Capacitor Network - Series or Parallel?

In summary: Therefore, (1 S 3) P (2 S 4) is not valid.In summary, the textbook solution states that 1 & 2 are in parallel and so is 3 & 4, with those two pairs being in series. However, the thinking that points A & B are of the same potential, as are C & D and E & F, leads to the incorrect conclusion that 1 and 3, as well as 2 and 4, are in series. This is due to the fact that there is no guarantee of the same current flow between these pairs, making the proposed combination of (1 S 3) P (2 S 4) invalid.
  • #1
Shreya
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Homework Statement
Find the equivalent capacitance.
Relevant Equations
Series & Parallel Capacitor formulae
My textbook solution states that 1 & 2 are in parallel and so is 3 & 4 and those 2 are in series. That is, (1 P 2) S (3 P 4). My thinking is such: points A & B are of same potential, say V, C & D are of same potential, say x and E & F are are of same potential, say 0. So I can say that 1 and 3 are in series and so is 2 &4. Therefore, I can say (1 S 3) P (2 S 4). I'm sure there is a flaw in my method. Please be kind to point it out.
 

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  • #2
Shreya said:
Homework Statement:: Find the equivalent capacitance.
Relevant Equations:: Series & Parallel Capacitor formulae

My textbook solution states that 1 & 2 are in parallel and so is 3 & 4 and those 2 are in series. That is, (1 P 2) S (3 P 4). My thinking is such: points A & B are of same potential, say V, C & D are of same potential, say x and E & F are are of same potential, say 0. So I can say that 1 and 3 are in series and so is 2 &4. Therefore, I can say (1 S 3) P (2 S 4). I'm sure there is a flaw in my method. Please be kind to point it out.
C and D are only guaranteed to be at the same potential because there is a wire connecting them.

If you had (1 S 3) P (2 S 4) then there would be no wire connecting the middle nodes in the two series chains and there would be no guarantee that the two middle nodes would be at the same potential.

If you had such a guarantee (say because the two series chains had capacitors with identical ratios of capacitance) then the two middle nodes would be at the same potential and the circuit would behave identically to the series chain of two parallel pieces (1 P 2) S (3 P 4).

It might be helpful to re-draw the circuit to eliminate the redundant nodes B, D and F (if two nodes are connected by a wire, there is only one node). Then the true nature of the circuit becomes more obvious.
 
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  • #3
That makes sense @jbriggs444 . But I don't see why 1 P 2 would be in series with 3 P 4 though
 
  • #4
Shreya said:
That makes sense @jbriggs444 . But I don't see why 1 P 2 would be in series with 3 P 4 though
There is no resistance between A and B, C and D, or E and F. You can combine each pair into a single node. The nature of the circuit will become clear when you do this.
 
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  • #5
Shreya said:
That makes sense @jbriggs444 . But I don't see why 1 P 2 would be in series with 3 P 4 though
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Last edited:
  • #7
Shreya said:
Homework Statement:: Find the equivalent capacitance.
Relevant Equations:: Series & Parallel Capacitor formulae

So I can say that 1 and 3 are in series and so is 2 &4. Therefore, I can say (1 S 3) P (2 S 4). I'm sure there is a flaw in my method. Please be kind to point it out
Two components are in series only if they carry the same current at any time.
That is not the case with 1 and 3 (or 2 and 4).
 
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1. What is a capacitor network?

A capacitor network is a collection of interconnected capacitors that are used to store and release electrical energy. It can be either a series or parallel configuration, depending on how the capacitors are connected.

2. What is the difference between a series and parallel capacitor network?

In a series capacitor network, the capacitors are connected end-to-end, with the positive terminal of one capacitor connected to the negative terminal of the next capacitor. In a parallel capacitor network, the capacitors are connected side-by-side, with all the positive terminals connected together and all the negative terminals connected together.

3. Which configuration is better for a capacitor network: series or parallel?

The better configuration depends on the specific application and desired outcome. In general, a series capacitor network is better for storing large amounts of energy, while a parallel capacitor network is better for providing a quick burst of energy.

4. What are the advantages of using a series capacitor network?

Series capacitor networks have a higher total capacitance, meaning they can store more energy. They also have a higher voltage rating, making them suitable for high voltage applications. Additionally, they have a lower equivalent series resistance (ESR), resulting in less energy loss and better efficiency.

5. What are the advantages of using a parallel capacitor network?

Parallel capacitor networks have a lower total capacitance, but they can provide a higher current output. They also have a lower equivalent series inductance (ESL), allowing for faster charging and discharging. Additionally, they can handle higher ripple currents, making them suitable for applications that require a steady power supply.

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