ElectroMagnetic Induction

Magnetic InductionAs the magnet moves back and forth a current is said

to be INDUCED in the wire.

Magnetic FluxThe first step to understanding the complex nature of

electromagnetic induction is to understand the idea of magnetic flux.

Flux is a general term associated with a FIELD that is bound by a certain AREA. So MAGNETIC FLUX is any AREA that has a MAGNETIC FIELD passing through it.

AB

Faraday’s LawFaraday learned that if you change any part of the flux over time

you could induce a current in a conductor and thus create a source of EMF (voltage, potential difference). Since we are dealing with time here were a talking about the RATE of CHANGE of FLUX, which is called Faraday’s Law.

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Nt

BANt

N B

Useful ApplicationsAC Generators use Faraday’s

law to produce rotation and thus convert electrical and magnetic energy into rotational kinetic energy. This idea can be used to run all kinds of motors. Since the current in the coil is AC, it is turning on and off thus creating a CHANGING magnetic field of its own. Its own magnetic field interferes with the shown magnetic field to produce rotation.

Lenz’s LawLenz's law gives the direction of the induced emf and current

resulting from electromagnetic induction. In effect, electro magnetically induced emf and hence the current flows in a coil or a circuit in such a direction that the magnetic field setup by it always opposes the cause which produces it.

tN B

Lenz’s Law

Inductance

The ratio of magnetic flux to current is the inductance.

Inductance is measured in henry. 1 H = 1 T m2 / A More common, 1 H = 1 V / A / s

The inductance can be derived for an ideal solenoid.

IL

lrN

lANL

220

20

Induced EMF

Faraday’s law gives the magnitude of the induced emf. Depends on rate of change

The definition of inductance gives a relationship between voltage and current. More useful in circuits

Inductive elements in a circuit act like batteries. Stabilizes current

tM

tIL

Self InductanceThe property of the coil due to which it opposes the change of current flowing through it is called self inductanceSuppose that we have a coil having N turns carrying a current I

That means that there is a magnetic flux through the coil

This flux can also be written as being proportional to the current

ILN B

with L being the self inductance having the same units as the mutual inductance

If the current changes, then the magnetic flux through the coil will also change, giving rise to an induced emf in the coil

This induced emf will be such as to oppose the change in the current with its value given by

dtdIL

If the current I is increasing, then

If the current I is decreasing, then

Self Inductance

There are circuit elements that behave in this manner and they are called inductors and they are used to oppose any change in the current in the circuit

As to how they actually affect a circuit’s behavior will be discussed shortly

Self Inductance

Mutual Inductance

The property of the coil due to which it opposes the change of current in neighboring coil is called mutual inductance.

The definition of inductance applies to transformers. Mutual inductance vs self-

inductance

Mutual inductance applies to both windings.

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AN BN

R

tNV M

BB

tIM

tN M

B

Transformers A transformer is a device that changes ac electric power at

one voltage level to ac electric power at another voltage level through the action of a magnetic field.

There are two or more stationary electric circuits that are coupled magnetically.

It involves interchange of electric energy between two or more electric systems

Transformers provide much needed capability of changing the voltage and current levels easily. They are used to step-up generator voltage to an appropriate

voltage level for power transfer. Stepping down the transmission voltage at various levels for

distribution and power utilization.

TransformersProbably one of the greatest inventions of all time is the

transformer. AC Current from the primary coil moves quickly BACK and FORTH (thus the idea of changing!) across the secondary coil. The moving magnetic field caused by the changing field (flux) induces a current in the secondary coil.

If the secondary coil has MORE turns than the primary you can step up the voltage and runs devices that would normally need MORE voltage than what you have coming in. We call this a STEP UP transformer.

We can use this idea in reverse as well to create a STEP DOWN transformer.

Single-Phase Transformers

• A transformer is a magnetically operated machine.

• All values of a transformer are proportional to its turns ratio.

Single-Phase Transformers

• The primary winding is connected to the incoming power supply.

• The secondary winding is connected to the driven load.

• This is an isolation transformer. The secondary winding is physically and electrically isolated from the primary winding.

Working of a transformer

1. When current in the primary coil changes being alternating in nature, a changing magnetic field is produced

2. This changing magnetic field gets associated with the secondary through the soft iron core

3. Hence magnetic flux linked with the secondary coil changes.

4. Which induces e.m.f. in the secondary.

Single-Phase Transformers

• The isolation transformer greatly reduces voltage spikes.

Single-Phase Transformers• Each set of windings (primary and secondary) is formed from loops of wire

wrapped around the core.• Each loop of wire is called a turn.• The ratio of the primary and secondary voltages is determined by the ratio of

the number of turns in the primary and secondary windings.• The volts-per-turn ratio is the same on both the primary and secondary

windings.

Constructional detail : Shell type

• Windings are wrapped around the center leg of a laminated core.

Core type

• Windings are wrapped around two sides of a laminated square core.

The Equivalent Circuit of a Transformer

The losses that occur in transformers have to be accounted for in any accurate model of transformer behavior.

1. Copper (I2R) losses. Copper losses are the resistive heating losses in the primary and secondary windings of the transformer. They are proportional to the square of the current in the windings.

2. Eddy current losses. Eddy current losses are resistive heating losses in the core of the transformer. They are proportional to the square of the voltage applied to the transformer.

3. Hysteresis losses. Hysteresis losses are associated with the rearrangement of the magnetic domains in the core during each half-cycle. They are a complex, nonlinear function of the voltage applied to the transformer.

4. Leakage flux. The fluxes which escape the core and pass through only one of the transformer windings are leakage fluxes. These escaped fluxes produce a self-inductance in the primary and secondary coils, and the effects of this inductance must be accounted for.

voltageload-novoltageload-fullvoltageload-noregulationVoltage

1

212 N

NVV

p

s

p

sNN

VV

Secondary voltage on no-load

V2 is a secondary terminal voltage on full load

1

21

21

21

regulationVoltage

NNV

VNNVSubstitute we have

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Voltage Regulation

% 100%

nl rated

rated

E Vreg per unit regulationV

regulation per unit

Enl = no-load output voltage

Vrated = voltmeter reading at the output terminals when the transformer is supplying the rated apparent power

25

When the breaker is open, no current flows in Req,LS , jXeq,LS , or ZLOAD,LS , therefore

Vout = VLS = E’LS = Enl

26

With rated load on the secondary, E’LS = ILSZeq,LS + VLS

ILS = rated low-side current at a specified power factor

VLS = rated low-side voltage

Zeq,LS = equivalent impedance of the transformer referred to the low-side

E’LS = no-load low-side voltage

Transformer EfficiencyTransformer efficiency is defined as (applies to motors, generators and transformers):

%100in

out

PP

%100

lossout

out

PPP

Types of losses incurred in a transformer:Copper I2R lossesHysteresis lossesEddy current losses

Therefore, for a transformer, efficiency may be calculated using the following:

%100cos

cos xIVPP

IV

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SS