01 Electricity Fundamentals ALT405 505

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Introduction to ElectromagneticEnergy Conversion

Devarajan Srinivasan (Srini)[email protected]

ALT 405/505

Power Conditioners for Alternative Energy

Systems
mailto:[email protected]:[email protected]


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Power Conditioners for Renewable Energy Systems 01-2

Introduction to Electromagnetic Energy

Conversion

Fundamentals of electricity

AC circuits

Single phase

Three phase

DC machines

Synchronous machines


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Fundamentals of Electricity

Units of electricity

Electrostatics

Electromagnetism


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Units of Electricity

Voltage

Volt (V): The electric potential of a point

is defined as work done in bringing apositive charge of one coulomb from

infinity to that point.

Coulomb

JouleVolt

1

11


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Current

Ampere (A): The current, which when

flowing in each of two infinitely longparallel conductors situated in vacuum

and separated 1 meter, produces on

each conductor a force of 2 x 10

-7

N permeter length.


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Power and Energy

Joule (J): Energy required to maintain a

current of 1 Ampere through a resistanceof 1 Ohm for 1 second

Watt (W): Rate of doing work

second

JouleWatt

1

11


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Frequency

Hz: Cycles per second

Resistance

Ohms (): A conductor is said to have a

resistance of 1 ohm if it permits a current

of 1 Ampere when 1 Volt is impressedacross it.


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Charge

Coulomb (C): The charge of 6.242 x 1018

electrons. Hence, the charge of a singleelectron is 1.602 x 10-19Coulomb


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Capacitance

Farad (F): The capacitance which requires

a charge of 1 Coulomb to establish apotential difference of 1 Volt


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Flux

Weber (Wb): A unit magnetic pole of 1

Weber, placed in vacuum at a distance ofone meter from a similar and equal pole

repels it with a force of 1/4ONewton


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Inductance

Henry (H): A coil has a self-inductance of

one Henry if a current of 1 Ampereflowing through it produces flux-linkages

of 1 Weber-turn in it


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Electrostatics

Deficiency or excess of electrons in abody is called its charge

Electrons = Negative charged accordingto convention

Surplus of electrons = Body is negativecharged

Deficit of electrons = Body is positivecharged


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Electrostatics

Electrostatics: Science of electricity atrest

Charges are not in motionCharges exert a force on other charges


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Electrostatics

Laws of electrostatics

Like charges repel

Unlike charges attractThe force exerted between two pointcharges is

Proportional to product of strengths

Inversely proportional to square of distance

Inversely proportional to permittivity ()


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Electrostatics

Electric field

Consider an isolatedpoint charge in amedium

Point charge: sphere body, radiuszero

Medium (three-dimensional)

For example: air

Other examples: vacuum, gas, insulators,conductors, semi-conductors, etc.


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Electrostatics

Electric field

The isolated point charge will exert aforce on any charge that enters themedium (neighborhood of the charge)

Hence, for any external charge, themediumaround the point charge is

always under stress (under the effect of aforce)


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Electrostatics

Electric field

At each point in space around theisolated charge

An unit positive chargeexperiences aforceof certain magnitude and direction

These lines of force in the medium

around the charge is called the electricfield


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Electrostatics

Electric field

Electric intensity

At any point within the electric fieldThe force experienced by a unit positivecharge at that point

Hence, the unit of electric intensity (E) is

N/C


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Electrostatics

Electric potentialConsider an electric field generated by anisolated positive charge +Q in a medium

(air).The field extends to infinity.

The force exerted on a positive charge,+q1, at infinity iszero.


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Electrostatics

Electric potentialAs +q1 is bought closer to +Q, it isrepelled by +Q

+q1 is now under the effect of theelectric field

Workhas to be done against this force ofrepulsion to move the charge closer to+Q


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Electrostatics

Electric potentialPerform work, by overcoming therepulsive force of the field to move

charge +q1 to an arbitrary point close to+Q

Hence, when charge +q1 is bought tosome point in the electric field, it has

some electrical potential energy


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Electrostatics

Electric potentialPotential at any point in the electric field

is equal to the work done

against the electric field

in bringing a positive charge of one coulomb

from infinity to that point

Potential is work done per unit charge

C

JV

1

11


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Electrostatics

Electric potential

Electric field is also called

potential gradientIn other words, electric

intensity is equal to the

rate of fall of potential inthe direction of the lines

of force

m

V

C

NE

C

mN

C

J

V


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Electrostatics

Capacitor

two conducting surfaces (plates)

separated by an insulating medium(dielectric)


