Parallel and Series Capacitors?

In summary, in the figure below, a potential difference V = 150 V is applied across a capacitor arrangement with capacitances C1 = 12.0µF, C2 = 6.00µF, and C3 = 16.0µF. Find the following values. C1 = 12.0µF, C2 = 6.00µF, C3 = 16.0µF
  • #1
ilovephysics16
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0
Moved from a technical forum, so homework template missing
In the figure below, a potential difference V = 150 V is applied across a capacitor arrangement with capacitances C1 = 12.0µF, C2 = 6.00µF, and C3 = 16.0µF. Find the following values.

Here's the diagram: http://www.webassign.net/hrw/hrw7_25-28.gif
upload_2016-3-15_13-38-10.png

I already solved this problem but I'm having some trouble understanding the concept behind it. I know that capacitors 1 and 2 are in parallel and that they are in series with capacitor 3, but I don't understand why. Especially because capacitors 1 and 2 aren't parallel in the way I'm used to seeing parallel capacitors, like this: http://www.rapidtables.com/electric/capacitor/parallel capacitors circuit.GIF.
upload_2016-3-15_13-38-47.png

Also, if you combine 1 and 2 in parallel, what does the resulting capacitor even look like? I'm having trouble visualizing this. Can anyone help me understand this problem? I would really appreciate it.
 
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  • #2
In your first diagram, mentally "slide" C2 along its wire to the right and down onto the vertical section at the right side. That makes C1 and C2 look more like the "standard" parallel capacitor diagram. Then "bend" the wires and slide the wire junctions around a bit, without moving them through any capacitors or breaking any connections. You should be able to make it look like a "standard" series + parallel combination.

None of the manipulations above affect the equivalent capacitance of the circuit, nor do they affect the equivalent resistance in similar problems involving resistors, because they don't change the topology of the circuit. Just don't break any wires or move any components through a junction, or a junction through a component.
 
  • #3
Got it. Thanks!
 
  • #4
I got a bit interested in capacitor networks because of the problems people were bringing here. Yes they often have problems through picturing them over-rigidly, the diagrams are abstract, topological, you can freely change them in a rubber sheet geometry way, i.e. with the limitations that jtbell has explained.

I think also many students end up with a purely formulaic rather than physical vision of these things based on remembering the series and parallel laws or formulae. I'm sure I did. Instead it is healthy to have some physics of it all in mind. For instance in your case the total charge on a C1 and C2 is the sum of the two charges. Because they are connected on both sides the potential across them is the same for both. So as capacitance is defined as ratio of charge to potential, sum divided by same thing, the total capacitance of 1 and 2 is the sum of the individual ones - general law for parallel capacitances.

Instead when capacitors are in series, (you have C3 in series with the effective capacitance C1 + C2) there is no adding up of charges, the charges on each capacitor is the same. Because the charge on each plate is equal in magnitude (though opposite in sign) to the plate facing it. What does add up is the potential across them of course. So same as before but the other way round, potential adds, charge same for each, this is a bit more difficult to see but V = Q/C, so for a series of potentials what adds up is not the charge - the only one that counts is one on an external plate,- but the 1/C 's. So the 1/C 's and up for capacitors in series the same way that 1/R 's add up for resistors in parallel.

Also I've found useful in solving more complicated problems to note that the conductively isolated part of the circuit has total charge 0 - that is, when charges are added algebraically, taking account of their signs. For example with two capacitors in series the isolated 'internal' plates have equal opposite charges, summing algebraically to 0. The total charge on the three connected isolated plates of your circuit is also algebraically 0. see Exercise with Capacitors
 
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FAQ: Parallel and Series Capacitors?

1. What is the difference between parallel and series capacitors?

Parallel capacitors are connected in such a way that the positive terminal of one capacitor is connected to the positive terminal of another capacitor, and the negative terminal of one capacitor is connected to the negative terminal of another capacitor. Series capacitors, on the other hand, are connected in a chain where the positive terminal of one capacitor is connected to the negative terminal of another capacitor.

2. How do the capacitance and voltage change in parallel and series capacitors?

In parallel capacitors, the overall capacitance is increased as the individual capacitances are added together. However, the voltage across each capacitor remains the same. In series capacitors, the overall capacitance is decreased as the individual capacitances are added together, but the voltage across each capacitor increases.

3. Can parallel and series capacitors have different values or types?

Yes, parallel and series capacitors can have different values and types. In parallel, capacitors with different capacitance values can be connected together, while in series, capacitors with the same capacitance values but different types (e.g. ceramic, electrolytic) can be connected together.

4. How do parallel and series capacitors affect the total capacitance in a circuit?

In parallel, the total capacitance is the sum of the individual capacitances. In series, the total capacitance is equal to the inverse of the sum of the inverses of the individual capacitances. For example, if two 10μF capacitors are connected in parallel, the total capacitance would be 20μF. If the same two capacitors are connected in series, the total capacitance would be 5μF.

5. What are some practical applications of parallel and series capacitors?

Parallel capacitors can be used to increase the overall capacitance in a circuit, which is useful in power factor correction, filtering, and energy storage. Series capacitors can be used for tuning, filtering, and coupling in electronic circuits. They can also be used to create voltage dividers in high voltage circuits.

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