Capacitors

From pwiki
Revision as of 13:40, 27 September 2024 by Brachers (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
Electronic components capacitor.jpg

Back to Electricity_and_Magnetism


Textbook

What is a Capacitor and what is Capacitance

A capacitor is an electronic component that stores electrical energy in an electric field, created between two conductive plates separated by an insulating material (called a dielectric). Capacitance is the measure of a capacitor's ability to store charge per unit voltage, typically measured in farads (F).

Capacitors are widely used in various applications, including:

  • **Energy storage** (e.g., in power supplies)
  • **Filtering** (e.g., in electronic circuits to smooth out fluctuations in voltage)
  • **Timing circuits** (e.g., controlling signal timing in oscillators)
  • **Signal coupling and decoupling** (e.g., in audio equipment).

Their ability to store and release energy quickly makes them essential in electronics.

Formulas

Capacitance Definition

The capacitance C of a capacitor is defined as the ratio of the charge Q stored on one plate to the voltage V across the plates.

  • Where:*
  • *C* is the capacitance (in farads, F)
  • *Q* is the charge (in coulombs, C)
  • *V* is the voltage (in volts, V)

Capacitance of a Parallel Plate Capacitor

For a parallel plate capacitor, the capacitance depends on the area A of the plates, the separation d between them, and the permittivity ε of the dielectric material between the plates.

  • Where:*
  • *C* is the capacitance (in farads, F)
  • *ε* is the permittivity of the dielectric material (in farads per meter, F/m)
  • *A* is the area of one plate (in square meters, m²)
  • *d* is the separation between the plates (in meters, m)

Energy Stored in a Capacitor

The energy E stored in a charged capacitor is proportional to its capacitance and the square of the voltage across it.

  • Where:*
  • *E* is the energy stored (in joules, J)
  • *C* is the capacitance (in farads, F)
  • *V* is the voltage (in volts, V)

Energy Density in a Capacitor

The energy density u represents the energy stored per unit volume in the electric field between the plates.

  • Where:*
  • *u* is the energy density (in joules per cubic meter, J/m³)
  • *ε* is the permittivity of the material (in farads per meter, F/m)
  • *E* is the electric field strength (in volts per meter, V/m)

Equivalent Capacitance in Series

For capacitors connected in series, the reciprocal of the total (or equivalent) capacitance is the sum of the reciprocals of the individual capacitances.

  • Where:*
  • *C_eq* is the equivalent capacitance (in farads, F)
  • *C_1, C_2, \dots, C_n* are the individual capacitances (in farads, F)

Equivalent Capacitance in Parallel

For capacitors connected in parallel, the total capacitance is the sum of the individual capacitances.

  • Where:*
  • *C_eq* is the equivalent capacitance (in farads, F)
  • *C_1, C_2, \dots, C_n* are the individual capacitances (in farads, F)

RC Circuits (Capacitor Discharge/Charging) (Voltage over Time)

See RC_Circuits


Videos

Capacitors

Capacitors in Series and in Parallel

Build your own capacitor


Simulations



Other Links


Back to Electricity_and_Magnetism