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is crucial concept in electromagnetic theory, describing how coils store energy in magnetic fields. It's influenced by factors like coil turns, area, and core material, with the as its unit of measurement.

Energy storage in inductors depends on their and current, following a quadratic relationship. Inductors generate when current changes, opposing the change due to . This property makes them valuable for smoothing current fluctuations in circuits.

Inductance

Inductance of coil configurations

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  • Inductance () quantifies a coil's capacity to store energy in its magnetic field
    • Unit of measurement is the (H)
  • Factors influencing inductance:
    • Number of turns () in the coil
      • Higher number of turns increases inductance (, )
    • Cross-sectional area (AA) of the coil
      • Greater area leads to higher inductance (toroid, )
    • Length (ll) of the coil
      • Increased length reduces inductance (solenoid, )
    • Type of core material
      • Materials with higher (μ\mu) enhance inductance (, )
  • Inductance calculation formula: L=μN2AlL = \frac{\mu N^2 A}{l}
    • μ\mu represents the core material's permeability
      • μ=μ0μr\mu = \mu_0 \mu_r, with μ0\mu_0 as free space permeability and μr\mu_r as relative permeability of the material (vacuum, air, iron)
  • occurs when the changing magnetic field of one coil induces a voltage in another nearby coil

Energy storage in inductors

  • Energy stored in an () is determined by its inductance (LL) and the current (II) passing through it
  • Stored energy calculation formula: UL=12LI2U_L = \frac{1}{2} L I^2
    • Energy is measured in joules (J)
  • The stored energy increases quadratically with increasing current
  • Inductors can store substantial energy in their magnetic fields (superconducting magnetic energy storage, pulse power systems)

Inductor emf generation

  • of induction states that a changing magnetic field induces an (emf) in a conductor
  • A changing current through an inductor creates a changing magnetic field
    • This changing magnetic field induces an emf within the inductor
  • The induced emf counteracts the change in current
    • This phenomenon is known as Lenz's law
    • The induced emf's direction opposes the change that caused it ( in motors, in circuits)
  • The induced emf's magnitude (ε\varepsilon) is proportional to the rate of change of current (dIdt\frac{dI}{dt}) and the inductance (LL)
    • Formula: ε=−LdIdt\varepsilon = -L \frac{dI}{dt}
    • The negative sign signifies that the emf opposes the current change
  • This opposing emf explains why inductors resist abrupt changes in current
    • Inductors are used to smooth current fluctuations in circuits (power supply filters, noise reduction)
  • is the process of generating voltage through a changing magnetic field
  • is the total magnetic field passing through a given area
  • The in inductive circuits determines how quickly current changes in response to voltage changes
  • is the opposition to current flow in AC circuits due to inductance

Key Terms to Review (39)

