How Do You Calculate Equivalent Capacitance in Complex Circuits?

[Frillth]

Homework Statement

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

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.

 

[jbsteele]

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.

 

[thomate1]

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.