Capacitance is directly proportional to__________

Question

Examoogle · Accepted Answer

Area of cross section between the plates

Explanation: The capacitance of a parallel-plate capacitor is directly proportional to the area of overlap between the two plates and inversely proportional to the distance separating them. This relationship is derived from the fundamental electrostatic definition of capacitance based on geometry and material properties.

Working Principle: As the surface area of the conductive plates increases, the capacity to store electric charge at a given potential difference increases due to the larger available space for charge accumulation. Conversely, as the distance between the plates decreases, the electric field strength increases for a constant voltage, leading to higher charge storage capacity. The medium between plates, represented by permittivity, also scales this capability.

Key Formulas: $C = \frac{\varepsilon A}{d}$ — where $C$ is capacitance, $\varepsilon$ is permittivity, $A$ is area, and $d$ is separation distance.

Key Points: Capacitance increases linearly with the surface area ($A$) of the plates.; Capacitance is inversely proportional to the separation distance ($d$) between the plates.; The permittivity ($\varepsilon$) of the dielectric material between the plates also directly impacts capacitance.; The unit of capacitance is Farad (F).

Advantages: High storage efficiency in compact designs; Predictable behavior based on physical geometry

Disadvantages: Physical constraints limit the maximum area achievable in integrated circuits; Decreasing distance too much risks dielectric breakdown

Applications: Filtering in power supplies; Energy storage in DC circuits; Signal coupling in electronics

Additional Info: The area $A$ refers to the overlapping area of the two conducting plates.. Option B is incorrect because capacitance is inversely proportional to distance $d$, not directly proportional.

Answer: A is correct — Capacitance is directly proportional to the area of cross-section of the plates as shown in $C = \frac{\varepsilon A}{d}$.

Exam Tip: Always check for 'inverse' vs 'direct' proportionality in physics formulas; remember that $d$ is in the denominator, hence it is inversely proportional.

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