- Electrical Machines Tutorial
- Electrical Machines - Home
- Basic Concepts
- Electromechanical Energy Conversion
- Energy Stored in a Magnetic Field
- Singly-Excited and Doubly Excited Systems
- Rotating Electrical Machines
- Faraday’s Laws of Electromagnetic Induction
- Concept of Induced EMF
- Fleming’s Left Hand and Right Hand Rules
- Transformers
- Electrical Transformer
- Construction of Transformer
- EMF Equation of Transformer
- Turns Ratio and Voltage Transformation Ratio
- Ideal and Practical Transformers
- Transformer on DC
- Losses in a Transformer
- Efficiency of Transformer
- Three-Phase Transformer
- Types of Transformers
- DC Machines
- Construction of DC Machines
- Types of DC Machines
- Working Principle of DC Generator
- EMF Equation of DC Generator
- Types of DC Generators
- Working Principle of DC Motor
- Back EMF in DC Motor
- Types of DC Motors
- Losses in DC Machines
- Applications of DC Machines
- Induction Motors
- Introduction to Induction Motor
- Single-Phase Induction Motor
- Three-Phase Induction Motor
- Construction of Three-Phase Induction Motor
- Three-Phase Induction Motor on Load
- Characteristics of 3-Phase Induction Motor
- Speed Regulation and Speed Control
- Methods of Starting 3-Phase Induction Motors
- Synchronous Machines
- Introduction to 3-Phase Synchronous Machines
- Construction of Synchronous Machine
- Working of 3-Phase Alternator
- Armature Reaction in Synchronous Machines
- Output Power of 3-Phase Alternator
- Losses and Efficiency of 3-Phase Alternator
- Working of 3-Phase Synchronous Motor
- Equivalent Circuit and Power Factor of Synchronous Motor
- Power Developed by Synchronous Motor
- Electrical Machines Resources
- Electrical Machines - Quick Guide
- Electrical Machines - Resources
- Electrical Machines - Discussion
Faraday’s Laws of Electromagnetic Induction
When a changing magnetic field links to a conductor or coil, an EMF is produced in the conductor or coil, this phenomenon is known as electromagnetic induction. The electromagnetic induction is the most fundamental concept used to design the electrical machines.
Michael Faraday, an English scientist, performed several experiments to demonstrate the phenomenon of electromagnetic induction. He concluded the results of all experiments into two laws, popularly known as Faraday’s laws of electromagnetic induction.
Faraday’s First Law
Faraday’s first law of electromagnetic induction provides information about the condition under which an EMF is induced in a conductor or coil. The first law states that −
When a magnetic flux linking to a conductor or coil changes, an EMF is induced in the conductor or coil.
Therefore, the basic need for inducing EMF in a conductor or coil is the change in the magnetic flux linking to the conductor or coil.
Faraday’s Second Law
Faraday’s second law of electromagnetic induction gives the magnitude of the induced EMF in a conductor or coil and it may be states as follows −
The magnitude of the induced EMF in a conductor or coil is directly proportional to the time rate of change of magnetic flux linkage.
Explanation
Consider a coil has N turns and magnetic flux linking the coil changes from $\mathit{\phi _{\mathrm{1}}}$ weber to $\mathit{\phi _{\mathrm{2}}}$ weber in time t seconds. Now, the magnetic flux linkage ($\mathit{\psi }$) to a coil is the product of magnetic flux and number of turns in the coil. Therefore,
$$\mathrm{\mathrm{Initial\: magnetic\: flux\: linkage,}\mathit{\psi _{\mathrm{1}}}\:=\:\mathit{N\phi _{\mathrm{1}}}}$$
$$\mathrm{\mathrm{Final\: magnetic\: flux\: linkage,}\mathit{\psi _{\mathrm{2}}}\:=\:\mathit{N\phi _{\mathrm{2}}}}$$
According to Faraday’s law of electromagnetic induction,
$$\mathrm{\mathrm{Induced\: EMF,}\mathit{e}\propto \frac{\mathit{N\phi _{\mathrm{2}}}-\mathit{N\phi} _{\mathrm{1}}}{\mathit{t}}\cdot \cdot \cdot (1)}$$
$$\mathrm{\Rightarrow \mathit{e}\:=\:\mathit{k}\left ( \frac{\mathit{N\phi _{\mathrm{2}}}-\mathit{N\phi} _{\mathrm{1}}}{\mathit{t}} \right )}$$
Where, k is a constant of proportionality, its value is unity in SI units.
Therefore, the induced EMF in the coil is given by,
$$\mathrm{\mathit{e}\:=\:\frac{\mathit{N\phi _{\mathrm{2}}}-\mathit{N\phi} _{\mathrm{1}}}{\mathit{t}}\cdot \cdot \cdot (2)}$$
In differential form,
$$\mathrm{\mathit{e}\:=\:\mathit{N}\frac{\mathit{d\phi }}{\mathit{dt}}\cdot \cdot \cdot (3)}$$
The direction of induced EMF is always such that it tends set up a current which produces a magnetic flux that opposes the change of magnetic flux responsible for inducing the EMF. Therefore, the magnitude and direction of the induced EMF in the coil is to be written as,
$$\mathrm{ \mathit{e}\:=\:\mathit{-N}\frac{\mathit{d\phi }}{\mathit{dt}}\cdot \cdot \cdot (4)}$$
Where, the negative (-) sign shows that the direction of the induced EMF is such that it opposes the cause that produces it, i.e., the change in the magnetic flux, this statement is known as Lenz’s law. The equation (4) is the mathematical representation of Lenz’s law.
To Continue Learning Please Login
Login with Google