I don't understand capacitance

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In summary, the conversation discussed various concepts related to capacitance, such as the relationship between charge and voltage, the effect of increasing the size of a capacitor, how capacitance is calculated, and the difference between capacitors in series and parallel. The conversation also touched on the concept of dielectrics and their effect on capacitance, as well as the storage of energy in a capacitor. One person also inquired about the reason for modeling capacitors with a dielectric as two separate capacitors. The last comment mentioned another person, but it is unclear what their role in the conversation was.
  • #1
member 392791
Hello,

So I am told that capacitance is a measure of how much charge can be stored in a capacitor. However, I don't have an intuitive understanding for why it is a relationship between charge and voltage. Can anyone help me in understanding it?

I'm imagining one capacitor attached to a battery. Electrons on one side of the plate leave that plate, go through the battery, and go over to the other side. If I increase the voltage of the battery, I would think even more electrons would leave the plate, yet the same amount always goes back to the other side. That ratio of charges to applied voltage is the same.

If I make the capacitor larger, is it the case that for a given amount of voltage, the same amount of electrons would leave one plate and go to the other side?
 
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  • #2
Woopydalan said:
Hello,

I'm imagining one capacitor attached to a battery. Electrons on one side of the plate leave that plate, go through the battery, and go over to the other side. If I increase the voltage of the battery, I would think even more electrons would leave the plate, yet the same amount always goes back to the other side. That ratio of charges to applied voltage is the same.

When you increase the voltage more charges do leave the plate.

If I make the capacitor larger, is it the case that for a given amount of voltage, the same amount of electrons would leave one plate and go to the other side?

No. A larger capacitor loses more charges for the same applied voltage than a smaller capacitor does. This is why they hold more energy.

Capacitance is given by the equation C=q/V, where C is capacitance, q is the charges on the plates, and V is the voltage between the plates. Notice that this means that capacitance is a ratio of charges to voltage. A higher capacitance means that q is larger while V stays the same, or that V is smaller while q stays the same.

Also, a parallel plate capacitor's capacitance can be found by: C=εr ε0 A/d.

εr is the dielectric constant of the capacitor
ε0 is the electric constant
d is the separation between the plates
A is the area of the plates

Capacitance is proportional to the area of the plates since A is in the numerator. Doubling A will double your capacitance. If we double capacitance by increasing the area, but keep the voltage applied the same, then by the first equation we must increase the number of charges (q) moved.
 
  • #3
Can you explain why the voltage is not the same for two capacitors in series? from a conceptual point of view, I understand mathematically why, but not conceptually.
 
  • #5
thank you for providing the links, I'll give it a read
 
  • #6
I believe it's because capacitors connected in series effectively cause the sum of the "gap" between the capacitor plates over the whole of the circuit to be larger. I.E, the total gap in a series circuit is G1+G2+G3 etc for each capacitor added.
 
  • #7
Also, I don't understand the connection between the capacitance of a lone object versus the parallel plate capacitors in a circuit.

Something like coaxial cables that are charged. If neither are connected to a battery, how do I know the capacitance of the cables?

This webpage derives the equation, but I don't understand why I only care about finding the electric field of the inner cable?

http://faculty.polytechnic.org/phys...._capacitors/2._pdf's/capac_of_coax_cable.pdf
 
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  • #8
Woopydalan,

Can you explain why the voltage is not the same for two capacitors in series? from a conceptual point of view, I understand mathematically why, but not conceptually.

Which voltage? The voltage across each capacitor? If the caps have the same value, then the sum of the caps have to equal the voltage source.

Also, I don't understand the connection between the capacitance of a lone object versus the parallel plate capacitors in a circuit.

What kind of lone object. Is not a single cap a lone object? What kind of connection?

This webpage derives the equation, but I don't understand why I only care about finding the electric field of the inner cable?

The line integral of the electric field gives you the voltage. The field is between the inner and outer parts of the cable.

Ratch
 
  • #9
Why is it that when you put a dielectric between the capacitors, they are modeled as being two separate plate capacitors? One with each plate and one part of the dielectric. I am not following the logic behind that.
 
  • #10
Woopydalan,

Why is it that when you put a dielectric between the capacitors, they are modeled as being two separate plate capacitors? One with each plate and one part of the dielectric. I am not following the logic behind that.

If you put nothing but vacuum between the plates, then they are vacuum capacitors. If air is between the plates, then they are air capacitors. Mica makes a mica capacitor. Vacuum has the poorest dielectric constant, air is a little better, and mica the the best of the three I listed.

Ratch
 
  • #11
Yes, but why is it that they are modeled as two separate capacitors?
 
  • #12
Woopydalan,

Yes, but why is it that they are modeled as two separate capacitors?

Where? Show me.

Ratch
 
  • #13
When it says that energy is stored in a capacitor, is that energy just the charges that are residing on the capacitor, or is the energy being held within the electric field between the two plates. If the latter, how is energy stored in an electric field if no charge is present?

Also, was that Ratch guy a crackpot or something? Looks like someone banned him
 
  • #14
Woopydalan said:
When it says that energy is stored in a capacitor, is that energy just the charges that are residing on the capacitor, or is the energy being held within the electric field between the two plates. If the latter, how is energy stored in an electric field if no charge is present?

