How Do You Calculate the Equivalent Capacitance in Mixed Capacitor Circuits?

In summary, the conversation discusses finding the relationship between C and C1 to make C equivalent to C1. The solution involves using the equations for capacitors in series and parallel. The final equation provided by the textbook is C=C1(1+√5)/2.
  • #1
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Please help :( -Capacitors in series and parallel

Homework Statement


Find the relationship between C and C1 to make C equivalent= C

The diagram is as shown below:-
Code: 
                                           C1 
               A---------------------------||----
                                        |                |
                                         =C1            = C
                                        |                |
                B---------------------------------

Homework Equations


C parallel= C1 + C2 + C3...
1/C series= 1/C1 + 1/C2 + 1/C3


The Attempt at a Solution



So on the right most of the diagram, C1 and C are in series, hence their combined capacitor is C1(C)/C1+C. And since the combined capacitor is in parallel with the other C1, C equivalent is C1(C)/C1+C + C1 = C

However, I can't seem to solve that particular equation by making C as the subject...

Please help..

The answer provided by the textbook is:
C=C1 (1+ square root of 5) / 2

Thanks...
 
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  • #2


I guess my diagram is messed up even though i tried to fixed it, but yeah,

C1 is in series with C

and those two combined are in parallel with C1...
 
  • #3


Let's see some of the mathematical steps you've taken to try to solve for C.
 

1. What is the difference between capacitors in series and parallel?

The main difference between capacitors in series and parallel is the way they are connected. In series, the capacitors are connected end-to-end, while in parallel, they are connected side-by-side. This results in different total capacitance values and charge distribution between the capacitors.

2. How do capacitors in series and parallel affect the overall capacitance?

In series, the total capacitance is lower than the individual capacitance of each capacitor. This is because the capacitors share the same charge and the total charge is divided between them. In parallel, the total capacitance is higher than the individual capacitance of each capacitor. This is because the capacitors add up their individual capacitance values, resulting in a larger overall capacitance.

3. Can capacitors in series and parallel have different capacitance values?

Yes, capacitors in series and parallel can have different capacitance values. In series, the capacitors must have the same capacitance to ensure equal charge distribution. In parallel, the capacitors can have different capacitance values, and the total capacitance will be the sum of all individual capacitances.

4. How does the voltage affect capacitors in series and parallel?

In series, the voltage is divided between the capacitors, so each capacitor has a fraction of the total voltage. In parallel, each capacitor has the same voltage as the source, as they are connected in parallel to the same voltage source.

5. Can capacitors in series and parallel be used in electronic circuits?

Yes, capacitors in series and parallel are commonly used in electronic circuits. They can be used for various purposes, such as filtering, energy storage, and timing. Each configuration has its own advantages and is chosen based on the specific needs of the circuit.

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