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Electrostatics

Capacitor

If anytwo conducting surfaces are notconnected, a capacitor is formed

Insulated wires in a cable or conduit

Traces on circuit boards

Device terminals

Terminal blocks, connectors

Switches

Coil windings


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Electrostatics

Parallel plate capacitor

Battery

Negative: surplus of electronsPositive: deficit of electrons

Connect battery to capacitor plates:

there is a transient flow of electrons from

the positive plate to the negative plate

A potential difference is establishedbetween the capacitor plates


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Electrostatics

Capacitor

An electric field exists between the plates

corresponding to this potential differenceElectric field in the insulator

Charge (electrons)

Attracted to positive plates

Repelled from negative plates


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Electrostatics

Capacitor charging

Increase electric potential between

platesAdd electrons to negative plate

Remove electrons from positive plate

As the capacitor is charged, work is doneagainst the repulsion force of the plates

to strengthen the field


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Electrostatics

Capacitor discharging

Decrease electric potential between

platesRemove electrons from negative plate

Add electrons to positive plate

As the capacitor is discharged, work isderived from the attraction force of the

plates to collapse the field


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Electrostatics

Capacitor

Hence, electric energy is stored in the

electric field of a capacitorCharge capacitor to add to the storage by

strengthening the field

Discharge capacitor to remove from thestorage by collapsing the field


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Electrostatics

Capacitance

The property of a capacitor to store

electricityThe capacity of a capacitor

Defined as the charge required per unit

potential difference

V

QC


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Electrostatics

Capacitance

Q Coulomb of charge is required

To establish a potential difference of VVolts between its plates

then capacitance is:V

QC


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Electrostatics

Capacitance

The unit of capacitance is Farad

One Farad is the capacitance whichrequires a charge of one Coulomb to

establish a potential of one Volt between

its platesV

QC


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Electrostatics

Capacitors in series

C1, C2, C3 = capacitance of

three capacitors

V1, V2, V3 = voltage across

each capacitorV = voltage across

combination

C = combined capacitance

In series combination, the

charge on all capacitors is

the same

CVVCVCVCQ

CCCC

C

Q

C

Q

C

Q

C

Q

VVVV

332211

321

321

321

1111


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Electrostatics

Capacitors in parallel

C1, C2, C3 = capacitance of

three capacitors

Q1, Q2, Q3 = charge on

each capacitor

V = voltage across

combination

C = combined capacitance

In parallel combination,

the voltage on all

capacitors is the same

321

321

321

CCCC

VCVCVCCV

QQQQ


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Electrostatics

Energy stored in a capacitor

Charging of a capacitor requires energy

from the charging sourceThis energy is stored in the electric field

set up in the dielectric


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Electrostatics

Energy stored in a capacitor

Discharging the capacitor recovers this

energy and collapses the field

C

QQVCVW

JCVW

22

2

2

1

2

1

2

1

2

1


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Electrostatics

Current in a capacitor

Current is the rate of change of charge

tdiCv

dt

dvCCv

dt

d

dt

dQi

t

0

1

)(


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Electrostatics

A capacitor has the ability to store charge

Voltage across a capacitor is proportional tocharge, NOTcurrent

A capacitor can have voltage across it evenwhen there is no current flowing


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Electrostatics

Current flows through a capacitor, onlywhen the voltage across it is changing.

If dv/dt=0 (dc voltage), the current is zero.

Hence for dc circuits, the capacitor is anopen circuit


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Electrostatics

dv/dt = i/C

For a given current, the rate of change ofvoltage is inversely proportional to

capacitance.

Larger the C, the more difficult it is tochange V.

The voltage across a capacitor cannotchange instantaneously (dt = 0)


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Electromagnetism

Magnets (medium, body) always havea pair (two) of magnetic poles:

North pole

South pole

Electromagnetism: science of

electricity and magnetism


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Electromagnetism

Laws of magnetic force

Like poles repel

Unlike poles attractThe force between two magnetic poles ina medium is

Proportional to pole strengths

Inversely proportional to square of distance

Inversely proportional to the permeability


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Electromagnetism

Magnetic flux

The strength of a magnetic pole

The strength of a magnetic pole can bedefined by the force it exerts on

another pole


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Electromagnetism

Magnetic flux

Unit of magnetic flux is called Weber

One Weberthe strength of a magnetic pole

which when placed in vacuum

at a distance of 1 meterfrom a similar and equal pole

repels it with a force of 1/4O


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Electromagnetism

Magnetic field

Consider an isolatedpoint pole in amedium

Point pole: sphere magnet, radiuszero

Medium (three-dimensional)

