Calculating Capacitance of a Capacitor

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    Capacitance Capacitor
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Discussion Overview

The discussion revolves around the equation q=CV, focusing on the calculation of capacitance (C) of a capacitor, particularly in an ideal parallel-plate configuration. Participants explore the relationship between charge (q), potential difference (V), and capacitance, questioning how these quantities interact given that capacitance is said to depend solely on the geometry of the capacitor.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that capacitance (C) is determined only by the geometry of the capacitor's plates and not by charge (q) or potential difference (V).
  • Others question how the equation C=q/V can be valid if C is independent of q and V, seeking clarification on the calculation of capacitance when both charge and potential difference are known.
  • A participant explains that while capacitance is fundamentally based on geometry, one cannot independently set charge and voltage; setting one determines the other based on the value of C.
  • Another participant suggests that measuring electric fields and voltage differences can demonstrate that voltage differences are proportional to charge, leading to the relationship 1/C = deltaV/q.
  • It is noted that for a given potential difference, a unique amount of charge develops on the capacitor, allowing the formula to be used consistently.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the implications of the relationship between charge, voltage, and capacitance. While there is some agreement on the geometric dependence of capacitance, the discussion remains unresolved on how to reconcile this with the equation C=q/V.

Contextual Notes

Participants highlight the need for clarity on the conditions under which capacitance is calculated, emphasizing that the values of charge and voltage cannot be arbitrarily chosen without considering the geometry of the capacitor.

skaterbasist
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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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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.
 
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?
 
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.
 
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.
 
For a given potential difference across a given capacitor a unique amount of charge develops. Hence the formula can be used.
 

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