What is Inductance Formula: Definition and Applications

When subjected to a changing magnetic field, a conductor can induce a voltage through inductance, a fundamental concept in physics and electrical engineering. The inductance formula has been developed to quantify this phenomenon by relating inductance, conductor turns, and magnetic flux. Circuits involving coils and transformers require understanding the inductance formula. Our article discusses inductance's wide-ranging applications, including power generation and magnetic resonance imaging (MRI), and delves into how it is defined, explored, and the inductance formula.

What is the Inductance Formula?

It calculates an inductance L of a coil or solenoid in response to a current flow, which represents its ability to store energy as magnetic fields. This formula can be expressed as follows:

𝐿=𝜇⋅𝑁2⋅𝐴𝑙

e, N, A, and I refer to coil length, cross-sectional area, and permeability, respectively, of the core material and the coil. There is a direct relationship between coil inductance and the square of the number of turns and cross-sectional area, and an inverse relationship between coil length and coil inductance.

Circuits containing inductive components must be designed and analyzed using the inductance formula. As energy is stored in magnetic fields and current is resistive, inductors are essential components in electronic circuits. Oscillators, filters, and power supplies are among the simplest applications of these circuits. Different electrical and electronic systems have different requirements for voltage regulation, signal filtering, and energy storage for inductors, which engineers can meet by manipulating parameters such as the number of turns and core material. You can learn more on our website about inductance.

Types of Inductance

Electric circuits are characterized by inductance, which has a variety of properties and uses. The main types are explained in detail below:

Self-Inductance

Changing currents in circuits induce an electromotive force (EMF) which induces self-inductance. A self-inductance measurement is made by measuring the coefficient L in henries (H). There are several factors that affect self-inductance, including coil turns, cross sectional area, and core permeability. An example of a component that exhibits self-inductance is a coil or a solenoid.

Mutual Inductance

An EMF is induced in another circuit by a changing current in one circuit. Mutual inductance is measured in henries (H), as well as with the coefficient of mutual inductance, denoted by M M. Depending on the coil configuration, number of turns and permeability of materials, mutual inductance can be measured. The transformer is the classic example of a device that transfers energy from its primary windings to its secondary windings through mutual inductance.

Distributed Inductance

The distributed nature of circuit elements leads to distributed inductance in transmission lines and distributed circuits. Transmission lines or circuits with large inductances do not have a concentrated inductance, but rather are distributed throughout the circuit or transmission line. An impedance and delay are determined by the distributed inductance of a transmission line or circuit, which varies with its physical dimensions and materials.

Eddy Current Inductance

During magnetic field changes, eddy currents are generated in conductors due to eddy current inductance. Due to these currents, both the original magnetic field and the current from these currents have their own magnetic fields, resulting in inductive effects. When alternating magnetic fields are used in transformers and magnetic bearings, eddy current inductance is a consideration, causing losses and inefficiencies.

Geometric Inductance

Inductance resulting from geometric placement of conductors in a circuit is also known as parasitic inductance or stray inductance. At high frequencies, inductive effects can significantly affect circuit performance without being intentional between adjacent conductors, lines, or components. Radio frequency systems, integrated circuits (ICs), and high-speed digital circuits are affected by geometric inductance.

Applications

Power Supplies and Converters

A power supply circuit and converter cannot function without inductors:

DC-DC Converters: Converting one voltage level to another is made more efficient by inductors, which are used in buck converters, boost converters, and buck-boost converters. In electronic devices, they improve stability and efficiency by smoothing out fluctuations in current and voltage.

Switching Regulators: By rapidly switching transistors on and off, inductors regulate output voltage efficiently in switching regulators. Inductor-based voltage regulation results in minimal power loss with precise voltage regulation during the on phase and release during the off phase.

Filtering: For clean, stable power delivery to sensitive electronic components, inductors are used in filter circuits, such as LC filters.

Signal Processing Circuits

There are a number of circuits that use inductors in signal processing:

Audio Equipment: An inductor filters out unwanted frequencies and improves the quality of audio in amplifiers, equalizers, and crossovers. As a result, high-fidelity audio can be reproduced due to their ability to shape the frequency response of audio signals.

Radio Frequency (RF) Circuits: The inductor plays an essential role in the operation of oscillators, filters, and antennas in RF circuits. A radio system, cellular phone, or Wi-Fi router is not reliable without them because they control frequency response, selectivity, and impedance matching.

Digital Signal Processing (DSP): Digital signals are transmitted and received accurately with the help of inductors in high-speed communication systems.

RFID and Wireless Communication

Wireless communication technologies and RFID (Radio Frequency Identification) systems depend heavily on inductors:

RFID Tags and Readers: Radio waves are generated and detected by inductors in RFID tags and readers for wirelessly identifying and tracking objects. RFID tags communicate with readers through resonant circuits, which facilitate data collection, asset tracking, and inventory management applications.

Wireless Charging: A wireless charger such as a Qi wireless charger for smartphones or another electronic device would not function without an inductor. Wireless power transfer over short distances is facilitated by magnetic fields generated and received by transmitter and receiver coils.

Sensors and Actuators

Sensors and actuators use inductors in a variety of ways:

Inductive Sensors: 

Detecting metallic objects using inductive proximity switches, metal detectors, and proximity sensors rely on changes in inductance to detect their presence. Security devices, automotive systems, and industrial automation all use them.

Solenoids and Actuators: Electrical energy is converted into linear or rotational motion by inductors, which are used in solenoids and electromechanical actuators. Actuators, door locks, valves, and relays all use these components.

Inductors are used in solenoids and electromechanical actuators to convert electrical energy into linear or rotational motion.

Unit of Inductance

Henrys (H) are used to represent inductances. In addition to his significant contributions to electromagnetism, Joseph Henry is the name of this unit. When the current changes at a rate of one amp per second in a circuit, one henry (1 H) may induce an electromotive force (EMF) of one volt.

The henry is a relatively large unit of inductance, so smaller values are often expressed in millihenries (mH) or microhenries (µH), where 1 mH equals 0.001 H and 1 µH equals 0.000001 H.

Power supplies and transformers typically use inductors with higher inductance values, while filters and oscillators typically use inductors with lower inductance values. Designing and specifying electronic circuits and systems that use inductive components requires an understanding of the unit of inductance.

Wrapping Up

To conclude, understanding the inductance formula is crucial in various applications of electronics, telecommunications, and electromechanical devices, as it quantifies a conductor's ability to store energy in a magnetic field. The permeability of material, coil turns, and cross-sectional area can be analyzed by engineers to design and analyze circuits that perform and are efficient.

Inductance shapes the behavior of electrical circuits and enables innovative technologies in everything from power supplies and converters to signal processing circuits. Electrical engineering advancements are made possible by the principles of inductance, which enable new solutions for a wide range of markets.