For example: air

Other examples: vacuum, gas, ferrousmetals


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Electromagnetism

Magnetic field

The isolated point magnetic pole willexert a force on any pole that enters themedium (neighborhood of the pole)

Hence, for any external pole, the mediumaround the pole is always under stress

(under the effect of a force)


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Electromagnetism

Magnetic field

At each point in space around theisolated pole

A North-pole of one Wbexperiences aforceof certain magnitude and direction

These lines of force in the medium

around the pole charge is called themagnetic field


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Electromagnetism

Magnetic field

Magnetic field intensity

At any point within the magnetic fieldThe force experienced by a unit North-pole at that point

Hence, the unit of magnetic fieldintensity (H) is N/Wb


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Electromagnetism

Flux density (B)

The amount of flux (Wb)

passing per unit area through a planeat right angles to the flux

The unit of flux density is Tesla

T = Wb/m2


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Electromagnetism

Magnetic induction

Consider a magnetic field around a

magnetPlace a bar of zero-strength (zero Wb)

magnetic material in the magnetic field

The bar gets magnetized by aphenomenon called magnetic induction


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Electromagnetism

Permeability ()

A bar of magnetic material is placed in a

uniform fieldthe bar is magnetized

Uniform external field intensity = H (N/Wb)

Bar induced flux density = B (Wb/m2)

theAbsolute Permeabilityof the bar is defined

as

H

B


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Electromagnetism

Electric current and magnetismAny current carrying conductor sets up amagnetic field

The magnetic field is created in the mediumsurrounding the conductor (wire)

The strength of the magnetic field depends onthe current magnitude and permeability of themedium

The direction of the field depends on thecurrent direction


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Electromagnetism

Work law of magnetismConsider N (e.g. N = 5) straight parallelwires

In a medium (e.g. air)Each carrying constant I (e.g. I = 10 A)

A magnetic field is set up by the current

This field will exert a force on anymagnetic pole


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Electromagnetism

Work law of magnetismMove a magnetic pole in a closed path inthe magnetic field set up by the current

carrying conductorsWork is done, along this closed path

On the pole if moving against the fielddirection or

By the pole if moving in the field direction


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Electromagnetism

Work law of magnetismThe net work in Joules done on or by aunit North pole

in moving around any completed path inthe magnetic field

is equal to the ampere-turns linked withthe path

If the path includes all N conductors, theampere-turns = NI (e.g. 5*10 = 50 J)


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Electromagnetism

Force on two parallel conductorsConsider two parallel conductors carryingcurrents

Each conductor sets up a magnetic fieldThe magnetic fields set up by the twoconductors exerts a force between them

The work law can be used to determinethe force between the two conductors


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Electromagnetism

Force on two parallel conductorsTwo parallel conductors

attract each other if the currents flow in

the same directionrepeleach other if the currents flow inthe opposite direction


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Electromagnetism

Force on two parallel conductorsThe force between two such parallelconductors is

Proportional to the product of the currentstrengths

Proportional to the length of the conductors

Inversely proportional to the distance

between them


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Electromagnetism

One Amperethe current which when flowing in eachof

two infinitely longparallel conductorssituated in vacuum

separated by 1 meterbetween centers

produces on each conductor a force of 2x 10-7Newtonper meter length


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Electromagnetism

Magneto-motive force (mmf)mmf is the work done in joules

in carrying a unit magnetic pole

once around a magnetic path

Magnetic path is also called magneticcircuit

m

AT

Wb

NH

ATWb

mN

Wb

Jmmf


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Electromagnetism

Magneto-motive force (mmf)The unit of mmf is ampere-turns

It is the product of

the number of turns in a magnetic circuitand the current in A through those turns

m

AT

Wb

NH

ATWb

mN

Wb

Jmmf


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Electromagnetism

Magneto-motive force (mmf)Drives or tends to drive a flux through amagnetic circuit

Corresponds to emf in an electric circuitHence, mmf between two points can bemeasured

by the work done in Joules

in carrying a unit magnetic pole

from one point to the other


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Electromagnetism

Electromagnetic interaction

When a current carrying conductor

is placed in a magnetic fieldit experiences a force

which acts in a direction perpendicular to

both the direction of the current and thefield


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Electromagnetism

Electromagnetic interaction

If a conductor of length Lm

lies in a magnetic field of flux density BWb/m2

carries a current IA

the force on the conductor is F = BIL N


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Electromagnetism

Electromagnetic induction

Consider an electrical circuit (branch, one

loop) in a magnetic fieldThis circuit (loop) has some magnetic flux

linked to it

Within the area of the loopPerpendicular to the loop

d l f l


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Electromagnetism


Flux-linkages of a coil is the product

the number of turns of the coilAnd the flux linked with the coil (Wb-turns)

