Hall Effect

The conductivity measurements are not sufficient for the determination of the number of conducting charge and their mobility. Moreover these measurements do not give any information about the sign of the prominent charge carrier.  The Hall Effect supplies the information of the sign of charge carrier.
    When a magnetic field is applied perpendicular to a conductor carrying current, a voltage is developed across the specimen in the direction perpendicular to both the current and magnetic field.  This phenomenon is known as Hall Effect.

    Consider that an external electric field is applied along the axis of specimen, and then the electrons will drift in opposite direction. When a magnetic field is applied perpendicular to the axis of the specimen, the electrons will tend to be deflected to one side. Of course, the electrons will not drift into space but a surface charge is developed.  The surface charge then gives rise to a transverse electric field which causes a compensating drift such that the carriers remain in the specimen.  This effect is known as Hall Effect. 
The Hall Effect is thus observed when a magnetic field is applied at right angle to a conductor carrying a current.

    Consider a slab of material subjected to an external electric field Ex along the x-direction and a magnetic field Hz along the z-direction as shown in Fig. 13.  Due to the electric field a current density Ix will flow in the direction of Ex.  Let us consider the case in which the current is carried by electrons of charge -e.  Under the influence of the magnetic field, the electron will be subjected to a Lorentz force such that the upper surface collects a positive charge while the lower surface a negative charge.

The accumulation of charge on the surface of the specimen continues until the force on moving charges due to the electric field associated with it is large enough to cancel the force exerted by the magnetic field.

    Ultimately a stationary state is reached when the current along y-axis vanishes, a field Ey is set up.  If the charges carriers are holes then the case will be reversed, i.e., the upper surface would become negative while the lower surface as positive.  Thus by measuring the Hall voltage in y - direction, the information about the sign of charges may be obtained.  In this way, the measurement of Hall voltage gives the information about the charge carriers.

Hall voltage and Hall Co-efficient

Importance of Hall Effect


1.   The sign of the current carrying charges is determined.

2.  From the magnitude of Hall coefficient the number of charge carriers per unit volume can be calculated.

3.  The mobility is measured

4. It can be used to decide whether a material is metal, semi conductor or insulator.

   
 Here we should remember that not all the metals have negative Hall constant but some metals have a positive hall constant. (i.e., charge carriers are holes) and if both holes and electrons contribute to conductivity then RHall can be positive or negative depending upon the relative densities and mobilities of the carriers.

REGULATION OF ALTERNATOR BY POTIER & ASA METHOD

THEORY

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POTIER METHOD

                         The zero power factor or Potier method is based on the separation of armature leakage reactance drop and the armature reaction effects. The experimental data required are ( i ) no load curve ( ii ) full load Zero power factor curve (not short circuit characteristics) which is also called wattles load characteristic. It is the curve of terminal volts against excitation when armature is delivering full load current at zero powerfactor. The reduction in voltage due to armature reaction is found from above and (iii) voltage drop due to armature leakage reactance XL ( also called as Potier reactance)   is found from both . By combining these two, E0 can be calculated. It should he noted that if we vectorically add to V the drop due to resistance and leakage reactance XL. We get E. If to E is further added the drop due to armature reaction (assuming lagging power factor) then we get Eo.

ASA METHOD

       This method is a modification of MMF and potier methods. The field current corresponding to the rated voltage V is found out by referring to the air gap line. So that  the field current  required to circulate the load current under short circuit conditions is added at an angle of ( 90 +  ) or ( 90 -  ) to get the resultant field current. This resultant field current is increased by a small amount which takes into account its saturation. For this total field current value, corresponding no load voltage ( Eo) is noted & the regulation of alternator  for the particular power factor can be calculated & This method is reliable for both salient and non-salient pole machines.


FULL LOAD ZERO POWER FACTOR TEST:

       The connections are given as shown in the circuit. The DC motor is started and the speed is adjusted to rated speed of the alternator. The terminal voltage is brought to its rated voltage by adjusting field rheostat of alternator. Then the load side TPST switch is closed. The inductive load is gradually increased up to rated stator current of alternator and wattmeter should be reads zero. Corresponding meters are noted down.

i) To find the field current required overcoming the saturation effects

1)  O.C.C curve and the air gap line are drawn.

