Electrical Machine Theory in PE Power

Electric machine theory in the PE Power exam includes some important laws and principles that govern the working and operations of different electrical machines, including motors, transformers, generators, etc.

We have already covered these topics individually, and this study guide will dig deeper into the prevailing principles and how they make these machines work as they do.

So, let’s start with the fundamentals of electrical machine theory in PE Power.

Basic Concepts of Electrical Machines

Electrical machine theory fundamentally deals with the principles and behavior of electromechanical systems that convert electrical energy into mechanical energy and vice versa.

This is not just a single theory but a set of theories encompassing many machines, including transformers, electric motors, and generators. The primary principles governing these machines are rooted in electromagnetic induction and the interaction of magnetic fields with conductors.

Principles of Electricity and Magnetism in a Nutshell

  • Electromagnetic Induction: Michael Faraday’s law of electromagnetic induction is the cornerstone of electrical machine theory. It states that a change in magnetic flux within a closed circuit induces an electromotive force (EMF) in the circuit.
  • Lorentz Force: This force acts on a conductor carrying current in a magnetic field, resulting in motion. It’s the principle behind electric motors.
  • Interaction of Magnetic Fields: The interaction between the magnetic fields produced by stator and rotor currents in motors and generators results in torque or electromotive force generation.

Types and Working of Different Electrical Machines

Electrical machines refer to every device that converts mechanical energy into electrical energy or vice versa, and they can also convert electrical energy from one form to another. In electrical machines theory in PE Power, they are classified into three categories.

  1. Generators
  2. Motors
  3. Transformers

The operation and principles of each type vary based on their construction and intended purpose or use cases.

1. Generators

Generators convert mechanical energy into electrical energy. This conversion is based on Faraday’s law of electromagnetic induction, which states that an electromotive force (EMF) is induced in a conductor that moves in a magnetic field.

Step by Step Operation
  • A prime mover (like a turbine) rotates the generator’s rotor.
  • The rotor’s movement within the stator’s magnetic field changes the magnetic flux linkage.
  • This change in flux induces an EMF in the stator windings.
  • The induced EMF generates alternating current (AC) electricity then supplied to the load.

2. Motors

Motors convert electrical energy into mechanical energy. The operation of motors is based on the Lorentz force principle, where a current-carrying conductor in a magnetic field experiences a force.

Step by Step Operation
  • Electrical power is supplied to the motor’s windings, creating a magnetic field.
  • The interaction of this field with the magnetic field of the rotor produces a torque.
  • This torque causes the rotor to rotate, converting the electrical energy into mechanical motion.
  • The mechanical output can drive various devices like pumps, fans, or conveyors.

3. Transformers

Transformers transfer electrical energy between two or more circuits through electromagnetic induction. They operate on the principle of mutual induction, where a changing magnetic field in one coil induces an EMF in another coil.

Step-by-Step Operation
  • AC voltage is applied to the primary winding, creating a varying magnetic field.
  • This magnetic field induces a varying magnetic flux in the transformer core.
  • The varying flux induces an EMF in the secondary winding due to electromagnetic induction.
  • The voltage across the secondary winding depends on the turn ratio between the primary and secondary windings.

Further Classification of Electrical Machines:

The electrical machines are further classified based on their construction and purpose. Let’s have a quick look at further categories.

  • AC Motors: Include induction motors (split-phase, capacitor start, and shaded pole) and synchronous motors. 
  • DC Motors: Include series, shunt, compound, and brushless DC motors.
  • Special Electrical Machines: These include stepper motors, servo motors, and linear motors, which are designed for specific industrial applications.

Each machine operates based on fundamental electromagnetic principles but is designed to perform specific functions in various applications. These machines’ efficiency, performance, and suitability depend on their design, construction materials, and the control methods employed in their operation. 

To understand how synchronous machines’ characteristics vary from asynchronous motors, read our detailed guide here.

Magnetic Fields and Electromagnetic Forces

Magnetic fields and electromagnetic forces are foundational concepts in electromagnetism, playing a central role in the operation of electrical machines. The key laws and phenomena governing these concepts include:

  • Faraday’s Law
  • Lenz’s Law
  • Principles of Mutual and Self-induction.

Let’s delve into each of these and their mathematical foundation.

1. Faraday’s Law of Electromagnetic Induction

It states that a change in magnetic flux through a loop induces an electromotive force (EMF) in the loop.


EMF=− dΦB/dt, 

where ΦB is the magnetic flux through the loop.

For instance, if the magnetic flux through a coil of 100 turns changes from 0.5 Wb to 0.1 Wb in 0.2 seconds, you can calculate the induced EMF as:

EMF=−N ΔΦB/Δt =−100×(0.1−0.5)/0.2 =200V

2. Lenz’s Law

It states that the direction of the induced EMF and current will be such that it opposes the change in flux that produced it.

Mathematically, Lenz’s Law is represented by the negative sign in Faraday’s Law, indicating the opposition to the change in flux.

3. Mutual Induction

It is the phenomenon where a change in current in one coil induces an EMF in a neighboring coil.


EMF(secondary coil) =−M dI(primary coil)/dt,


  • M is the mutual inductance, and 
  • I(primary) is the current in the primary or first coil.

The source current is produced in the Primary coil. Hence, the secondary coil’s EMF depends on the primary coil’s current.

For instance, If the current in the primary coil changes at a rate of 4 A/s and the mutual inductance is 0.5 H, you can find the induced EMF in the secondary coil:

EMF (sec) =−0.5×4=−2V

4. Self-Induction

Principle: It is the phenomenon where a change in current in a coil induces an EMF in the same coil.


