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QNEET-2024-Ph-150: NEET 2024 Physics - Class 12 NEET-2024-Ph-150 Solution: The capacitance of a capacitor with charge q and a potential…
The capacitance of a capacitor with charge q and a potential difference V depends on both q and V the geometry of the capacitor q only V only
Multiple Choice Options
- A both q and V
- B the geometry of the capacitor
- C q only
- D V only
Step-by-Step Verified Solution
The correct answer is Option B: the geometry of the capacitor . Here's why:
Capacitance (denoted by *C*) is a fundamental property of a capacitor that describes its ability to store electrical energy. It's defined by the ratio of the charge stored on the capacitor ( q ) to the potential difference across its plates ( V ):
C = q V
While the formula seems to suggest that capacitance depends on both charge and voltage, the reality is that the geometry of the capacitor determines its capacitance. Here's a breakdown:
Charge ( q ) : The charge stored on a capacitor is directly proportional to the applied voltage. If you increase the voltage, you increase the charge stored. However, the capacitance itself remains constant for a given capacitor.
Voltage ( V ) : Similarly, the voltage across a capacitor is directly proportional to the charge stored. Increasing the charge increases the voltage, but again, the capacitance remains unchanged.
Geometry : The geometry of a capacitor dictates how much electric field is created between its plates for a given charge. This electric field determines the potential difference between the plates. Here are some key factors:
Area of plates (A) : Larger plates can hold more charge for a given voltage, resulting in higher capacitance.
Distance between plates (d) : Smaller distances between plates create a stronger electric field, which leads to higher capacitance.
Dielectric material : The material between the plates (dielectric) affects the strength of the electric field and therefore the capacitance. A material with a higher dielectric constant increases the capacitance.
In summary, while charge and voltage are related to capacitance through the formula, they are not the determining factors. It's the capacitor's physical characteristics � its geometry � that ultimately determine its capacitance.