Question

a full elaborate explanation on the theory behind induction type Instruments including calculations pertaining to them

mathematical derivations

Answer 1

INDUCTION TYPE INSTRUMENTS
The operation of induction type instruments depends on the production of torque due to the reaction between two magnetic fluxes having some phase difference or reaction between them. these two fluxes are the flux of an AC magnet and the eddy current induced by this flux in the disc.
NOTE:-These types of instruments are used only for AC measurements.

The single-phase supply is converted into two phases in the instrument, which is done by the split-phase or shaded pole arrangement. Accordingly, induction instruments are classified as:-
1. Split phase type
2. Shaded pole type

Basic working principle
When a drum or disc of a non - magnetic conducting material is placed in a rotating magnetic field, eddy currents are induced in it. The reaction between the rotating flux and the eddy current produced by it creates a torque that rotates the disc or drum. The rotating flux is produced by the current or voltage to be measured. The eddy current again is proportional to the flux.

TORQUE PRODUCED:

Before getting into the constructional details of these instruments; let us first have a general look at the torque produced in these instruments.

Let us consider the flux, produced by the electromagnet is

The phase angle between that flux and induced eddy current is α. Hence, we can write the expression of the eddy current as

Again, the instantaneous torque is directly proportional to the instantaneous eddy current and the flux. Hence, we can write,

So, the mean torque can be found out as follows,

The above expression tells that the torque is zero if α is 90°. Here α is the phase angle between the flux and the eddy current.

1. SPLIT-PHASE TYPE –
The diagram for the split-phase type induction instrument is shown here.

1.2 CONSTRUCTION –
In this arrangement, there are two electromagnets M1 and M2, which are connected in series. The winding in M2 is shunted by a resistance R. A rotating disc D is placed between two electromagnets and pointer is attached to the spindle of the disc. The current in the M2 winding lags with respect to the total line current. This helps to develop the necessary phase angle α between the two fluxes.

1.3DAMPING –
Eddy current damping is used in this instrument.

2. SHADED POLE TYPE –
Shaded pole type induction instrument uses a single winding to produce flux. The flux produced by this winding is split up into two fluxes, having phase difference with respect to each other. The phase difference is usually 40 to 50 degrees and can be varied by varying the size of the shading band. This is done by making a narrow slot in the poles of the electromagnet. A copper strip is placed around the smaller of the two areas formed by the slot. This copper shading band acts as a short-circuited secondary winding.

2.1 CONSTRUCTION –
The constructional features of a shaded pole type induction instrument are shown in the figure below.

The exciting coil is placed on the poles and a current proportional to current or voltage being measured is passed through it. An aluminum disc that is mounted on a spindle is inserted in the air gap of the electromagnet. The spindle carries a pointer and has a control spring attached to it. The controlling torque is provided by this spring only.

2.3 DAMPING –
Damping is provided by a permanent magnet placed at the opposite side of the electromagnet so that the disc can be used for the production of both deflecting and damping torque.

ADVANTAGES –
1) A full-scale deflection of over 300 degrees can be obtained.
2) Good damping.
3) Less effect of stray magnetic fields as the operating fields is large.

DISADVANTAGES –

1) Errors are caused due to changes in frequency and temperature.
2) Non-uniform scale.
3) Large power consumption and high cost.
4) It Can be used for AC only.