# Equivalent Capacitance of Complex Circuit

• megaspazz
In summary, the homework statement is asking for you to find the equivalent capacitance of the combination shown in Figure P26.75. The equivalent capacitance is found to be 4/3 C, which is the correct answer.
megaspazz

## Homework Statement

Determine the equivalent capacitance of the combination
shown in Figure P26.75. Suggestion: Consider the symmetry
involved.

## Homework Equations

Parallel is: C1+C2+C3+...
Series is: (C1^-1 + C2^-1 + C3^-1 + ...)^-1
q = CV

## The Attempt at a Solution

I have no idea how to do it for a complex circuit. I think it might have something to do with Kirchhoff's Law, but the book never mentioned it and neither did the professor, so I'm thinking it can do it without. And I am not sure what "the symmetry involved" is supposed to mean.

Do you see any change if you turn the figure upside down?
Is there any reason that both "C" capacitors are different or the both 2C capacitors are?

If they are equivalent, so is the charge and voltage across them.What is the voltage across the 3C capacitor then?

ehild

ehild, thank you so much! Since the voltage across it is zero, it's like the 3C capacitor isn't there, right?

Solving the simple circuit then gives 4/3 C, which is the correct answer. Is my way of solving it correct? Or did I simply get the right answer the wrong way?

Many thanks!

Also, this isn't a problem I have to do, but what if the circuit were asymmetrical? Then what would you do?

It is a very useful trick for symmetric circuits, that we can connect those points which are at the same potential with a single wire, so the points become a single node. Symmetrically equivalent points are at the same potential.

In general problems, you need to apply Kirchhoff's voltage Law and also the equivalent of Current Law, but with charges.

Every capacitor has its own charge, q at one plate and -q on the other plate.
The net charge at a node is zero. When the capacitors are connected in series, they all have the same charge.
And you know the relation between charge and voltage: q=CV.

Set up all equations and solve.

ehild

can you do Kirchoff's Law for this problem? How would you take into account the initial part before the loops and the last wire after the loops?

Connect a voltage source to the terminals with arbitrary emf E. Write up the equations in term of E, and solve for the whole charge Q on the connected plates.
Te circuit can be représented by an equivalent capacitor connected to the same voltage source and you can apply C(equivalent)=Q/Eehild

## 1. What is the equivalent capacitance of a series circuit?

In a series circuit, the equivalent capacitance is equal to the sum of all individual capacitances. This is because the capacitors are connected end-to-end, so the same amount of charge is stored in each capacitor, resulting in an increased overall capacitance.

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

In a parallel circuit, the equivalent capacitance is calculated by adding the reciprocals of all individual capacitances and taking the reciprocal of the sum. This is because the capacitors are connected side-by-side, so the voltage across each capacitor is the same, resulting in a decreased overall capacitance.

## 3. Can the equivalent capacitance of a complex circuit be greater than the individual capacitances?

Yes, in some cases the equivalent capacitance of a complex circuit can be greater than the individual capacitances. This is because the different capacitors in the circuit can interact with each other and influence the overall capacitance, resulting in a larger value.

## 4. How does the presence of a dielectric material affect the equivalent capacitance of a complex circuit?

A dielectric material, such as an insulating material, can increase the equivalent capacitance of a complex circuit. This is because the dielectric material reduces the electric field between the plates of a capacitor, allowing more charge to be stored, thus increasing the overall capacitance.

## 5. Can a complex circuit have an infinite equivalent capacitance?

No, a complex circuit cannot have an infinite equivalent capacitance. The equivalent capacitance can only increase up to a certain limit, which is determined by the circuit's geometry and the properties of the capacitors used. Beyond this limit, adding more capacitors will not change the overall capacitance.

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