19.5 Capacitors and Dielectrics
3 min read•june 18, 2024
Capacitors are essential components in electrical circuits, storing electric charge and energy between two conducting plates. They're measured in farads and their depends on plate area, separation, and material. Understanding capacitors is crucial for grasping electrical energy storage.
Capacitors can be arranged in series or parallel, affecting total capacitance and charge distribution. Dielectrics increase capacitance and prevent . Energy storage in capacitors is proportional to capacitance and voltage squared, making them vital for power management in electronic devices.
Capacitor Fundamentals
Capacitance and charge storage
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- Capacitance () measures a device's ability to store electric charge
- Defined as the ratio of stored charge to applied voltage,
- Measured in farads (F), where 1 F = 1 C/V ( per )
- Capacitors store electric charge and energy in an between two conducting plates
- Plates are separated by an insulating material called a (air, paper, plastic)
- Connecting a voltage source causes positive charge to accumulate on one plate and negative charge on the other
- Opposite charges attract, but the dielectric prevents charge flow between plates
- Stored charge creates a potential difference (voltage) between the plates
- The between the plates maintains the separation of charges
Capacitance of parallel plate capacitors
- capacitance depends on plate area (), plate separation (), and ()
- Formula: , where F/m
- Capacitance is directly proportional to plate area
- Larger plate area () increases capacitance by providing more space for charge storage
- Capacitance is inversely proportional to plate separation
- Smaller distance () between plates increases capacitance by strengthening the electric field
Dielectrics and Capacitor Configurations
Dielectrics and capacitance increase
- Dielectrics are insulating materials placed between capacitor plates (air, paper, plastic, ceramic)
- Dielectrics increase capacitance by a factor called the ()
- Capacitance with a dielectric: , where
- Dielectrics have practical roles in capacitors:
- Prevent electrical breakdown (sparking) between plates at high voltages
- Allow higher voltage to be applied without discharge, increasing energy storage
- Increase capacitance and energy storage capacity for a given plate area and separation
- Dielectrics undergo when placed in an electric field, aligning their molecules
Problem-solving for capacitor configurations
- Charge stored in a capacitor:
- is charge (coulombs, C), is capacitance (farads, F), is voltage (volts, V)
- :
- Total capacitance is less than the smallest individual capacitance
- Inverse of total capacitance equals sum of inverses of individual capacitances:
- Voltage divides among capacitors in proportion to their capacitances
- :
- Total capacitance is the sum of individual capacitances:
- Voltage across each capacitor equals the source voltage
- Charge divides among capacitors in proportion to their capacitances
Energy Storage in Capacitors
- Capacitors store in their electric field
- The energy stored in a capacitor is given by:
- The on the plates affects the amount of energy stored
- The electric field strength between the plates is related to the stored energy
Key Terms to Review (27)
Capacitance: Capacitance is a measure of the amount of electric charge that can be stored in an electrical component or system. It is a fundamental concept in the study of electrostatics and the behavior of electric circuits. Capacitance is a crucial factor in understanding the storage and release of electrical energy, as well as the behavior of electrical components like capacitors.
Charge Density: Charge density is a measure of the amount of electric charge per unit volume or unit area in a given material or region of space. It is a fundamental concept in electromagnetism and is crucial in understanding the behavior of conductors, insulators, and capacitors.
Coulomb: Coulomb is the fundamental unit of electric charge, named after the French physicist Charles-Augustin de Coulomb. It is a measure of the amount of electric charge and is a crucial concept in understanding various topics in electricity and magnetism, such as static electricity, electric fields, electric potential, and the behavior of charged particles.
Coulomb force: Coulomb force, also known as the electrostatic force, is the force of attraction or repulsion between two charged particles. It follows an inverse-square law and is governed by Coulomb's law.
Dielectric: A dielectric is an insulating material that increases the storage capacity of a capacitor by reducing the electric field within it. Dielectrics are characterized by their ability to be polarized in the presence of an electric field.
Dielectric: A dielectric is an electrical insulator that can be polarized by an applied electric field. It is a material that does not conduct electric current under normal conditions, but it can support an electrostatic field by storing energy in the form of an electric field. Dielectrics play a crucial role in various topics related to electrostatics and capacitors.
Dielectric Constant: The dielectric constant is a measure of a material's ability to store electrical energy in an electric field. It is a dimensionless quantity that describes how an electric field affects, and is affected by, a dielectric medium. The dielectric constant is an important parameter in understanding the behavior of conductors, insulators, and capacitors.
Dielectric strengths: Dielectric strength is the maximum electric field that a material can withstand without experiencing electrical breakdown. It is typically measured in volts per meter (V/m).
