Question

full theory and mathematical derivatives behind induction type Instruments

Answer 1

Induction Type Instrument Working Principle :>

We use induction type instrument for AC measurement only. This is because the induction phenomenon only occurs in AC. An induction instrument has multiuse. For example, we use the instruments as ammeters, voltmeters, wattmeters, and energy meters.

Induction type instruments essentially have an electromagnet to produce the required magnetic field. AC in the electromagnet produces changing flux between its poles. Here, we place one aluminium disc (or aluminium drum) in the magnetic field. Hence, the changing flux links with the aluminium disc. As a result, the flux induces an eddy current on the disc. This eddy current interacts with the flux which has induced it. Consequently, there is a mechanical torque acting on the disc. This mechanical torque rotates the disc.

Torque in Induction Type Instrument:>

The torque produced in induction type instruments depends on the two fluxes; the net torque acting on the disc is

T=Kω.ϕ1m.ϕ2m.sinα

Where, ϕ1m,ϕ2m = maximum fluxes produced by the currents

               α = phase difference between the two fluxes

And if both the fluxes are produced by the same alternating current, then

  T=Kω. I_m^2.sinα

Where, I_m= maximum value of current. Therefore, torque is proportional to the square of current for a given value of frequency  and angle . If the disc has spring control, then at some point the controlling torque will be equal to the deflecting torque which will help the disc to attain a steady deflected position. And if the disc is attached to a pointer, then this arrangement can be used for measurement of current.

Induction type instruments are of two types: :

1) split phase type

2)shaded pole type

SPLIT-PHASE TYPE –

The diagram for the split phase type induction instrument is shown here.

SPLIT PHASE TYPE INDUCTION INSTRUMENT

CONSTRUCTION –

In this arrangement, there are two AC magnets M₁and M₂, which are connected in series. The winding in M₂ is shunted by a resistance R. 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.

  

DEFLECTION –

If the hysteresis effects are neglected, then deflecting torque is

                     

Td∝ϕ1m.ϕ2m.sinα

(Where all the signs have their usual meanings as stated before)

Or, Td∝I^2 (if fluxes are produced by the same current)

Note that, here I is the r.m.s value of current.

Also, Tc∝θ (Because spring control is used)

In the final deflected position, T_c=T_d.

Therefore, deflection (θ)∝I^2

DAMPING –

Eddy current damping is used in this instrument

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 flux, 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 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.

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 aluminium disc which 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.

DEFLECTION –

As the net driving torque is due to the fluxes and the difference in the phase angle of these fluxes, then deflecting torque can be written as

                        

Td∝ϕ1.ϕ2.sinα

If are produced by same current I, then Td∝I^2

As the instrument is spring controlled, Tc∝θ

For steady deflection, Tc=Td⇒θ∝I^2

DAMPING –

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