EMF=−L dI/dt,

where L is the self-inductance of the coil.

There is only one coil in self-induction, so there is no debate about primary and secondary currents or voltages.

For instance, you can calculate the EMF induced in a coil with a self-inductance of 2 H when the current changes at a rate of 3 A/s:


You can also covert these formulas for voltage by substituting V=IR (Ohm’s Law).

5. Ampère’s Law

Ampère’s Law states that for any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.

It calculates the magnetic field produced by a given current distribution, such as in coils like solenoids and toroids.



6. Biot-Savart Law

The Biot-Savart Law relates the magnetic field generated by a steady current.

This law is crucial for calculating the magnetic field in scenarios where the current has an arbitrary shape and distribution, such as in a single loop or a wire segment.



Application of Ampere’s and Biot Sawat Laws – Selenoid and Toroid

Toroids and solenoids, through their distinct shapes and configurations, effectively utilize the principles of Ampère’s Law to generate magnetic fields required in various functionalities of electrical motors.

With their closed-loop structure, Toroids are efficient in minimizing external magnetic interference, while solenoids generate a uniform magnetic field crucial for precise electromagnetic applications.

Understanding their working principles and applications is fundamental to designing and operating efficient and effective electrical motor systems.

Let’s discuss each of these in detail.


Toroids and solenoids are integral components in electrical engineering, particularly in the design and function of electrical motors. Their significance and operation can be well understood through Ampère’s Law, which is central to the theory of electromagnetism.

A toroid, characterized by its donut-shaped coil, is essentially a wire loop often wound around a magnetic core. This configuration is crucial in electrical motors, primarily serving as inductors.

In electrical motors, toroids are employed to limit the fluctuations in current, which is crucial for the smooth and efficient operation of the motor. They are also used in filtering applications and as integral components of transformers within motor circuits.

The operational efficiency of toroids in these roles can be attributed to their unique shape and design, ensuring that their magnetic field is largely confined within the core.

This confinement is crucial as it minimizes the external magnetic fields, thereby reducing the electromagnetic interference with other components.

The working of a toroid can be understood through Ampère’s Law, which states that the magnetic field inside a closed loop is proportional to the electric current passing through the loop. 

The working of a toroid can be understood through Ampère’s Law, which states that the magnetic field inside a closed loop is proportional to the electric current passing through the loop.

Mathematically, this relationship is expressed as B=μ0NI/2πr, where B is the magnetic field, is the permeability of free space, N represents the number of turns in the toroid, and I is the current flowing through the coil. R is the radius of the toroid.


a solenoid is characterized as a long coil of wire wound in a helical shape. Solenoids find their application in electrical motors in creating controlled magnetic fields.

These fields are essential for operating the motor’s electromagnetic clutches and actuation mechanisms. The uniformity of the magnetic field inside a solenoid is a critical attribute that makes it suitable for these applications.

As governed by Ampère’s Law, the magnetic field within a solenoid is given by B=μ0nI, where n is the number of turns of the coil per unit length, and I is the current through the coil.

The uniform magnetic field generated along the solenoid axis is a direct outcome of its elongated helical shape, and this uniformity is pivotal in applications requiring precise and consistent electromagnetic force or motion, such as in the control mechanisms of motors.

Use-case of Electric Motor Generating Electrical Energy with Hydro Energy

To understand how the laws of electromagnetism influence electricity generation in a water dam (Hydro Power Generation), it’s essential to consider the entire system:

  • The dam (water storage body),
  • The generator,
  • Transformers. 

This system is a prime example of the practical application of Faraday’s Law, Ampère’s Law, and the principles of electromagnetic induction we discussed above.

Hydro Power Generator

In a typical hydroelectric power setup, a water dam stores potential energy in the form of water at a height. When this water is released, it flows through turbines, converting potential energy into mechanical energy.

The turbines are connected to generators, which work on the electromagnetic induction principle, as Faraday’s Law describes. When the turbine blades rotate, they turn the rotor (a series of magnets or electromagnets) inside the generator.

The rotation of the magnetic field around the stator (the stationary part of the generator, often a coil of wire) changes the magnetic flux through the stator. According to Faraday’s Law, a change in magnetic flux induces an electromotive force (EMF), generating alternating current (AC) electricity.

Transformation and Transmission

The electricity generated is usually at a voltage level different from that required for distribution. Here, transformers, working on the principle of mutual induction, step up the voltage for efficient transmission over long distances. The operation of transformers is a direct application of the principles of electromagnetic induction.

Combined System Efficiency:

The overall efficiency of this system, from potential energy in the dam to mechanical work performed by the motor, depends on the efficiency of each component. The turbines and generators must effectively convert mechanical energy to electrical energy, minimizing friction and electrical resistance losses.

The transformers must efficiently step up and down the voltage with minimal energy loss due to hysteresis and eddy currents.


This is it for Electrical Machines Theory in PE Power. To get a deeper understanding of the laws and principles that are discussed, don’t forget to read the dedicated guides on these topics attached.

These topics are highly correlated and implemented in other key areas of the PE Power exam. Therefore, understanding Electrical Machines Theory in PE Power, along with all the set of laws that govern the electromagnetic process, is crucial. 

For an effective and seamless PE Power Exam Preparation, explore what Study for FE offers as your go-to platform for PE Power exam preparation.


Licensed Professional Engineer in Texas (PE), Florida (PE) and Ontario (P. Eng) with consulting experience in design, commissioning and plant engineering for clients in Energy, Mining and Infrastructure.