What is the equivalent capacitance between points A & B?

In summary, the equivalent capacitance between points A and B can be found by considering the capacitors in the circuit as being connected in parallel and then in series. The capacitance between points A and B can then be simplified to 2C and C/2, respectively. Additionally, the potential difference between the capacitors is zero at steady state, simplifying the circuit further.
  • #1
Kronos
3
0

Homework Statement


Find the equivalent capacitance between points A & B

1.png

Homework Equations



Ceq1 = C + C
1/Ceq2 = 1/2C + 1/2C + ...

The Attempt at a Solution


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It is my understanding that each capacitor top and bottom are connected in parallel, so their equivalent is 2C.

2.png

Now, they are all connected in series, so their equivalent would be:
1/Ceq2 = 1/2C + 1/2C + 1/2C + 1/2C

Thus,
Ceq2 = C/2

Is my reasoning acceptable?
Thank you.
 
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  • #2
Kronos said:
each capacitor top and bottom are connected in parallel
If the effective capacitance sought were between the left hand side and the right hand side, that would work. But it isn't.

Is there more context here, like an applied varying potential?
If not, think about potentials. What might the potential difference be between the right hand side of the top left capacitor and the right hand side of the bottom left capacitor?
 
  • #3
The potential difference would just be zero since the capacitors are at steady state. Thus, there is no current flowing through the wire w/ resistor, and by Ohm's law:
V = I*R
V = (0) * R
V = 0
 
  • #4
Kronos said:
The potential difference would just be zero since the capacitors are at steady state. Thus, there is no current flowing through the wire w/ resistor, and by Ohm's law:
V = I*R
V = (0) * R
V = 0
Right. Does that help you simplify the circuit?
 
  • #5
haruspex said:
Right. Does that help you simplify the circuit?
Yes. That means that the capacitor on the top left and the capacitor on the bottom left are connected in series, correct? Since the same charge will flow through them.
 
  • #6
Kronos said:
Yes. That means that the capacitor on the top left and the capacitor on the bottom left are connected in series, correct? Since the same charge will flow through them.
That's how I read it.
 

FAQ: What is the equivalent capacitance between points A & B?

1. What is equivalent capacitance?

Equivalent capacitance refers to the combined capacitance of a circuit or system that is made up of multiple capacitors. It is the single capacitance value that can replace the multiple capacitors, while still maintaining the same overall effect on the circuit.

2. How do you calculate equivalent capacitance?

The method for calculating equivalent capacitance varies depending on the type of capacitors and how they are connected in the circuit. For capacitors in series, the equivalent capacitance is equal to the reciprocal of the sum of the reciprocals of the individual capacitances. For capacitors in parallel, the equivalent capacitance is equal to the sum of the individual capacitances. There are also different formulas for calculating equivalent capacitance for more complex circuits.

3. Why is it important to find equivalent capacitance?

Finding equivalent capacitance is important because it simplifies the analysis of a circuit. Instead of dealing with multiple capacitors, we can use a single equivalent capacitance to determine the behavior of the circuit. This is especially useful in more complex circuits where using individual capacitances would be much more difficult and time-consuming.

4. Can equivalent capacitance ever be greater than the individual capacitances?

Yes, in some cases, the equivalent capacitance can be greater than the individual capacitances. This occurs in circuits with capacitors connected in parallel, as the equivalent capacitance is equal to the sum of the individual capacitances. However, in circuits with capacitors connected in series, the equivalent capacitance will always be less than the smallest individual capacitance.

5. How does temperature affect equivalent capacitance?

The temperature of a capacitor can have an impact on its capacitance, which can in turn affect the equivalent capacitance of a circuit. Generally, as temperature increases, the capacitance of a capacitor decreases. Therefore, in circuits with multiple capacitors, the equivalent capacitance may also decrease as the temperature increases. However, this effect may be negligible depending on the type of capacitors and their specific temperature coefficients.

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