capacitance
Summary
Capacitance is a capacitor's ability to store charge per unit potential difference, C = Q/V, measured in farads. For a parallel-plate capacitor, C = κε₀A/d, so it rises with plate area and dielectric constant and falls with plate separation.
Detail
Meaning: Capacitance is the charge a capacitor holds for each volt across its plates. It is set by geometry and the material between the plates, not by the charge or voltage present. A dielectric weakens the field for a given charge, lowering V and so raising C.
Equation: C = Q/V = κε₀A/d, where C is capacitance (farad, F), Q is the charge magnitude on one plate (coulomb), V is the potential difference (volt), κ is the dielectric constant (unitless), ε₀ is the permittivity of free space (F/m), A is plate area (m²), and d is plate separation (m). Stored energy is U = ½CV² (joule). Series: 1/Ceq = 1/C₁ + 1/C₂. Parallel: Ceq = C₁ + C₂.
On the MCAT: A passage changes a parallel-plate capacitor (pulls the plates apart, inserts a dielectric) and asks what happens to C, Q, V, field or energy. First check whether a battery stays connected. Connected: V is fixed and Q changes. Disconnected: Q is fixed and V changes.
Common confusion: Students think doubling the voltage doubles the capacitance. It doubles the charge, and C = Q/V stays the same. Also, the series and parallel rules are the reverse of those for resistors: capacitors in parallel add directly.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- College Physics (Serway and Vuille)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.