Capacitance: Equivalent C of a Network

In summary, the question is asking for the equivalent capacitance between points y and z of the capacitor network. To find this, one must collapse the circuit starting from the far right and working towards the nodes x and y. Elements that share the same current are in series, while elements with the same voltage across them are in parallel. The correct equation for a series combination for capacitors is 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ..., not Ceq = 1/C1 + 1/C2 + 1/C3 + .... It is important to note that with the ideal battery or power supply connected in parallel, the circuit is a short circuit for AC between y and z,
  • #1
calvert11
32
0

Homework Statement



A capacitor network is shown below.
http://img99.imageshack.us/img99/9967/79727282.gif

What is the equivalent capacitance between
points y and z of the entire capacitor network?

Homework Equations



In parallel: C = c1 + c2 + ...
In series: 1/C = 1/c1 + 1/c2 + ...

The Attempt at a Solution



I'm not sure exactly which capacitors are in series and which are parallel.

But I was thinking that the capacitors in series are the ones that form an isolated system. This seems to be all the capacitors with 15 mF, which is C2 = 15/6. The remaining capacitor C1 = 10 mF seems to be parallel with C2 so C = C2 + C1 = 15/6 + 10 = 12.5 mF. But this is the wrong answer.

I'm a bit stumped. I'd appreciate any help.
 
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  • #2
Start collapsing the circuit from the far right, back towards the nodes x and y. Try re-drawing the circuit after each combination for clarity. If an element shares the same current with another element, it is in series. If an element has the same voltage across it as another element, it is in parallel.

Remember that a series combination for a capacitor is: 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ...
and NOT Ceq = 1/C1 + 1/C2 + 1/C3 + ...

I see that mistake often on here.
 
  • #3
Actually, it's a trick question (or a poorly asked question). With the ideal battery or power supply connected in parallel, the circuit is a short circuit for AC between y and z, so the equivilant capacitance is infinite.

The problem probably means to ask what the equivalent capacitance is for the set of capacitors to the right of the battery, not including it. In that case, mplayer has given you the hints.
 
Last edited:
  • #4
Collapsing the circuit step by step worked. Thanks for the help.
 

1. What is capacitance and how does it relate to equivalent C of a network?

Capacitance is the ability of a system to store an electric charge. Equivalent C of a network is the total capacitance of a circuit, which is the sum of all individual capacitances within the circuit. In other words, it is the measure of a network's ability to store electric charge.

2. How is equivalent C of a network calculated?

To calculate the equivalent C of a network, you add up all the individual capacitances in the circuit. In series circuits, the equivalent C is equal to the reciprocal of the sum of the reciprocals of each individual capacitance. In parallel circuits, the equivalent C is equal to the sum of all the individual capacitances.

3. What factors affect the equivalent C of a network?

The equivalent C of a network is affected by the physical characteristics of the capacitors, such as the size and material of the plates, the distance between the plates, and the dielectric constant of the material between the plates. Additionally, the arrangement of the capacitors in the circuit, whether in series or parallel, will also affect the equivalent C.

4. What is the unit of measurement for equivalent C of a network?

The unit of measurement for equivalent C of a network is the farad (F). However, in most circuits, the equivalent C is in the microfarad (μF) or picofarad (pF) range.

5. How does equivalent C of a network impact the behavior of a circuit?

The equivalent C of a network affects the circuit's ability to store and release electric charge. A higher equivalent C means that the circuit can store more charge, which can affect the circuit's response time and overall performance. Additionally, equivalent C can also impact the frequency response of a circuit, which is important in applications such as filtering and tuning.

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