P
PromptSchola Prompt-based STEM subjects mastery
Sign In Register for Free
Electricity · Physics

A capacitor stores charge and field energy.

Capacitance measures how much charge a system can store per volt. Geometry matters, and the energy ends up in the electric field between conductors.

This topic

Capacitance

Define capacitance, analyze the parallel-plate capacitor, compare common geometries, and interpret energy storage.

Definition
What capacitance means
Capacitance is a property of a conductor arrangement. It tells you how much charge is stored for a given potential difference.
  • Definition: C = Q/ΔV
  • Units: farad (C/V)
  • Depends on geometry and materials, not on Q or V separately
  • Physical picture: more “ability to separate charge” means larger C
Start nano-lesson C is set by the geometry.
Classic
Parallel-plate capacitors
For two large parallel plates separated by a small gap, the field is nearly uniform between plates. This leads to a simple capacitance formula.
  • Uniform-field approximation and when it is valid
  • Relation between E, ΔV, and plate separation
  • Result: C ∝ A/d (bigger area, smaller gap → larger C)
  • Fringing fields: what is ignored in the ideal model
Start nano-lesson Think “area helps, distance hurts.”
Geometry
Capacitance with different geometries
Different conductor shapes change how the electric field fills space and therefore change capacitance. The key idea is still charge per voltage.
  • Isolated sphere: capacitance set by size
  • Coaxial cylinders: cylindrical symmetry picture
  • Concentric spheres: radial fields and voltage difference
  • What matters: field distribution between conductors
Start nano-lesson Same definition, new field geometry.
Energy
Energy stored in a capacitor
Charging a capacitor requires work. That work becomes energy stored in the electric field, not “in the charges” themselves.
  • Energy grows as charge accumulates
  • Energy expressions in terms of C, Q, and ΔV
  • Interpretation: energy density in the field (preview)
  • Qualitative: why sparks and discharges release energy
Start nano-lesson Energy is in the field between plates.
Practice
Practice & Exercises
Practice using C = Q/ΔV, analyzing parallel plates, and applying energy relationships.
  • Compute Q from C and ΔV (and reverse)
  • Parallel-plate scaling: how C changes with A and d
  • Concept checks on fringing and model assumptions
  • Energy computations using equivalent formulas
  • Exam-style capacitance and energy sets
Open practice sets Write C = Q/ΔV first, then choose a model.