The energy is stored in a capacitor as charges in an electric field. If you short the two terminals of a capacitor together work will be performed on the charges by the electric field and current will flow. That's where energy comes from. The ability to perform work.

Note that you cannot separate charges and the EM field. Even when neutral there is a field present, it's just not capable of performing any work.
 
  • #15
Even when neutral there is a field present, it's just not capable of performing any work.
This is an interesting statement, can you explain/give examples of what it means?
 
  • #16
Emilyjoint said:
Even when neutral there is a field present, it's just not capable of performing any work.
This is an interesting statement, can you explain/give examples of what it means?

I use the basic definition of a field from wiki:

A field is a physical quantity that has a value for each point in space and time.[1] For example, in a weather forecast, the wind velocity during a day over a country is described by assigning a vector to each point in space. Each vector represents the direction of the movement of air at that point. As the day progresses, the directions in which the vectors point change as the directions of the wind change.

A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor (e.g., a Dirac electron) or, more generally, a tensor, respectively. For example, the Newtonian gravitational field is a vector field: specifying its value at a point in spacetime requires three numbers, the components of the gravitational field vector at that point. Moreover, within each category (scalar, vector, tensor), a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively.

While the field is a "construct" of ours using math, it represents what we think is a "real" field. We think this for a variety of reasons, one of the main ones is that energy is transferred through fields. We don't like to think that energy just disappears until it is transferred to another object so we say it has been transferred to the field.

When I say that the field is still there, but it can't do any work, I mean that the field, as per the description above remains, only the values change. Now that I think about it I am not 100% sure this is a correct view, so don't try to use this on any homework questions or anything.
 
  • #17
I do not recognise your wiki definition of a field. There is no reference to energy or energy transfer and it is not clear what is meant by classical fields or quantum fields.
If you are not sure of your facts or cannot back them up with recognised standard textbooks then you should think twice about what you present.
There is a great risk that students will be confused by opinions rather than knowledge.
 
  • #18
Emilyjoint said:
I do not recognise your wiki definition of a field. There is no reference to energy or energy transfer and it is not clear what is meant by classical fields or quantum fields.

My apologies I forgot to include the link to the article that touches each of those topics.
http://en.wikipedia.org/wiki/Field_(physics)

If you are not sure of your facts or cannot back them up with recognised standard textbooks then you should think twice about what you present.
There is a great risk that students will be confused by opinions rather than knowledge.

A reasonable objection. But I find that, in general, my opinions are usually accurate. Not always, but usually. If that changes then I will stop giving opinions.
 
  • #19
so how is it that the energy is being stored within the confines of the two capacitor plates? For the electric potential energy to be present, doesn't there need to be actual charges that are present within the electric field? Or is it that the charges that are bounded to the plate capacitors are within the field, and that is the electric potential energy?
 
  • #20
Woopydalan said:
so how is it that the energy is being stored within the confines of the two capacitor plates? For the electric potential energy to be present, doesn't there need to be actual charges that are present within the electric field?

Let's be clear. When a capacitor has a voltage applied to it and charges move from one plate to the other, we say that an electric field is developed between the plates. If you had a vacuum between the plates there would be no charges "within" this field. But that's okay. The field is still there and the energy is stored in the separation of the charges.
 
  • #21
Ok, so the voltage pushes electrons on one plate over to the other plate through the circuit, not from some sort of spontaneous jump from one plate to the other. Got it.

Now, there are more charges on one plate than the other, and thus there is an Electric field between the plates.

now with the point charge examples, there is a certain potential energy if another charge is present within the field of the other charge. There are charges in the presence of an electric field in a capacitor, but they are on the surface of the capacitor.

So it is those charges on the surface of the plates that are in the presence of the electric field that contain the energy?
 
  • #22
There are not more charges on one plate than the other. The charge on each plate is the same. What is removed from one plate (by the battery...source of energy) is placed on the other plate.
You do not need different amounts of charge to have an electric field...you need different charges (+ and -) but not different amounts
 

1. What is capacitance?

Capacitance is the ability of a system to store an electric charge. It is a measure of how much charge can be accumulated on a capacitor for a given potential difference between its plates.

2. How is capacitance related to charge and voltage?

Capacitance is directly proportional to the amount of charge stored on a capacitor and inversely proportional to the voltage across the plates. This means that an increase in charge will result in an increase in capacitance, while an increase in voltage will result in a decrease in capacitance.

3. What factors affect capacitance?

The capacitance of a system is affected by several factors, including the geometry of the capacitor, the distance between the plates, the dielectric material between the plates, and the surface area of the plates. The type of material used for the plates can also affect capacitance.

4. How is capacitance measured?

Capacitance is typically measured using a device called a capacitance meter, which measures the amount of charge stored on a capacitor for a given voltage. The unit of measurement for capacitance is the farad (F).

5. What are some practical applications of capacitance?

Capacitance has many practical applications, including in electronic circuits, power transmission systems, and energy storage devices such as batteries and capacitors. It is also used in sensors and touch screens, as well as in various medical and scientific equipment.

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