2)Rated voltage (V) is plotted at the power factor angle  of with the X - axis. A scale of voltage scale of OCC may be used.

3)  IRa drop line is drawn from V (which is parallel to X – axis)

4)  IXI, drop line is to IRa. (Taken from Potier triangle)

5)  Eg line is drawn (join IXI, to the origin).

6)  Project V & Eg by arcs to the vertical axsis.

7)  These points are projected horizontally to cut the OCC curve.

8)  Measure the difference between the air gap line & O.C.C corresponding to projected Eg which gives IFs, to overcome the saturation effects.

ii) To find the field current corresponding to Eg

       1) Measure Ifn ( upto air gap line ) corresponding to rated voltage.

       2) Add voctorizally or using the formula (shown below) the Ifsc, (required to
          Circulate load current under short circuit condition) at the required power factor to Ifn which is designated as Ifg.

          Formula:

        i)    Ifg =  (Ifn 2 + If sc2 + 2 Ifn   Ifsc  Cos ( 180 - (90 +))

       ii) Circulation of voltage regulation

       1) Ifo =  Ifs + lfg

       2) Obtain the value or E0 for Ifo from OCC

       3) Percentage regulation is calculated.

REGULATION OF THREE PHASE ALTERNATOR BY EMF METHOD & MMF METHOD

AIM:

    To determine the regulation of an Alternator at full load and  at various power factor by EMF and MMF method.

APPARATUS REQUIRED:

THEORY:
                                The voltage regulation of all alternator is defined as the" rise in voltage when full load is removed (field excitation and speed remaining the same) divided by the rated terminal voltage”.

                                %Regulation = (Eo –V) /  V * 100
                                Eo - No load induced emf or open circuit voltage per phase
                                V - Rated terminal voltage per phase.
                             The no load induced emf can be, found by,
                                1. Synchronous impedance or EMF method
                                2. Ampere turn method
                                3. Zero power or Potier method
                                4. ASA method

All these method require the following,
                                1. Armature or stator a. c resistance Rac,
                                2. Open circuit or no load characteristics
                                3. Short circuit characteristics
                                4. Zero power factor lagging characteristics for Potier method

.                                In this method, the Armature reaction is treated as another armature    leakage reactance. The synchronous impedance ZS , found is always more than its  value under normal voltage conditions and saturation. Hence, the value or regulation so obtained is always more, than that found from an actual test. That is why it is called pessimistic method.

FORMULA USED:

1. Synchronous Impedance, Zs = (E1 / I1). (From Graph)
2. Synchronous Reactance, Xs  = (Zs2-Ra2)
3. Open Circuit Voltage (Eo)
  (i) For leading power factor
    Eo = (Vph Cos + IRac) 2 + (Vph Sin _ IaXs) 2
  (ii) For lagging power factor
          Eo = (Vph Cos + IRac) 2 + (Vph Sin+IaXs) 2
   (iii) For unity power factor:
          Eo = (Vph Cos + IRac) 2 + ( IaXs) 2
    4. Percentage Regulation = (Eo – Vph) / Vph*100



Stator resistance method:

Rdc=Measured value/2
Ra(ph)=Rac=1.6 Rdc


PROCEDURE:

Open circuit test:

•    Connections are given as per the circuit diagram.
•    The motor field rheostat should be kept in minimum resistance position
•    The D.C Motor is started and its speed is adjusted to the synchronous speed of the alternator.
•    The field rheostat (Alternator) is varied and for various values of field current, the corresponding values of open circuit voltage are noted down.
•    The open circuit characteristic is drawn. (If Vs Eo)

Short circuit test:

•    The alternator is made to run at synchronous speed.
•    The Armature terminals of the alternator are shorted by an Ammeter.
•    The field rheostat (Alternator) is varied up to rated current (short circuit current) is circulating in short circuited stator winding corresponding meters reading is noted down.
•    The Short circuit characteristic is drawn. (If Vs Isc).


 Result:

    The Regulation of an alternator at full load ant at various power factors by EMF and MMF method was determined and the characteristics curves are drawn.