Difference between revisions of "Capacitors"

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[[File:Electronic_components_capacitor.jpg|right|400px]]
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= Textbook =
= Textbook =
*[https://openstax.org/books/university-physics-volume-2/pages/8-introduction University Physics Volume 2: Chapter 8 - Capacitance]
*[https://openstax.org/books/university-physics-volume-2/pages/8-introduction University Physics Volume 2: Chapter 8 - Capacitance]
*[https://openstax.org/books/university-physics-volume-2/pages/10-5-rc-circuits University Physics Volume 2: Chapter 10.5 - RC Circuits]
 
= 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.
<math> C = \frac{Q}{V} </math>
*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.
<math> C = \frac{\varepsilon A}{d} </math>
*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.
<math> E = \frac{1}{2} C V^2 </math>
*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.
<math> u = \frac{1}{2} \varepsilon E^2 </math>
*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.
<math> \frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n} </math>
*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.
<math> C_{\text{eq}} = C_1 + C_2 + \cdots + C_n </math>
*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 =
= Videos =
== Capacitors ==
<youtube>ZrMltpK6iAw</youtube>
<youtube>BimpNou0orc</youtube>
== Capacitors in Series and in Parallel ==
<youtube>g7eNTwJGhio</youtube>
<youtube>zaT4JorVUz0</youtube>
== Build your own capacitor ==
<youtube>rG7N_Zv6_gQ</youtube>
<youtube>rG7N_Zv6_gQ</youtube>


= Simulations =
= Simulations =
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*[http://www.regentsprep.org/Regents/physics/phys03/aparplate/ Charged Parallel Plates]
*[http://www.regentsprep.org/Regents/physics/phys03/aparplate/ Charged Parallel Plates]
*[http://tutor-homework.com/Physics_Help/rc_circuit_simulation.html RC circuit simulator]
*[http://tutor-homework.com/Physics_Help/rc_circuit_simulation.html RC circuit simulator]
<br class="clear"/>
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Latest revision as of 13:40, 27 September 2024

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