Book Reference : Pages 127-129Book Reference : Pages 127-129

1.1. To understand how we generate alternating To understand how we generate alternating current (A.C.)current (A.C.)

2.2. To begin to appreciate some of the To begin to appreciate some of the advantages of A.C.advantages of A.C.

A simple A.C. generator consists of a spinning A simple A.C. generator consists of a spinning rectangular coil in a uniform magnetic field.rectangular coil in a uniform magnetic field.

A slip ring / brush A slip ring / brush arrangement is used to arrangement is used to allow electrical allow electrical connections to be connections to be maintained as the coil maintained as the coil spinsspins

As the coil spins the flux As the coil spins the flux linkage changes linkage changes continuouslycontinuously

When the When the normal to the plane normal to the plane of the coil is at an of the coil is at an angle angle to the field lines the flux linkage is given to the field lines the flux linkage is given by:by:

NN = BAN cos = BAN cos

If the coil is spinning with a steady frequency f If the coil is spinning with a steady frequency f then at time t after then at time t after =0, =0, =2=2ft soft so

NN = BAN cos 2 = BAN cos 2ftft

The flux linkage changesThe flux linkage changes

with time as shown : with time as shown :

+BAN

-BAN

T (1/f)

T/2 (1/2f)

The gradient of the flux linkage (cosine) curve is The gradient of the flux linkage (cosine) curve is the change in flux linkage per second Nthe change in flux linkage per second N/t /t which as we have seen before represents the which as we have seen before represents the induced EMF.induced EMF.

Mathematically the gradient of the curve is the Mathematically the gradient of the curve is the first differential and so the alternating induced first differential and so the alternating induced EMF is given byEMF is given by

= = 00 sin 2 sin 2ftft

Where Where 00 is the peak EMF. Note this can be re- is the peak EMF. Note this can be re-written using an angular frequency written using an angular frequency = = 00 sin sin tt

[acsin.swf]

The diagram below shows how the induced emf changes The diagram below shows how the induced emf changes with timewith time

The induced EMF is The induced EMF is zero when the sides zero when the sides of the coil are of the coil are parallel to the field parallel to the field lineslines

The EMF is a The EMF is a maximum when the maximum when the sides of the coil cut sides of the coil cut at right angles across at right angles across the field linesthe field lines

When the induced EMF is at a maximum, the When the induced EMF is at a maximum, the induced EMF in induced EMF in eacheach wire on wire on eacheach side is given by side is given by BBllv. Where B is the magnetic flux density, v. Where B is the magnetic flux density, ll is the is the length of the wire and v is the speed.length of the wire and v is the speed.

The coil has 2 sides & N turns and so the maximum The coil has 2 sides & N turns and so the maximum induced EMF is given by :induced EMF is given by :

00 = 2N B = 2N Bllvv

This shows that the maximum induced EMF will This shows that the maximum induced EMF will increase with the strength of the magnetic field, increase with the strength of the magnetic field, the number of turns, the size of the coil & the the number of turns, the size of the coil & the speed (frequency) of rotationspeed (frequency) of rotation

D.C. generators can be made by using a split ring D.C. generators can be made by using a split ring commutator (much like the electric motor)commutator (much like the electric motor)

EMF1 cycle

The induced EMF does The induced EMF does not reverse direction not reverse direction each half cycle because each half cycle because the connection the connection arrangement for the arrangement for the split commutator also split commutator also reverses each half cyclereverses each half cycle

Note this DC is very Note this DC is very “lumpy” “lumpy” and typically and typically smoothing capacitors smoothing capacitors will be used to reduce will be used to reduce the bumpsthe bumps

While the underlying principles are the same, power While the underlying principles are the same, power stations actually generate electricity slightly differently.stations actually generate electricity slightly differently.

Firstly, they generate what is Firstly, they generate what is called “three phase” electricity. called “three phase” electricity. Three sets of coils are offset by Three sets of coils are offset by 120120 & generate 3 separate & generate 3 separate EMFs which are 120EMFs which are 120 out of out of phase with each otherphase with each other

Secondly, to remove the need for slip rings, the 3 sets of Secondly, to remove the need for slip rings, the 3 sets of coils are kept stationary (they are called stators). coils are kept stationary (they are called stators).

In this case the magnetic In this case the magnetic field must move to cause a field must move to cause a change in flux linkage. An change in flux linkage. An electromagnet, (called the electromagnet, (called the rotor) is driven from a DC rotor) is driven from a DC source and spins insides the source and spins insides the stators. stators.

The electricity leaving the power station is “stepped up” The electricity leaving the power station is “stepped up” to a very high voltage (lower current) by a to a very high voltage (lower current) by a transformertransformer. . The three phases are distributed to factories and local The three phases are distributed to factories and local substations where it is “stepped down” by a further substations where it is “stepped down” by a further transformer.transformer.

It is common for the local substation to supply different It is common for the local substation to supply different streets with one each of the different phasesstreets with one each of the different phases

In contrast industry will use all three phases together for In contrast industry will use all three phases together for high powered machineryhigh powered machinery

The coil of an AC generator has 80 turns, a length of The coil of an AC generator has 80 turns, a length of 65mm & a width of 38mm. It spins at 50Hz in a magnetic 65mm & a width of 38mm. It spins at 50Hz in a magnetic field with a flux density of 130mTfield with a flux density of 130mT

Calculate the maximum flux linkage through the coilCalculate the maximum flux linkage through the coil

[26 mWb][26 mWb]

Show that each side of the coil moves at a speed of 6 m/sShow that each side of the coil moves at a speed of 6 m/s

Show that the peak voltage is 8.1VShow that the peak voltage is 8.1V

A rectangular coil of N turns, with an area A spins at a constant A rectangular coil of N turns, with an area A spins at a constant frequency f in a uniform magnetic field which has a flux density of frequency f in a uniform magnetic field which has a flux density of B. Complete the tableB. Complete the table

Time Orientation of the coil

Flux linkage Induced EMF

0 Parallel to field +0

1/4f Perpendicular to field +BAN

1/3f Parallel to field

3/4f Perpendicular to field

Flux linkage 0, 0, -BANFlux linkage 0, 0, -BAN

EMF : 0 -EMF : 0 -00, 0, 0