Capacitor Network - Series or Parallel?

Click For Summary
SUMMARY

The discussion centers on the configuration of capacitors in a circuit, specifically whether capacitors 1 and 2 are in parallel and capacitors 3 and 4 are also in parallel, leading to a series connection between the two groups. The correct interpretation is that capacitors 1 and 2 are indeed in parallel, as are capacitors 3 and 4, resulting in the overall configuration being (1 P 2) S (3 P 4). Misunderstandings arise when assuming that capacitors 1 and 3 or 2 and 4 are in series without a direct connection ensuring equal potential between nodes. The flaw in the original reasoning is clarified by emphasizing that series components must carry the same current, which is not the case here.

PREREQUISITES
  • Understanding of capacitor configurations: series and parallel
  • Familiarity with circuit theory concepts, including node potential
  • Knowledge of equivalent capacitance calculations
  • Ability to interpret circuit diagrams accurately
NEXT STEPS
  • Study the principles of series and parallel capacitor combinations
  • Learn how to calculate equivalent capacitance for complex circuits
  • Explore circuit simplification techniques, including node reduction
  • Review electrical circuit analysis methods to ensure accurate interpretations
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing or designing capacitor networks will benefit from this discussion.

Shreya
Messages
187
Reaction score
64
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.
 

Attachments

  • Screenshot from 2022-10-12 19-54-51.png
    Screenshot from 2022-10-12 19-54-51.png
    9.7 KB · Views: 149
Physics news on Phys.org
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.
 
  • Like
Likes   Reactions: Shreya
That makes sense @jbriggs444 . But I don't see why 1 P 2 would be in series with 3 P 4 though
 
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.
 
  • Like
Likes   Reactions: Shreya and jbriggs444
Shreya said:
That makes sense @jbriggs444 . But I don't see why 1 P 2 would be in series with 3 P 4 though
1665588294859.png
 
  • Like
Likes   Reactions: Shreya and erobz
Last edited:
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).
 
  • Like
Likes   Reactions: Shreya

Similar threads

  • · Replies 14 ·
Replies
14
Views
1K
Replies
10
Views
1K
Replies
20
Views
2K
Replies
5
Views
774
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
835
  • · Replies 14 ·
Replies
14
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
4
Views
2K