How Do You Calculate the Equivalent Capacitance in a Complex Circuit?

• holymoly
In summary, the question asks to find the equivalent capacitance of a system with given values for voltage and capacitance. The solution involves combining capacitors in series and parallel. After combining C1 and C3 in series, C2 is then combined with the resulting equivalent capacitor in parallel. The final answer is 5.14 uF.
holymoly

Homework Statement

In the diagram V = 12.0V, C1 = 23 uF, C2 = 4.00 uF, C3 = 12.0 uF and C4 = 9.00uF. Calculate the equivalent capacitance of the system.

http://img403.imageshack.us/img403/6346/eqam8.jpg

Homework Equations

Just combinding capacitors in parallel and in series.

The Attempt at a Solution

This question is giving me a headache when it should be simple. I must be overlooking something stupid, and hopefully someone will please lead me in the right direction.

I start by taking capacitors C1 and C3, which are in series, and combine them :
1/C13 = 1/24 + 1/12
1/C13 = 3/24
C13 = 8

Doesn't that leave C13, C2, and C4 in parallel? (this is where I'm getting sidetracked i think. the middle one is throwing me for a bit of a loop). In parallel, that would just be 8+4+9 = 21 uF, which is not the answer. The answer should be 5.14 uF.

I'd appreciate any pointers.

Last edited by a moderator:
Doesn't that leave C13, C2, and C4 in parallel?

No, only C13 and C2 are in parallel for the next step.

You are on the right track with combining capacitors in series and parallel. However, it looks like you may have made a mistake in your calculation for C13. Remember that when capacitors are in series, their equivalent capacitance is given by 1/Ceq = 1/C1 + 1/C2. So for C1 and C3, the equivalent capacitance would be 1/C13 = 1/23 + 1/12 = 5/69. Solving for C13, we get C13 = 13.8 uF.

Now, for the remaining capacitors in parallel, we can use the equation Ceq = C1 + C2 + C3. In this case, Ceq = 13.8 uF + 4.00 uF + 9.00 uF = 26.8 uF. This is the equivalent capacitance of the system. However, the question specifically asks for the equivalent capacitance of the system, not the total capacitance of the remaining capacitors in parallel. To find the equivalent capacitance of the system, we need to combine this value with the 8 uF from C13. So the final answer should be 26.8 uF + 8 uF = 34.8 uF. It is important to note that when capacitors are in series, they add inversely, while in parallel, they add directly. Keep practicing and you will get the hang of it!

What is Equivalent Capacitance?

Equivalent Capacitance is a measure of the combined capacitance of multiple capacitors connected in a circuit. It represents the total amount of charge that can be stored in the circuit.

How is Equivalent Capacitance calculated?

The calculation of Equivalent Capacitance depends on the arrangement of the capacitors in the circuit. For capacitors connected in series, the equivalent capacitance is equal to the reciprocal of the sum of the reciprocals of each individual capacitance. For capacitors connected in parallel, the equivalent capacitance is equal to the sum of the individual capacitances.

What is the significance of Equivalent Capacitance?

Equivalent Capacitance is important in circuit analysis as it simplifies complex circuits and makes it easier to calculate the overall capacitance. It also helps in understanding the behavior of the circuit and determining the amount of charge that can be stored.

How does Equivalent Capacitance affect the total energy stored in a circuit?

The total energy stored in a circuit is directly proportional to the equivalent capacitance. This means that as the equivalent capacitance increases, the amount of energy that can be stored also increases. Similarly, if the equivalent capacitance decreases, the energy stored will also decrease.

Can the Equivalent Capacitance of a circuit ever be less than the capacitance of any individual capacitor?

No, the Equivalent Capacitance of a circuit can never be less than the capacitance of any individual capacitor. The equivalent capacitance is always equal to or greater than the individual capacitances, depending on the arrangement of the capacitors in the circuit.

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