capacitances

Capacitance is the property of a system to store electric energy per unit voltage. In electronics, a capacitor is a device that stores energy as an electric field, described by its capacitance C, measured in farads. The basic relation is Q = C V, and the energy stored is E = 1/2 C V^2. For alternating current, the impedance of a capacitor is Z = 1/(jωC), so its reactance is X_C = 1/(2π f C).

Capacitance depends on geometry and the dielectric material between the conductors. For a parallel-plate capacitor, C = ε_r ε_0 A/d, where ε_r is the dielectric constant, ε_0 is the vacuum permittivity, A is the plate area, and d is the separation. Real capacitors can include parasitic elements such as equivalent series resistance (ESR) and equivalent series inductance (ESL), as well as leakage resistance.

When multiple capacitors are connected, their effective capacitance combines according to the network: in series, 1/C_eq = Σ(1/C_i); in parallel, C_eq = Σ C_i. Capacitances may vary with frequency, temperature, and applied voltage, and are described by tolerances and temperature coefficients.

Common capacitor types include ceramic (such as multilayer ceramic capacitors), film, electrolytic, tantalum, mica, and supercapacitors. Each type offers trade-offs among size, voltage rating, stability, ESR, cost, and intended application.

Capacitances are used for energy storage, filtering and decoupling, coupling signals between stages, timing and frequency-selective circuits, and impedance matching in RF systems.