Introduction
Capacitance is the property of a system that allows it to store electric charge. Capacitors are widely used in circuits to store and release energy, filter signals, and manage voltage fluctuations.
Definition of Capacitance
Capacitance is defined as the ratio of the charge stored on each conductor to the potential difference between them:
C = Q / V
Parallel-Plate Capacitor
A parallel-plate capacitor with plate area A and separation d has capacitance:
C = ε₀ (A / d) (in vacuum)
With a dielectric of relative permittivity εr inserted:
C = εrε₀ (A / d)
Energy Stored in a Capacitor
The energy stored in a capacitor is given by:
- U = ½ QV
- U = ½ CV²
- U = Q² / 2C
Capacitors in Series
For capacitors in series, the reciprocal of the equivalent capacitance is the sum of reciprocals:
1 / Ceq = 1 / C₁ + 1 / C₂ + …
Capacitors in Parallel
For capacitors in parallel, the total capacitance is the sum of individual capacitances:
Ceq = C₁ + C₂ + …
Dielectrics
Dielectrics increase capacitance by reducing the effective electric field inside the capacitor. They also prevent breakdown by allowing higher voltages to be applied without discharge.
Example Problem
Example: A parallel-plate capacitor with area 0.02 m² and separation 1 mm is filled with a dielectric of εr = 4. Find its capacitance.
Solution:
C = εrε₀ (A / d) = (4)(8.85 × 10⁻¹²)(0.02 / 0.001) ≈ 7.08 × 10⁻¹⁰ F
Summary
- Capacitance measures charge stored per unit potential difference.
- Parallel-plate capacitors depend on area, separation, and dielectric constant.
- Energy stored in capacitors can be expressed in different equivalent forms.
- Capacitors combine differently in series and parallel connections.