Equivalent capacitance

In summary, The conversation highlights a problem with the application of Kirchhoff's Loop Rule to the given circuit. The speaker suggests that there may be a sign problem with the voltage drops across the capacitors and that additional equations based on charge conservation may be needed to solve the problem.
  • #1

The "C"s stand for capacitor.
The capacitance of C2 is 10 μF and others are 4 μF.

The book contains neither the answer nor solution.

I tried to apply Kirchhoff's Loop Rule:
q_4 / 4 + q_2 /10 + q_3 / 4 = 0
q_1 / 4 + q_2 /10 + q_5 / 4 = 0
q_1 + q_4 + q_3 + q_5 = 0

Then I got the equivalent capacitance=0. What is the problem with my argument?
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  • #2
My guess is you have a sign problem. It's not obvious to me that you have assumed one sign for the voltage drop across each capacitor and used it consistently. In fact, it looks very much like you have not. There must be some additional equations based on charge conservation.
  • #3

There are a few issues with your argument. First, you have not taken into account the fact that capacitors in series have an inverse relationship, while capacitors in parallel have an additive relationship. In this circuit, C1, C2, and C3 are in series, while C4 and C5 are in parallel. This means that the equivalent capacitance will be different for these two sets of capacitors.

Secondly, your equations seem to be missing some key information. The Kirchhoff's Loop Rule only applies to circuits with resistors, not capacitors. In order to find the equivalent capacitance, you will need to use the formula 1/Ceq = 1/C1 + 1/C2 + 1/C3 + 1/C4 + 1/C5.

Lastly, it is important to note that the value of the equivalent capacitance will not be 0. It will be a non-zero value, as there are capacitors in the circuit with non-zero values. It is possible that your calculations may have resulted in an error, which is why you are getting a value of 0.

To correctly find the equivalent capacitance, you will need to apply the formula mentioned above and take into account the relationships between capacitors in series and parallel. It may also be helpful to redraw the circuit to better visualize the relationships between the capacitors.

What is equivalent capacitance?

Equivalent capacitance is the total capacitance of a combination of capacitors connected in a circuit. It is the single capacitor that would have the same effect as the entire combination in terms of storing and releasing electrical charge.

How is equivalent capacitance calculated?

There are different ways to calculate equivalent capacitance depending on the type of circuit. In series circuits, equivalent capacitance is equal to the reciprocal of the sum of the reciprocals of each individual capacitor. In parallel circuits, equivalent capacitance is equal to the sum of all the individual capacitances.

What is the difference between series and parallel equivalent capacitance?

In series circuits, the equivalent capacitance is always less than the smallest individual capacitor, while in parallel circuits, the equivalent capacitance is always greater than any individual capacitor. This is because in series circuits, the capacitors share the same charge, while in parallel circuits, the capacitors have the same potential difference.

Why is equivalent capacitance important?

Equivalent capacitance is important because it allows us to simplify complex circuits and analyze them more easily. It also helps us determine the total amount of charge that a circuit can hold and how quickly it can be discharged.

Can capacitors be combined in both series and parallel?

Yes, capacitors can be combined in both series and parallel in a circuit. In fact, many circuits have a combination of series and parallel capacitors to achieve the desired equivalent capacitance.

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