# Find the equivalent capacitance of the circuit

• Krushnaraj Pandya
In summary, C1 and C2 are in parallel and C4 is in series with C12. C2 and C3 are in series with C123. C234 is in series with C1.
Krushnaraj Pandya
Gold Member

## Homework Statement

Find equivalent capacitance between A and B of the given figure (pardon camera quality)

All related

## The Attempt at a Solution

marking junctions, From left to right, starting from original point A-and ending at B I wrote potential at them as follows. A-(A)-(x)-(A)-(B)-B. I labelled the capacitor out of line as C4, and moving from left to right, the ones in line as C1, C2 and C3.
I noticed C1 and C2 are connected across same potential difference and therefore are in parallel connection, I don't know where to place their equivalent capacitor though, I'd appreciate some help, thank you

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• WIN_20180807_19_47_26_Pro.jpg
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This is a standard circuit (whether with resistors or capacitors) that is used to see if you really understand how to redraw circuits (which is a VERY necessary skill if you are going to learn circuit analysis).

So far, in saying "I noticed C1 and C2 are connected across same potential difference and therefore are in parallel connection", you only have it part right. Keep going.

EDIT: OOPS. I looked at this too quickly. It has one more component than I am used to. Have to relook.

OK, you're right so far, you just have to redraw the circuit then it will become apparent how to simplify.

ALWAYS redraw such circuits otherwise you're likely to just confuse yourself.

As you said, C1 and C2 are in parallel. So call that C12 and redraw the circuit.
You will have to do one one capacitor series equivalence and one more capacitor parallel equivalence.

Krushnaraj Pandya and Delta2
That second lower wire has no use. I decided to replace capacitors with resistor symbols and saw that C4 and ((C2,C3) are in parallel which in turn is in series with C1. I got the answer, verified by my textbook as 5C/3

.Scott said:
As you said, C1 and C2 are in parallel. So call that C12 and redraw the circuit.
You will have to do one one capacitor series equivalence and one more capacitor parallel equivalence.
I was confused where to place C12, but this won't be necessary, I can write C234 and place it in series with C1

any insights? I did it the correct way-right?

Krushnaraj Pandya said:
I was confused where to place C12, but this won't be necessary, I can write C234 and place it in series with C1
##C_{234}## ?
No. I think you're heading down the wrong path.
Do ##C_{12}## first. Then you will have a 3-capacitor circuit.
Next will be ##C_{124}##. Then ##C_{1234}## and you're done.

Krushnaraj Pandya said:
I was confused where to place C12, but this won't be necessary, I can write C234 and place it in series with C1
EXACTLY the kind of confusion I was talking about. Stop writing words and REDRAW THE CIRCUIT. That should always be the first thing you do on this kind of problem.

GrahamN-UK and Krushnaraj Pandya
.Scott said:
C234 ?
No. I think you're heading down the wrong path.
Do C12 first. Then you will have a 3-capacitor circuit.
Next will be C124. Then C1234 and your done.
1)C4 is connected across 'D' and 'B'.
2)C2 and C3 are in series
3)C23 is in parallel with C4
4)C234 is then in series with C1.

I have the correct answer, but am I wrong in the steps?

##C_2## and ##C_3## are not in series.
After you did ##C_{12}## you needed to redraw.
##C_3## goes directly from A to B, so there is nothing in series with it.

Here is you net list:
##C_1##: A to D
##C_2##: A to D
##C_3##: A to B
##C_4##: D to B

Krushnaraj Pandya
.Scott said:
##C_2## and ##C_3## are not in series.
After you did ##C_{12}## you needed to redraw.
##C_3## goes directly from A to B, so there is nothing in series with it.

Here is you net list:
##C_1##: A to D
##C_2##: A to D
##C_3##: A to B
##C_4##: D to B
are C12 and c4 in series? I think I got it. but it was barely apparent after redrawing, just the net list provoked the thought

Got it perfectly! 1) C1 and C2 in parallel from A to D, therefore C12 from A to D.
2)C4 from D to B and C12 from A to D, so in series.
3)C124 from A to B, so in parallel with C3
Finally the correct answer is 5C/3.
Thank you very much for your help.

Delta2 and .Scott
Krushnaraj Pandya said:
Got it perfectly! 1) C1 and C2 in parallel from A to D, therefore C12 from A to D.
2)C4 from D to B and C12 from A to D, so in series.
3)C124 from A to B, so in parallel with C3
Finally the correct answer is 5C/3.
Thank you very much for your help.
And here are the drawings :

#### Attachments

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Delta2

## 1. How do you calculate the equivalent capacitance of a circuit?

The equivalent capacitance of a circuit can be calculated by adding up all the individual capacitances in parallel and all the individual capacitances in series, and then combining them using the appropriate equations.

## 2. What is the purpose of finding the equivalent capacitance of a circuit?

Finding the equivalent capacitance of a circuit is important because it helps simplify complex circuits and allows for easier analysis and calculation of other circuit parameters, such as voltage and current.

## 3. Is the equivalent capacitance of a circuit always smaller than the individual capacitances?

No, the equivalent capacitance of a circuit can sometimes be larger than the individual capacitances. This is because when capacitors are connected in parallel, their total capacitance is equal to the sum of their individual capacitances, while in series, their total capacitance is less than the smallest individual capacitance.

## 4. Can the equivalent capacitance of a circuit be negative?

No, the equivalent capacitance of a circuit cannot be negative. Capacitance is a physical property of a material and can only have positive values. If the calculation results in a negative value, it means an error has been made in the analysis or calculation.

## 5. How does the placement of capacitors in a circuit affect the equivalent capacitance?

The placement of capacitors in a circuit can affect the equivalent capacitance. When capacitors are connected in parallel, the equivalent capacitance increases, while in series, it decreases. Therefore, the arrangement of capacitors in a circuit is important in determining the equivalent capacitance.

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