Study notes on Measurement & Electrical Quantities-2 For Electrical Engineering

By Yash Bansal|Updated : May 31st, 2021

In this article, you will find the study notes on Measurement & Electrical Quantities-2 which will cover the topics such as Moving Iron Instrument Working Operation, Radial Vane type & Co-Axial Vane type, Electro-Dynamometer Type Wattmeter, Construction of Electrodynamometer Wattmeter, Rectifier Type Instrument, Factors affecting the Performance of Rectifier type instruments, Advantages of Rectifier Type Instruments & Thermocouple Instrument.

In this article, you will find the study notes on Measurement & Electrical Quantities-2 which will cover the topics such as Moving Iron Instrument Working Operation, Radial Vane type & Co-Axial Vane type, Electro-Dynamometer Type Wattmeter, Construction of Electrodynamometer Wattmeter, Rectifier Type Instrument, Factors affecting the Performance of Rectifier type instruments, Advantages of Rectifier Type Instruments & Thermocouple Instrument.

Moving Iron Instrument Working Operation

The moving iron instruments are classified as:

  1. Moving iron attraction type instruments
  2. Moving iron repulsion type instruments

Attraction Type Instrument Working Operation

Moving Iron Instrument Working Principle: The basic working principle of these instruments is very simple that a soft iron piece if brought near magnet gets attracted by the magnet.

 The construction of the attraction type moving iron instrument is shown in the below figure.


  • lt consists of a fixed coil C and moving iron piece D. The oil is flat and has narrow slot like opening.
  • The moving iron is a flat disc which is eccentrically mounted on the spindle. The spindle is supported between the jewel bearings. The spindle carries a pointer which moves over a graduated scale.
  • The number of turns of the fixed coil are dependent on the range of the instrument. For passing the large current through the coil only a few turns are required.
  • The Controlling Torque is provided by the springs but gravity control may also be used for vertically mounted panel type instruments.
  • The Damping Torque is provided by the air friction.
  • A light aluminium piston is attached to the moving system. it moves in a fixed chamber. The chamber is closed at one end. it can also be provided with the help of vane attached to the moving system.

Torque in Moving Iron Instrument

Deflecting torque

04-Digital-voltmeters (10) Newton meter


04-Digital-voltmeters (11)

as θ ∞ I2, the scale is non-linear in moving iron type.

For linear scale 04-Digital-voltmeters (12)

For scale to be linear 04-Digital-voltmeters (13) constant

Where, θ = Deflection of the pointer

L = Inductance of the coil

I = RMS value of current in the coil

The curve between dL/dθ and θ is a rectangular hyperbola.

Shunt of Moving Iron Instrument

Division of current between coil and shunt remain same only if the time constant of the coil is equal to time constant of the shunt.

04-Digital-voltmeters (15)

As, 04-Digital-voltmeters (16)

The range of ammeter can be increased by using current transformer.

04-Digital-voltmeters (17)

Multiplier of Moving Iron Instrument

Multiplier factor

04-Digital-voltmeters (18)

The error due to frequency in moving iron type instrument can be eliminated by using capacitor across multiplier resistance as  04-Digital-voltmeters (19) farad

04-Digital-voltmeters (20)

The moving iron instrument used only up to 125 Hz.

Electro Dynamometer Type Instrument

The basis of the electro-dynamometer instrument is its operation and the magnetic effect of electric current.

For DC; torque 04-Digital-voltmeters (21)

If 04-Digital-voltmeters (22)

Where, I1 = Current in fixed coil

I2 = Current in moving coil

Where M is mutual inductance between the coils.

For AC 04-Digital-voltmeters (23)

If I1 = I2 = and φ = 0°

04-Digital-voltmeters (24)

Control torque TC = Kθ

Deflection 04-Digital-voltmeters (25)

04-Digital-voltmeters (26)

As θ proportional to I2, scale is non-linear in electro dynamometer Instrument.

These instruments are also called as transfer instrument. Their sensitivity is smaller than PMMC and also smaller than moving iron instruments.

Electro Dynamometer Type Ammeter

04-Digital-voltmeters (29)

(L/R)shunt =(L/R)coil

04-Digital-voltmeters (25)04-Digital-voltmeters (29)

Electro Dynamometer Type Voltmeter

04-Digital-voltmeters (30)

04-Digital-voltmeters (31)

Sensitivity of electro dynamometer is 10 – 30 Ω/V

Sensitivity of PMMC type = 20 k Ω/V

Rectifier Type Instrument

The rectifier used to convert AC to DC signal. Depending upon the output the rectifier can be classified as

Half Wave Rectifier

For DC, 

For AC, 

Sensitivity of AC = 0.45 SDC

The two different designs of repulsion type instruments are:

  1. Radial vane type and
  2. Co-axial vane type 

Radial Vane Emulsion Type Instrument

The fixed vane is attached to the coil. The movable vane is attached to the spindle and suspended in the induction field of the coil. The needle of the instrument is attached to this vane. Below shows the radial vane repulsion type instrument.


