Capacitor design fundamentals: which single design change will increase the capacitance value of a parallel-plate capacitor, all else being equal?

Introduction / Context:
Capacitance measures a component’s ability to store electric charge per unit voltage. For the widely taught parallel-plate model, geometric and material parameters determine the capacitance. Knowing which adjustments raise the capacitance is crucial for design, tuning, and selection of capacitors in circuits.

Given Data / Assumptions:

• Parallel-plate capacitor approximation applies.
• Plate separation and dielectric permittivity remain unchanged unless stated.
• We compare the effect of changing a single parameter.

Concept / Approach:
The ideal formula for a parallel-plate capacitor is C = epsilon * A / d, where epsilon is the absolute permittivity (epsilon = epsilon_r * epsilon_0), A is plate area, and d is plate separation. From this, increasing A increases C linearly, decreasing d increases C, and using a higher-permittivity dielectric increases C. Changing frequency or applied voltage does not change the intrinsic capacitance of a linear capacitor; those affect reactance Xc = 1 / (2 * pi * f * C) and stored energy E = 0.5 * C * V^2, respectively, but not C itself.

Step-by-Step Solution:

Verification / Alternative check:
Doubling plate area doubles capacitance in the ideal model. Practical capacitors use stacked or rolled plates to maximize effective area for higher C values, confirming the principle in real-world designs.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing frequency-dependent reactance with capacitance, and assuming voltage level alters C. Only geometry and dielectric properties set C for linear capacitors.

Final Answer:
Increasing the area of the plates