Parallel-plate capacitor dependence – Area and spacing Statement: “Capacitance is directly proportional to plate area and plate separation.” Assess the statement.

Introduction / Context:
Geometry strongly influences capacitor value. Designers select plate areas and spacings to achieve target capacitance and voltage ratings. This question probes the correct proportionalities.

Given Data / Assumptions:

• Parallel-plate capacitor with uniform dielectric of permittivity ε = ε0εr.
• Neglect fringing for the basic formula.
• Variables: A = plate area, d = plate separation.

Concept / Approach:

The well-known relation is C = εA/d. Capacitance is directly proportional to area A and inversely proportional to separation d. The statement claims direct proportionality to both A and d, which is incorrect.

Step-by-Step Solution:

Verification / Alternative check:

Energy density u = (1/2) * ε * E^2 and E = V/d. For a given V, larger d reduces E and stored charge per volt, consistent with smaller C.

Why Other Options Are Wrong:

Air or temperature do not change the sign of the proportionalities; different geometries (coaxial, spherical) still keep C inversely related to distance between conductors.

Common Pitfalls:

Memorization slip: mixing up series/parallel effects with geometry; forgetting that higher voltage rating usually requires larger spacing, which lowers C.

Final Answer:

False.