d l f l i i


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Electromagnetism


Whenever the magnetic flux linked with

a circuitChanges

an emf is always induced in it

dt

dNN

dt

de

)(

F d l f El i i


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Electromagnetism


The magnitude of the induced emf is

equal to the rate of change of flux-linkages

dt

dNN

dt

de

)(

F d l f El i i


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Electromagnetism


Lenzs law

The induced emf sets up a current

in such a direction

that magnetic effect produced by the current

opposes the very cause producing it

dt

dNN

dt

de

)(

F d t l f El t i it


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Electromagnetism

Inductance

Consider a coil

N turns wound on a magnetic material

carrying a constant dc current of I A

This produces an mmf of NI AT in themagnetic material

F d t l f El t i it


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Electromagnetism

Inductance

This mmf drives a flux of Wb in themagnetic circuit

NI produces flux density B (Wb/m2)depending on of the magnet

B = *A, where A is the cross sectional areaof the magnet

Hence, the coil has a flux-linkage of NWb-turns

F d t l f El t i it


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Electromagnetism

Inductance

If the current through is slowly changed:

The flux-linkages associated with the coil

changes

An emf is induced in the coil

The emf opposes the changein flux-linkage

and hence the changein current (Lenzs law)

F d t l f El t i it


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Electromagnetism

Inductance

The property of the coil to resist thechange of current through it is called self-

inductance

Inductance is defined as the flux-linkageper ampere in the coil

Inductance is a function of the magneticmaterial and dimensions of the coil

F ndamentals of Electricit


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Electromagnetism

Inductance

A coil is said to have a self-

inductance of one Henryif a current of 1 A

produces flux-linkage of 1

Wb-turn in it

t

dteL

i

dt

diLN

dt

de

L IN

HI

NL

0

1

)(



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Electromagnetism

Inductance

A coil is said to have a self-

inductance of one Henryif 1 V is induced in it

when current through it

changes at the rate of 1A/s

t

dteL

i

dt

diLN

dt

de

L IN

HI

NL

0

1

)(



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Electromagnetism

Inductors in series

L1, L2, L3 = Inductance of

three coils

V1, V2, V3 = voltage induced

across each coil

V = voltage across

combination

L = combined inductance

In series combination, thecurrent through each coil is

the same

321

321

321

LLLL

dt

diL

dt

diL

dt

diL

dt

diL

VVVV



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Electromagnetism

Inductors in parallel

L1, L2, L3 = Inductance of

three coils

V1, V2, V3 = voltage

induced across each coilV = voltage across

combination

L = combined inductance

In parallel combination,

the induced emf acrosseach coil is the same

321

321

3

3

2

2

1

1

1111

LLLL

dtdi

dtdi

dtdi

dtdi

dt

diL

dt

diL

dt

diL

dt

diLV



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Electromagnetism

Inductor charging

Coil with N turns and zero current

Slowly increase current from zero to Ithe self-induced emf opposes this change

Work must be done to overcome this

opposition and strengthen the magneticfield



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Electromagnetism

Inductor discharging

Coil with N turns and current I A

Slowly decrease current from I to zerothe self-induced emf opposes this change

and slows the collapse of flux (and flux-

linkages) till current is zero

Work is derived from the coil to collapse

the magnetic field



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Electromagnetism

Energy stored in magnetic field

Charge inductor to add to the storage

by strengthening the fieldDischarge inductor to remove from the

storage by collapsing the field



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Electromagnetism


Charging the inductor requires energy

from the charging sourceThis energy is stored in the magnetic field

of the inductor



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Electromagnetism


Discharging the inductor recovers this

energy and collapses the field

L

N

INLIW

JL IW

2

2

2

)(

2

1

2

1

2

1

2

1



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Electromagnetism

An inductor has the ability to store energy

Current through a coil is proportional to V-s(Wb-turn), NOTvoltage

An inductor can have current through it,even when there is no voltageacross it



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Electromagnetism

Voltage is induced across an inductor onlywhen the current through it is changing.

If di/dt = 0, the voltage is zero.

Hence for dc circuits, the inductor is a shortcircuit.



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Electromagnetism

di/dt = v/L

For a given induced voltage, the rate ofchange of current is inversely proportional

to inductance. Larger the L, the more difficult it is to

change i.

The current through an inductance cannotchange instantaneously (dt = 0)

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01 Electricity Fundamentals ALT405 505