Direction of polarization: Direction of polarization refers to the orientation of the electric field vector in an electromagnetic wave. It describes how the electric field oscillates as the wave propagates.
Elastic potential energy: Elastic potential energy is the energy stored in an object when it is deformed elastically, such as when a spring is stretched or compressed. It can be calculated using the formula $U = \frac{1}{2} k x^2$, where $k$ is the spring constant and $x$ is the displacement from equilibrium.
Electric Field: The electric field is a vector field that describes the force experienced by a stationary, positive test charge at any given point in space. It represents the strength and direction of the electric force exerted on a charged particle by other charges in the vicinity, and is a fundamental concept in the study of electromagnetism and the behavior of charged particles.
Electrical Breakdown: Electrical breakdown is the phenomenon where an insulating material or a gas loses its insulating properties and becomes conductive, allowing electric current to flow through it. This occurs when the applied electric field exceeds the material's breakdown strength, causing the formation of a conductive path.
Electrostatic force: Electrostatic force is the force of attraction or repulsion between two charged objects. It operates according to Coulomb's Law, which quantifies the magnitude of this force.
Electrostatic Force: Electrostatic force is the attractive or repulsive force that exists between electrically charged particles or objects. It is a fundamental force in nature that governs the behavior of static electricity and the interactions between charged entities.
Epsilon Naught: Epsilon naught, also known as the vacuum permittivity or the electric constant, is a fundamental physical constant that represents the electric permittivity of free space or a vacuum. It is a crucial parameter in the study of electromagnetism and the behavior of electric fields and charges.
Farad: The farad (symbol: F) is the unit of electrical capacitance in the International System of Units (SI). It measures the amount of electric charge that a capacitor can store for a given potential difference across its terminals.
Faraday cage: A Faraday cage is an enclosure made of conductive material that blocks external static and non-static electric fields by channeling electricity along and around the exterior. This effect is used to protect sensitive electronic equipment from electromagnetic interference.
Kappa: Kappa, denoted by the Greek letter κ, is a dimensionless constant that represents the relative permittivity or dielectric constant of a material. It is a crucial parameter in the study of capacitors and dielectrics, as it describes the ability of a material to store electrical energy when an external electric field is applied.
The value of kappa determines the capacitance of a capacitor and the behavior of electric fields within dielectric materials. Understanding the concept of kappa is essential for analyzing the performance and applications of capacitors and dielectric materials in various electrical and electronic systems.
Parallel Capacitors: Parallel capacitors are two or more capacitors connected in a parallel configuration, where the positive terminal of one capacitor is connected to the positive terminal of the other capacitors, and the negative terminal of one capacitor is connected to the negative terminal of the other capacitors. This arrangement allows the capacitors to share the same voltage but have individual charge and capacitance values.
Parallel plate capacitor: A parallel plate capacitor consists of two conductive plates separated by a dielectric material. It stores electrical energy in the electric field created between the plates.
Parallel Plate Capacitor: A parallel plate capacitor is a type of capacitor consisting of two conductive plates separated by an insulating material called a dielectric. This arrangement creates an electric field between the plates, allowing the capacitor to store electrical energy.
Permittivity of Free Space: The permittivity of free space, also known as the electric constant or the vacuum permittivity, is a fundamental physical constant that describes the ability of free space, or a vacuum, to support an electric field. It is a measure of the amount of electric flux generated per unit electric field strength and is a crucial parameter in many areas of electromagnetism and electrostatics.
Polar molecule: A polar molecule has a net dipole moment due to the uneven distribution of electrons between atoms with different electronegativities. This results in one end of the molecule having a partial positive charge and the other end having a partial negative charge.
Polarization: Polarization is a fundamental property of electromagnetic waves, including light, that describes the orientation of the electric field oscillations within the wave. It is a crucial concept that underlies many important phenomena in the fields of static electricity, electromagnetism, and optics.
Potential Energy: Potential energy is the stored energy an object possesses due to its position or state, which can be converted into kinetic energy or other forms of energy. This term is central to understanding various physical phenomena and energy transformations in the context of introductory college physics.
Series Capacitors: Series capacitors are a configuration where multiple capacitors are connected end-to-end in a single circuit path. This arrangement allows the capacitance values to be combined in a specific way, creating a total effective capacitance that can be used to store and release electrical charge.
Volt: A volt is the unit of electric potential difference, which measures the amount of electric potential energy per unit charge between two points in an electric circuit. It helps us understand how much energy is available to move electric charges through a conductor, connecting it to concepts like power, energy storage, and circuit behavior.