Question

The capacitance of a capacitor with charge q and a potential difference V depends on :

• A. both q and V
• B. the geometry of the capacitor
• C. q only
• D. V only

Answer 1

The Correct Option is B

The capacitance of a capacitor is a measure of its ability to store charge per unit voltage. The relationship between these quantities can be summarized by the formula: 

\(C = \frac{q}{V}\)

where:

• \(C\) is the capacitance,
• \(q\) is the charge stored on the capacitor,
• \(V\) is the potential difference across the capacitor.

To understand what determines the capacitance, let's explore the factors:

1. The capacitance is independent of both the charge \((q)\) and the voltage \((V)\). It depends on the physical characteristics of the capacitor like:
   • The area \((A)\) of the plates: Larger plate areas increase capacitance because there is more room to store charge.
   • The distance \((d)\) between the plates: Smaller distances increase capacitance because the charge is more concentrated.
   • The dielectric material between the plates: A material with higher permittivity increases capacitance.
2. Option: 'Both \(q\) and \(V\)': This is incorrect because, although capacitance relates these values, it is not determined by them.
3. Option: '\(q\) only': Incorrect because only variating charge \(q\) does not determine capacitance but adjusts with respect to capacitance and voltage.
4. Option: '\(V\) only': Incorrect because the voltage does not independently determine capacitance.

Therefore, the correct answer is that the capacitance depends on the geometry of the capacitor and the material used, which fundamentally define the capacitor's ability to store charge for a given potential difference.