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Electromagnetic Induction and Transformers: Calculating Induced EMF, Exercises of Mathematical Physics

Solution available with explanation

Typology: Exercises

2021/2022

Uploaded on 07/03/2024

rododer738
rododer738 🇮🇳

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Answer
Step 1 of 2
Introduction
An electrical device called a transformer uses electromagnetic induction t o move
electrical energy from one circuit to another. It comprises two or more insulated wire
coils, called windings, wound around a shared magnetic core made of a high-
permeability material like iron or steel, which enhances the magnetic coupling
between t he windings.
Given:
The f requency
The relative permeability of core
The current in the core
Expalantion
The primary winding connects to t he input voltage source, while the secondary
winding links to the load or the device requiring the transformed electrical energy.
The voltage in the secondary winding varies based on the t urn ratio between the
primary and secondary windings. If the secondary winding has more t urns than the
primary, it becomes a step-up transformer, increasing the voltage. Conversely, if the
secondary has fewer turns than t he primary, it becomes a step-down transformer,
reducing the voltage.
f
= 60
Hz
μr
= 4000
I
0= 50
A
pf3

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Question

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Answer

Step 1 of 2

Introduction

An electrical device called a transformer uses electromagnetic induction to move electrical energy from one circuit to another. It comprises two or more insulated wire coils, called windings, wound around a shared magnetic core made of a high- permeability material like iron or steel, which enhances the magnetic coupling between the windings.

Given:

The frequency The relative permeability of core The current in the core

Expalantion

The primary winding connects to the input voltage source, while the secondary winding links to the load or the device requiring the transformed electrical energy. The voltage in the secondary winding varies based on the turn ratio between the primary and secondary windings. If the secondary winding has more turns than the primary, it becomes a step-up transformer, increasing the voltage. Conversely, if the secondary has fewer turns than the primary, it becomes a step-down transformer, reducing the voltage.

f = 60 Hz μr = 4000 I 0 = 50 A

Step 2 of 2

To determine the expression: The induced is given by;

The magnetic flux through the coil is;

For a straight long wire the magnetic field is given as;

From equations and ;

Now, the induced expression is;

emf emf

Vemf = −N dϕ dt

ϕ = ∫ s

B. ds

B =

μI 2 πr

xˆ.... (2)

ϕ = ∫

b a

ˆx^ ⋅^ μI 2 πr

. xcdrˆ

μIc 2 π [ln(r)]ba

μIc 2 π [ln(b) − ln(a)]

μIc 2 π ln( b a

emf

Vemf = −N d dt

μIc 2 π

ln( b a

) V

μcN 2 π ln(

b a

dI dt

V

μcNωI 0 2 π ln( b a ) sin ωt V