Calculating Capacitance of a Capacitor

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!
 

berkeman

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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!
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?
 

berkeman

Mentor
54,767
5,020
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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