Chapter 22: Mutual Inductance

22.1 Introduction

In this chapter, we will explore the concept of mutual inductance, which describes how the magnetic field generated by one coil affects another nearby coil. Mutual inductance plays an essential role in understanding transformers, which are used to convert alternating current (AC) voltages and currents in various applications, such as power transmission.

22.2 Mutual Inductance Basics

Mutual inductance occurs when the change in current in one coil generates a magnetic field that induces a voltage in a nearby coil. This phenomenon is due to Faraday’s law of electromagnetic induction, which states that a changing magnetic field generates an electromotive force (EMF) in a conducting loop.

22.3 Calculating Mutual Inductance

The mutual inductance between two coils can be calculated using the following formula:

where is the permeability of free space, and are the number of turns in each coil, is the overlapping area between the coils, and is the distance between the coils.

The induced EMF () in the second coil can be calculated using the following formula:

where is the change in current in the first coil, and is the time interval over which the change occurs.

22.4 Transformers

Transformers are electrical devices that use mutual inductance to transfer electrical energy from one coil (the primary) to another coil (the secondary) without any physical contact. The main purpose of a transformer is to change the voltage and current levels in an AC circuit.

Transformers consist of two coils wrapped around a shared magnetic core, which is typically made of laminated iron or ferrite. The primary coil is connected to an AC power source, while the secondary coil is connected to the load. The ratio of the number of turns in the primary coil to the number of turns in the secondary coil determines the voltage transformation ratio:

where and are the voltages across the primary and secondary coils, respectively.

22.5 Types of Transformers

There are two main types of transformers:

1. Step-up Transformers: These transformers increase the voltage from the primary to the secondary coil They are commonly used in power transmission to reduce the energy losses associated with high currents.
2. Step-down Transformers: These transformers decrease the voltage from the primary to the secondary coil They are commonly used in electronic devices that require lower voltage levels than provided by the main power source.

Chapter Summary

In this chapter, we examined the concept of mutual inductance, which occurs when the changing magnetic field generated by one coil induces a voltage in another nearby coil. We explored the principles behind transformers, which use mutual inductance to change voltage and current levels in AC circuits, and discussed the applications of step-up and step-down transformers. Understanding mutual inductance and transformers is essential for efficiently transferring electrical energy in various applications, including power transmission and electronics.

Continue to Chapter 23: RL and LC Circuits

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