How Do You Calculate Equivalent Capacitance in Complex Circuits?

In summary, to find the equivalent capacitance between points 1 and 2 in a circuit with capacitors of capacitance C, you can use the equations for capacitors in series and parallel. However, in this specific circuit, the voltage across the central capacitor is the same as the voltage across either of the end capacitors, resulting in the equivalent capacitance being simply C.
  • #1
Frillth
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Homework Statement



I need to find the equivalent capacitance between points 1 and 2 in the following circuit, with each capacitor having capacitance C:

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Homework Equations



For n capacitors in series: 1/C_t = 1/C_1 + 1/C_2 + ... + 1/C_n
For n capacitors in parallel: C_t = C_1 + C_2 + ... + C_n

The Attempt at a Solution



I know that the answer is C, because it is in the back of the book, but I can't figure out how to get there. I don't have any idea how this can be reduced to just series or parallel capacitors.

Edit: Ah, I figured it out. It had to do with the voltage across the central capacitor.
 
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  • #2
Since the voltage across the central capacitor is the same as the voltage across either of the end capacitors, then the equivalent capacitance between points 1 and 2 is just C.
 
  • #3


I understand your frustration with not being able to figure out a solution immediately. However, it is important to remember that problem-solving and critical thinking are key skills in the field of science. In this case, it is helpful to start by identifying the type of circuit (series or parallel) and then using the appropriate equations to find the equivalent capacitance. In this circuit, all the capacitors are connected in parallel, so you can use the equation C_t = C_1 + C_2 + ... + C_n to find the equivalent capacitance. Additionally, it may be helpful to draw a simplified version of the circuit and use Kirchhoff's laws to analyze the voltage and current across each capacitor. With practice and perseverance, you will become more comfortable with solving these types of problems.
 

Related to How Do You Calculate Equivalent Capacitance in Complex Circuits?

What is Equivalent Capacitance?

Equivalent Capacitance refers to the total capacitance of a circuit that is combined or connected in parallel or series. It is a measurement of the overall ability of a circuit to store electric charge.

How is Equivalent Capacitance calculated in a series circuit?

In a series circuit, the Equivalent Capacitance is calculated by adding the reciprocals of the individual capacitance values and then taking the reciprocal of the sum. The formula is:
Ceq = 1/ (1/C1 + 1/C2 + 1/C3 +...)

How is Equivalent Capacitance calculated in a parallel circuit?

In a parallel circuit, the Equivalent Capacitance is calculated by adding the individual capacitance values. The formula is:
Ceq = C1 + C2 + C3 +...

What is the significance of Equivalent Capacitance in a circuit?

Equivalent Capacitance is important because it helps to simplify complex circuits and make calculations easier. It also helps to determine the total energy storage capacity of a circuit and how it will respond to different frequencies.

Can the Equivalent Capacitance of a circuit ever be greater than the largest individual capacitance?

No, the Equivalent Capacitance can never be greater than the largest individual capacitance in a circuit. It can only be equal to or less than the largest capacitance value.

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