Equivalent Capacitance

Summary = In summary, the equivalent capacitance of the arrangement shown in the figure is C1, as the additional capacitor C2 does not affect the overall capacitance due to its placement and symmetry in the circuit.
  • #1
Sami Lakka
11
0

Homework Statement


What is the equivalent capacitance of the arrangement shown in figure. (Answer is C1)


Homework Equations


Cparallel = C1+C2+...Cn
Cseries = 1/(1/C1+1/C2+...+1/Cn)


The Attempt at a Solution

 

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  • #2
Sami Lakka said:

Homework Statement


What is the equivalent capacitance of the arrangement shown in figure. (Answer is C1)


Homework Equations


Cparallel = C1+C2+...Cn
Cseries = 1/(1/C1+1/C2+...+1/Cn)


The Attempt at a Solution

It is easier to see what is happening if you change the drawing to a square with 2 C1s on each side in series and a C2 attached across the middle (from points between the C1s).

By the symmetry of the circuit, you can see that there is 0 voltage across the C2 capacitor. So the C2 really does nothing to change the capacitance of the circuit - ie. it never stores charge. So the capacitance is the same as the circuit without C2.

AM
 
  • #3


The equivalent capacitance of the arrangement shown in the figure can be found by using the formula for capacitors in parallel, which is to add all the individual capacitances together. In this case, the arrangement only has one capacitor, C1, so the equivalent capacitance is simply C1. This is because in a parallel arrangement, the capacitors are connected side by side and thus have the same voltage across them. Therefore, the total capacitance is the sum of all the individual capacitances.
 

1. What is Equivalent Capacitance?

Equivalent capacitance refers to the capacitance of a combination of capacitors connected in a circuit. It is the single value that represents the combined effect of multiple capacitors in a circuit.

2. How is Equivalent Capacitance calculated?

The equivalent capacitance of capacitors connected in series can be calculated by adding the reciprocals of each individual capacitance and taking the reciprocal of the sum. For capacitors connected in parallel, the equivalent capacitance is calculated by summing the individual capacitance values.

3. Why is Equivalent Capacitance important?

Equivalent capacitance is important because it simplifies complex circuits and allows us to easily analyze the behavior of the circuit. It also helps in designing circuits that require specific capacitance values.

4. How does Equivalent Capacitance affect the overall capacitance of a circuit?

The equivalent capacitance of a circuit is always less than the smallest individual capacitance in the circuit for capacitors in series, and it is always greater than the largest individual capacitance in the circuit for capacitors in parallel. In other words, the equivalent capacitance affects the overall capacitance of a circuit by either decreasing or increasing it, depending on how the capacitors are connected.

5. Can capacitors with different values be combined to achieve an equivalent capacitance?

Yes, capacitors with different values can be combined to achieve an equivalent capacitance. This is possible by using a combination of series and parallel connections. By using the appropriate combination, the desired equivalent capacitance can be achieved.

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