Calculating Capacitance of a Capacitor

In summary, the value of capacitance C is determined by the geometry of the capacitor only. The equation C=q/V can be used to find C when given the potential difference and charge of the capacitor. However, the C value is fundamental based on the geometry, so given a specific geometry, the potential difference and charge cannot be set arbitrarily.
  • #1
skaterbasist
13
0
Hello,

I have a question regarding the equation q=CV, where q is the charge and V is the potential difference of a capacitor, and C is the proportionately constant C of the capacitor.

From what I understand, the value of C depends only on the geometry of the plates and NOT on their charge or potential difference. If that's the case, then how can the manipulated equation of C=q/V be valid? If we are given the potential difference and charge of a capacitor, how does one go about calculating the capacitance of a capacitor?

The arrangement of the capacitor is an ideal parallel-plate situation.

Many thanks!
 
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  • #2
skaterbasist said:
Hello,

I have a question regarding the equation q=CV, where q is the charge and V is the potential difference of a capacitor, and C is the proportionately constant C of the capacitor.

From what I understand, the value of C depends only on the geometry of the plates and NOT on their charge or potential difference. If that's the case, then how can the manipulated equation of C=q/V be valid? If we are given the potential difference and charge of a capacitor, how does one go about calculating the capacitance of a capacitor?

The arrangement of the capacitor is an ideal parallel-plate situation.

Many thanks!

The capacitance C is determined by the geometry of the capacitor only.

If you set the voltage at some voltage V, then the charge on the capacitor is Q = CV.

If you instead set the charge on the capacitor to Q, then the voltage is V = Q/C.

Given a capacitor C, you cannot independently set V and Q. You can set one or the other, and the value of the capacitance C determines the value of the remaining quantity.
 
  • #3
Thank you very much.

So, just to be clear, if we were given the potential difference V and charge Q of Capacitor C, then based on that equation we may find C with C=Q/V? Or does that contradict the fact that C is determined by geometry only?
 
  • #4
skaterbasist said:
Thank you very much.

So, just to be clear, if we were given the potential difference V and charge Q of Capacitor C, then based on that equation we may find C with C=Q/V? Or does that contradict the fact that C is determined by geometry only?

No, all three numbers will be consistent. The only caveat is that the C value is fundamental based on the geometry, so given a geometry, you cannot arbitrarily set V and Q.
 
  • #5
What you actually do is to put a proof charge q on the conductor and calculate/measure electric fields and voltage differences. You will find out that deltaV is ALWAYS proportional to q, so it cancels out when you calculate 1/C = deltaV/q.
 
  • #6
For a given potential difference across a given capacitor a unique amount of charge develops. Hence the formula can be used.
 

1. What is a capacitor and how does it work?

A capacitor is an electronic component that stores electrical energy in an electric field. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied to the capacitor, one plate accumulates a positive charge and the other accumulates a negative charge, creating an electric field between them. This allows the capacitor to store energy in the form of separated charges.

2. How do you calculate the capacitance of a capacitor?

The capacitance of a capacitor can be calculated using the equation C = Q/V, where C is the capacitance in farads, Q is the charge stored on the capacitor in coulombs, and V is the voltage applied to the capacitor in volts. Alternatively, the capacitance can also be calculated using the equation C = εA/d, where ε is the permittivity of the dielectric material, A is the area of the plates, and d is the distance between the plates.

3. What factors affect the capacitance of a capacitor?

The capacitance of a capacitor is affected by three main factors: the surface area of the plates, the distance between the plates, and the type of dielectric material used. A larger surface area and a smaller distance between the plates will result in a higher capacitance, while using a material with a higher permittivity will also increase the capacitance.

4. What happens to the capacitance if the distance between the plates is decreased?

If the distance between the plates is decreased, the capacitance of the capacitor will increase. This is because the electric field between the plates will become stronger, allowing for a greater amount of charge to be stored on the plates.

5. How can I determine the maximum voltage that can be applied to a capacitor?

The maximum voltage that can be applied to a capacitor is determined by the breakdown voltage of the dielectric material. This is the point at which the electric field within the dielectric becomes too strong and causes the material to break down, leading to a sudden discharge of the stored energy. It is important to choose a capacitor with a breakdown voltage higher than the expected operating voltage to prevent damage to the capacitor.

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