(peak) emf: Peak electromotive force (emf) is the maximum voltage generated in an AC generator during one cycle. It occurs when the rate of change of magnetic flux through the coil is at its highest.
$ ext{mu}_0$: $ ext{mu}_0$ is the permeability of free space, a fundamental physical constant that describes the magnetic properties of a vacuum. It is a crucial parameter in various electromagnetic phenomena and is essential for understanding the behavior of magnetic fields, particularly in the context of Ampere's law and inductance.
$ ext{mu}_r$: $ ext{mu}_r$ is the relative permeability, a dimensionless quantity that describes the ability of a material to support the formation of a magnetic field within itself. It is a fundamental property that determines the inductance of a component or circuit.
$ u$: $ u$ is a Greek letter that is commonly used to represent various physical quantities in physics, including magnetic permeability, which is a measure of a material's ability to support the formation of a magnetic field within itself. This term is particularly important in the context of inductance, as it is a crucial parameter in determining the inductance of a coil or inductor.
$ rac{dI}{dt}$: $ rac{dI}{dt}$ represents the rate of change of current with respect to time, also known as the time derivative of current. This term is crucial in understanding the concept of inductance, which describes the ability of a circuit component to store energy in the form of a magnetic field and oppose changes in the flow of electric current.
$arepsilon$: $arepsilon$ is a Greek letter that represents a small quantity or change in a physical quantity. In the context of physics, it is often used to denote an induced electromotive force (emf) or voltage that opposes the change in the magnetic field, as described by Faraday's law of induction and Lenz's law. It is also associated with the concept of back emf in electric motors and the inductance of a circuit.
$L$: $L$ is a fundamental quantity that describes the inductance of an electrical circuit or component. Inductance is a measure of the magnetic field produced by an electric current, and it is a crucial concept in understanding the behavior of circuits involving inductors, transformers, and other electromagnetic devices.
$N$: $N$ is a fundamental quantity in the study of inductance, a property of electrical circuits that describes the ability of a conductor to store energy in the form of a magnetic field. $N$ is a crucial parameter that directly affects the magnitude of the induced voltage in a circuit, making it an essential concept in understanding electromagnetic induction and the behavior of inductive components.
$U_L$: $U_L$ is the voltage drop across an inductor in an electrical circuit. It represents the potential difference that arises due to the changing current flowing through the inductor, which opposes this change in current according to Faraday's law of electromagnetic induction.
A: In the context of physics, the symbol $A$ often represents area. Area is a two-dimensional measurement that describes the extent of a surface or shape. Understanding area is crucial for applying principles like Bernoulli’s equation, where it helps relate flow speed and pressure in fluids, and in inductance, where it impacts the magnetic field strength in a coil based on its cross-sectional area.
Back EMF: Back EMF, or back electromotive force, is an induced voltage that opposes the change in current flowing through an inductor. It is a fundamental concept in understanding the behavior of electrical circuits involving inductors, such as in the context of 23.6 Back EMF, 23.9 Inductance, and 23.10 RL Circuits.
Characteristic time constant: The characteristic time constant in an RL circuit, denoted as $\tau$, is the time it takes for the current to reach approximately 63% of its final value after a sudden change in voltage. It is calculated as the ratio of inductance $L$ to resistance $R$, i.e., $\tau = \frac{L}{R}$.
Electromagnetic Induction: Electromagnetic induction is the process by which a changing magnetic field induces an electromotive force (EMF) in a conductor, causing an electric current to flow. This phenomenon is the fundamental principle behind the operation of many electrical devices and systems, including transformers, generators, and motors.
Electromotive force: Electromotive force (emf) is the energy provided by a source per unit charge to move electrons through a circuit. It is measured in volts (V) and drives the current around the circuit.
Electromotive Force: Electromotive force (EMF) is the voltage or potential difference generated in an electrical circuit, typically by a source of electrical energy such as a battery or generator. It represents the driving force that causes electric charge to flow through a circuit, enabling the conversion of other forms of energy into electrical energy.
EMF: EMF, or electromotive force, is a fundamental concept in electricity and magnetism that represents the potential difference or voltage generated by a source of electrical energy, such as a battery or a generator. It is the driving force that causes electric charges to move through a circuit, and it is a crucial factor in understanding various electrical phenomena, including terminal voltage, Faraday's law of induction, eddy currents, and inductance.
Faraday's Law: Faraday's law describes the relationship between a changing magnetic field and the electric field it induces. It states that the magnitude of the induced electromotive force (emf) in a circuit is proportional to the rate of change of the magnetic flux through the circuit.
Ferrite Core: A ferrite core is a type of magnetic core used in various electronic devices and circuits, particularly in inductors and transformers. It is composed of a ferromagnetic ceramic material that has high magnetic permeability, low electrical conductivity, and high electrical resistance, making it an effective material for applications involving alternating current (AC) magnetic fields.
Helical Coil: A helical coil is a type of electromagnetic coil that is wound in a spiral or helix-like shape. It is commonly used in various electrical and electronic devices to create magnetic fields and store energy through the phenomenon of inductance.
