Book Reference : Pages To understand how we generate alternating current (A.C.) 2.To begin to appreciate some of the advantages of A.C.

A simple A.C. generator consists of a spinning rectangular coil in a uniform magnetic field. A slip ring / brush arrangement is used to allow electrical connections to be maintained as the coil spins As the coil spins the flux linkage changes continuously

When the normal to the plane of the coil is at an angle  to the field lines the flux linkage is given by: N  = BAN cos  If the coil is spinning with a steady frequency f then at time t after  =0,  =2  ft so N  = BAN cos 2  ft The flux linkage changes with time as shown : +BAN -BAN T (1/f) T/2 (1/2f)

The gradient of the flux linkage (cosine) curve is the change in flux linkage per second N  /t which as we have seen before represents the induced EMF. Mathematically the gradient of the curve is the first differential and so the alternating induced EMF is given by  =  0 sin 2  ft Where  0 is the peak EMF. Note this can be re- written using an angular frequency  =  0 sin  t [acsin.swf]

The diagram below shows how the induced emf changes with time The induced EMF is zero when the sides of the coil are parallel to the field lines The EMF is a maximum when the sides of the coil cut at right angles across the field lines

When the induced EMF is at a maximum, the induced EMF in each wire on each side is given by B l v. Where B is the magnetic flux density, l is the length of the wire and v is the speed. The coil has 2 sides & N turns and so the maximum induced EMF is given by :  0 = 2N B l v This shows that the maximum induced EMF will increase with the strength of the magnetic field, the number of turns, the size of the coil & the speed (frequency) of rotation

D.C. generators can be made by using a split ring commutator (much like the electric motor) EMF 1 cycle The induced EMF does not reverse direction each half cycle because the connection arrangement for the split commutator also reverses each half cycle Note this DC is very “lumpy” and typically smoothing capacitors will be used to reduce the bumps

While the underlying principles are the same, power stations actually generate electricity slightly differently. Firstly, they generate what is called “three phase” electricity. Three sets of coils are offset by 120  & generate 3 separate EMFs which are 120  out of phase with each other

Secondly, to remove the need for slip rings, the 3 sets of coils are kept stationary (they are called stators). In this case the magnetic field must move to cause a change in flux linkage. An electromagnet, (called the rotor) is driven from a DC source and spins insides the stators.

The electricity leaving the power station is “stepped up” to a very high voltage (lower current) by a transformer. The three phases are distributed to factories and local substations where it is “stepped down” by a further transformer. It is common for the local substation to supply different streets with one each of the different phases In contrast industry will use all three phases together for high powered machinery

The coil of an AC generator has 80 turns, a length of 65mm & a width of 38mm. It spins at 50Hz in a magnetic field with a flux density of 130mT Calculate the maximum flux linkage through the coil [26 mWb] Show that each side of the coil moves at a speed of 6 m/s Show that the peak voltage is 8.1V

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 B. Complete the table TimeOrientation of the coil Flux linkageInduced EMF 0Parallel to field +0+0 1/4fPerpendicular to field+BAN 1/3fParallel to field 3/4fPerpendicular to field Flux linkage 0, 0, -BAN EMF : 0 -  0, 0