What is the capacitance of a parallel-plate capacitor (vacuum), and how does a dielectric affect it?

What is the capacitance of a parallel-plate capacitor (vacuum), and how does a dielectric affect it?

• A. C = ε0 A / d
• B. C = ε0 A / (κ d)
• C. C = κ ε0 A / d
• D. C = κ ε0 A d

Answer: (C)

Capacitance for a parallel-plate capacitor depends on the geometry and the material between the plates. The general formula is C = ε A / d, where ε is the permittivity of the medium between the plates. In vacuum, ε = ε0, so the capacitance is C = ε0 A / d. If a dielectric with relative permittivity κ fills the space, the permittivity becomes ε = κ ε0, giving C = κ ε0 A / d. Since κ is typically greater than 1, the dielectric increases the capacitance by that factor. The other options misrepresent either the role of the dielectric, place κ incorrectly, or include a dimensionally incorrect term.

Capacitance for a parallel-plate capacitor depends on the geometry and the material between the plates. The general formula is C = ε A / d, where ε is the permittivity of the medium between the plates. In vacuum, ε = ε0, so the capacitance is C = ε0 A / d. If a dielectric with relative permittivity κ fills the space, the permittivity becomes ε = κ ε0, giving C = κ ε0 A / d. Since κ is typically greater than 1, the dielectric increases the capacitance by that factor. The other options misrepresent either the role of the dielectric, place κ incorrectly, or include a dimensionally incorrect term.