6.2 Inductors and inductance

Inductors are magnetic field powerhouses, storing energy when current flows through their coiled wire. They're the unsung heroes of electronics, smoothing power supplies and tuning radios. Their ability to resist current changes makes them essential in many circuits.

Inductance, measured in henries, is an inductor's superpower. It depends on coil turns, area, and core material. Understanding inductors is key to grasping how magnetic fields interact with electric currents, a fundamental concept in electrical engineering.

Inductor Fundamentals

Inductor Components and Characteristics

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• Inductor consists of a coil of wire that stores energy in a magnetic field when an electric current passes through it
  • Can be made with or without a core material (air, ferromagnetic materials like iron or ferrite)
  • Core materials with high permeability concentrate the magnetic field and increase inductance
• Inductance measures an inductor's ability to store energy in its magnetic field
  • Represented by the symbol $L$ and measured in henries (H)
  • $1 \text{ [henry](https://www.fiveableKeyTerm:Henry)} = 1 \text{ volt-second/ampere}$
  • Inductance depends on the number of turns in the coil, the coil's area, and the core material's permeability
• Henry is the SI unit of inductance
  • Named after American scientist Joseph Henry who discovered self-inductance
  • Defined as the inductance required to induce an electromotive force of one volt when the current is changing at a rate of one ampere per second

Inductor Applications

• Inductors are used in various electrical and electronic applications
  • Filter out AC ripple in power supplies (smoothing inductors)
  • Tune resonant circuits in radio and television receivers (tuning inductors)
  • Store energy in switched-mode power supplies and boost converters
  • Limit current in transformers and electric motors

Magnetic Fields and Induction

Magnetic Field Properties

• Magnetic field is a region around a magnet or current-carrying conductor where magnetic forces can be detected
  • Represented by magnetic field lines that show the direction and strength of the field
  • Magnetic field lines form closed loops and never cross each other
  • Magnetic field strength is measured in teslas (T) or gauss (G)
• Electromagnetic induction occurs when a changing magnetic field induces an electromotive force (EMF) in a conductor
  • Discovered by Michael Faraday in 1831
  • The induced EMF is proportional to the rate of change of the magnetic flux through the conductor
  • Faraday's law of induction: $\mathcal{E} = -N \frac{d\Phi}{dt}$, where $\mathcal{E}$ is the induced EMF, $N$ is the number of turns in the coil, and $\Phi$ is the magnetic flux

Lenz's Law

• Lenz's law states that the direction of the induced EMF is such that it opposes the change that caused it
  • If a magnetic field is increasing, the induced current will create a magnetic field that opposes the increase
  • If a magnetic field is decreasing, the induced current will create a magnetic field that opposes the decrease
  • Helps explain the negative sign in Faraday's law of induction
• Applications of Lenz's law include:
  • Eddy current brakes in trains and roller coasters
  • Electromagnetic damping in galvanometers and other sensitive instruments

Types of Inductance

Self-Inductance

• Self-inductance is the property of an inductor that opposes changes in the current flowing through it
  • Caused by the changing magnetic field created by the current itself
  • The self-induced EMF is proportional to the rate of change of the current: $V_L = L \frac{dI}{dt}$
  • Self-inductance is the ratio of the induced voltage to the rate of change of the current: $L = \frac{V_L}{dI/dt}$
• Factors affecting self-inductance:
  • Number of turns in the coil (more turns, higher inductance)
  • Cross-sectional area of the coil (larger area, higher inductance)
  • Permeability of the core material (higher permeability, higher inductance)

Mutual Inductance

• Mutual inductance occurs when the magnetic field created by one inductor induces an EMF in another nearby inductor
  • The mutual inductance depends on the geometry of the inductors and their relative positions
  • Mutual inductance is represented by the symbol $M$ and measured in henries (H)
  • The induced EMF in the secondary coil is given by: $V_2 = M \frac{dI_1}{dt}$, where $I_1$ is the current in the primary coil
• Applications of mutual inductance:
  • Transformers for stepping up or down AC voltages
  • Coupled inductors in filters and impedance matching networks
  • Wireless power transfer systems (e.g., charging pads for smartphones)