Henry: The henry (H) is the SI unit of inductance. It measures the amount of electromotive force generated when the current through an inductor changes by one ampere per second.
Henry: The henry (H) is the SI unit of inductance, which is a measure of the amount of magnetic flux produced by an electric current. It is named after the American scientist Joseph Henry, who independently discovered the principle of electromagnetic induction around the same time as Michael Faraday.
Inductance: Inductance is a property of an electrical conductor that opposes a change in current. It is measured in henrys (H) and results from the magnetic field generated by the current flowing through the conductor.
Inductance: Inductance is a property of an electrical circuit or component that opposes changes in the electric current flowing through it. It is a measure of the magnetic field generated by a current-carrying conductor, which in turn induces a voltage that opposes the change in current.Inductance is a fundamental concept in understanding the behavior of electrical circuits, particularly in the context of RL circuits and RLC series AC circuits.
Inductor: An inductor is a passive electrical component that stores energy in its magnetic field when electric current flows through it. It typically consists of a coil of wire and opposes changes in current.
Iron Core: An iron core is a crucial component in the design of transformers and inductors. It is a solid or laminated iron structure that serves to concentrate and guide the magnetic flux generated by the coils, improving the efficiency and performance of these electromagnetic devices.
Lenz's Law: Lenz's law is a fundamental principle in electromagnetism that describes the direction of the induced current or electromotive force (emf) generated by electromagnetic induction. It states that the direction of the induced current is always such that it opposes the change in the magnetic field that caused it, in accordance with Faraday's law of induction.
Magnetic field strength inside a solenoid: Magnetic field strength inside a solenoid is the intensity of the magnetic field created within a coil of wire when an electric current passes through it. It is uniform and parallel to the axis of the solenoid.
Magnetic flux: Magnetic flux is the measure of the quantity of magnetism, taking into account the strength and extent of a magnetic field. It is calculated as the product of the magnetic field and the area through which it passes, perpendicular to the field.
Magnetic Flux: Magnetic flux is a measure of the total amount of magnetic field passing through a given surface or area. It represents the strength and distribution of a magnetic field and is a fundamental concept in the study of electromagnetism and its applications.
Magnetic Permeability: Magnetic permeability is a measure of the ability of a material to support the formation of a magnetic field within itself. It is a fundamental property that describes the degree of magnetization of a material in response to an applied magnetic field.
Mutual inductance: Mutual inductance is the phenomenon where a change in the current in one coil induces a voltage in another coil that is magnetically coupled to it. It is quantified by the mutual inductance coefficient, which depends on factors like the number of turns in each coil and their relative positioning.
Mutual Inductance: Mutual inductance is a measure of the magnetic coupling between two electrical circuits or coils. It describes the amount of induced electromotive force (emf) in one circuit due to a changing current in a neighboring circuit, and is a fundamental concept in the study of electromagnetic induction.
Planar Spiral Inductor: A planar spiral inductor is a type of electrical inductor that is fabricated in a flat, spiral-shaped configuration on a planar substrate, such as a printed circuit board or a semiconductor chip. This design allows for the creation of compact and integrated inductors that can be easily incorporated into electronic circuits and devices.
Reactance: Reactance is a measure of the opposition to the flow of alternating current (AC) in an electrical circuit, caused by the inductive or capacitive elements of the circuit. It represents the imaginary component of the circuit's impedance, which is distinct from the real component known as resistance.
Self-inductance: Self-inductance is the property of a coil (or circuit) that allows it to oppose the change in current flowing through it by generating an electromotive force (EMF). This EMF is proportional to the rate of change of current.
Self-Inductance: Self-inductance is a property of an electrical circuit or component that describes the ability of the circuit or component to generate an opposing electromotive force (emf) within itself when the current flowing through it changes. It is a measure of how much the magnetic field created by a changing current in a circuit opposes changes in that current.
Solenoid: A solenoid is a type of electromagnet consisting of a coil of wire wound into a tight spiral. When an electric current flows through the coil, it creates a magnetic field inside the solenoid, which can be used to produce a strong and uniform magnetic field in a specific region of space.
Time Constant: The time constant is a fundamental concept in the study of electrical circuits, particularly those involving resistors and capacitors (RC circuits) or inductors and resistors (RL circuits). It represents the time required for a circuit to reach a specific percentage of its final value when subjected to a step change in input.
Toroid: A toroid is a three-dimensional geometric shape that resembles a doughnut or a torus. It is formed by rotating a closed curve, typically a circle, around an axis that does not intersect the curve. Toroids have a wide range of applications, particularly in the context of inductance, which is a fundamental concept in electromagnetism and electrical circuits.
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Glossary
Glossary
23.10 RL Circuits