two, please do not try to extend this equation for three or for four because you'll most likely get the wrong answer, if it's more than two just use the reciprocal equation, okay? So, the upper capacitance is going to be 1 times 3 over the sum of 1 plus 3 which is 4, so this is 3 over 4, which is 0.75 farad, the lower capacitance is going to be 4 times 2 over the sum of 4 and 2, which is 6, so this is going to be 8 over 6 which is like 4/3, 1.3 about, okay? So, we have the upper one, is 0.75 farads, the lower one is 1.3 farads. Now, these two have what connection? They have a parallel connection, so this is absolutely equivalent to a single equivalent capacitor where the equivalent capacitance is the sum of the two capacitances since they were in parallel, so this is 0.75 plus 1.3, which is 2.05 farads, okay? So, the equivalent capacitance is about 2. Alright, that wraps up our discussion on the connections between capacitors in series in parallel, thanks for watching guys.

Example #1: Find Equivalent Capacitance #1

**Transcript**

Hey guys. Let's do an example. What is the equivalent capacitance of the following combination of capacitors, right? Whenever you're given an arbitrary arrangement of capacitors you always want to go after the loops first, okay? So, we have this loop right here, which we want to sort of attack first, the problem is that we can't say that the capacitors are in parallel because we have two capacitors on the upper part of the loop. So, we can combine those first, those two are in series, so this is going to absolutely be equivalent to a single capacitor up there and a single capacitor below connected to our 5 farad capacitor.

So, we didn't change the 5 farad, we didn't change the 3 farads, we just combined the two 2 farad capacitors and the question is, what is that capacitance? Well, the equivalent capacitance is going to be C1, C2 over C1 plus C2, which is going to be 2 times 2 over the sum which is 4, and that's going to be one farad, okay? So, that's one farad. Now, we can address the loop because now it's two capacitors in parallel, whenever two capacitors are in parallel we just sum their capacitances. So, 1 plus 3 is 4 farads and lastly we'll combine this into a single equivalent capacitance and we'll use the same shortcut equation, where we'll say C equivalent is 4 times 5 over 4 plus 5, which is 9, this is 20 over 9, which is about 2.2 farads, okay? That's it guys, thanks for watching,

Practice: What is the equivalent capacitance of the following capacitors?

0 of 3 completed

Concept #1: Combining Capacitors in Series & Parallel

Example #1: Find Equivalent Capacitance #1

Practice #1: Find Equivalent Capacitance #2

What is the equivalent capacitance of the five capacitors? All capacitors are identical and have capacitance of C = 40 nF.
a. 15 nF
b. 24 nF
c. 25 nF
d. 64 nF
e. 200 nF

Consider the group of capacitors shown in the figure. Find the equivalent capacitance Cad between points a and d.
1. Cad = 4 C
2. Cad = 2/5 C
3. Cad = 3/5 C
4. Cad = 2 C
5. Cad = 3/4 C
6. Cad = 1/3 C
7. Cad = 5 C
8. Cad = 1/2 C
9. Cad = 3 C
10. Cad = 2/3 C

Consider the circuit of capacitors shown below. The equivalent capacitance of the circuit is 9.0 μF.
Determine the value of the capacitance C.

Consider the capacitor network. Find the equivalent capacitance for the combination shown.

What is the equivalent capacitance of the combination shown?
(a) 30 μF
(b) 10 μF
(c) 40 μF
(d) 25 μF

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