  • Out of the other moving iron mechanisms, this is the most sensitive and has most linear scale.

Concentric Vane Repulsion Type Instrument

The instrument has two concentric vanes. One is attached to the coil frame rigidly while the other can rotate co-axially inside the stationary Vane. Both the vanes are magnetized to the same polarity due to the current in the coil. Thus the movable vane rotates under the repulsive force. As the movable vane is attached to the pivoted shaft, the repulsion results in a rotation of the shaft. The pointer deflection is proportional to the current in the coil.

The figure shows the concentric vane repulsion type instrument.

  • The instrument has two concentric vanes.
  • One is attached to the coil frame rigidly while the other can rotate co-axially inside the stationary vane.


  • Error due to variation in temperature.
  • Error due to friction is quite small as the torque-weight ratio is high in moving coil instruments.
  • Stray fields cause relatively low values of magnetizing force produced by the coil.
  • Efficient magnetic screening is essential to reduce this effect.
  • Error due to variation of frequency causes change of reactance of the coil and also changes the eddy currents induced in neighboring metal
  • Deflecting torque is not exactly proportional to the square of the current due to non-linear characteristics of the iron material.

Electro-Dynamometer Type Wattmeter


  • The two coils are connected in different circuits for measurement of power.
  • The fixed coil arc connected in series with the load and so carry the current in the circuit.  The fixed coils, therefore, form the current coil or simply C.C. of the wattmeter.
  • The moving coil is connected across the voltage and, therefore, carries a current proportional to the voltage.
  • A high non-inductive resistance is connected in series with the moving coil to limit the current to a small value.
  • Since the moving coil carries a current proportional to the voltage, it is called the "pressure coil" or “voltage coil” or simply called P.C. of the wattmeter.

Construction of Electrodynamometer Wattmeter

byjusexamprepFixed Coils

  • The fixed coils carry the current of the circuit.
  • They are divided into two halves.
  • The fixed coils are wound with heavy wire. This wire is stranded or laminated especially when carrying heavy currents in order to avoid eddy current losses in conductors. 

Moving Coil

  • The moving coil is mounted on a pivoted spindle and is entirely embraced by the fixed spindle & is entirely embraced b the fixed current coils.
  • Spring control is used for the movement.
  • The use of moving coil as pressure coil is a natural consequence of design requirements.

Controlling Force 

  • Spring control is used for the instrument.

Damping Force

   • Air friction damping is used.
   • The moving system carries a light aluminium vane which moves in a sector-shaped box.

If the pressure coil has a very high resistance then it can be treated as a purely Resistive. Therefore current Ip in the Pressure coil is in Phase with the voltage & its instantaneous value 


It is clear from above that there is a component of power which varies as twice the frequency of the current & voltage (containing term of 2ωt)

Average Deflecting Torque


Errors in Electrodynamometer

Errors due to pressure coil inductance for

lagging loads can be given as

 04-Digital-voltmeters (56)

04-Digital-voltmeters (57)

For leading loads

04-Digital-voltmeters (58)

04-Digital-voltmeters (59)

True power = VI cosφ

Measured power = VI cos β cos(φ-β)

Correction factor (l) is a factor by which the actual wattmeter reading or measured power is multiplied to get true power.

04-Digital-voltmeters (60)  for lagging power factor

04-Digital-voltmeters (61) for leading power factor

where, ϕ = Angle between the current coil and pressure coil

β = Angle between current and the voltage of the pressure coil

True power = correction factor k × measured power as is very small so

Correction factor 04-Digital-voltmeters (62)

Percentage error = tan φ tan β × 100

Error = VI sin φ tan β (for zero power factor)

  • Errors due to inductance effects
  • Stray magnetic field errors
  • Eddy current errors
  • Temperature error.

Rectifier Type Instrument 

It measures the alternating voltage and current with the help of rectifying elements and permanent magnet moving coil type of instruments. However, the primary function of rectifier type of instruments work as voltmeter. Now one question must arises in our mind why we use rectifier type of instruments widely in the industrial world though we have various other AC voltmeter like electrodynamometer type instruments, thermocouple type instruments etc.


  • Cost of electrodynamometer type of instruments is quite high than rectifier type of instruments. However rectifier type of instruments as much accurate as electrodynamometer type of instruments. So rectifier type of instruments are preferred over electrodynamometer type instruments.
  • However, thermocouple type of instruments is more widely used at very high frequencies.
  • Before we look at the construction principle and working of rectifier type instruments, there is need to discuss in detail about the voltage-current characteristics of ideal and practical rectifier element called diode.
  • Now, what is an ideal rectifying element? A rectifying element is one which offers zero resistance if it is forward biased and offers infinite resistance if it is reversed biased.

Factors affecting the Performance of Rectifier type instruments: 


  • Rectifier type of instruments is calibrated in terms of root mean square values of the sinusoidal wave of voltages and current. The problem is that the input waveform may or may not have same form factor on which the scale of these meter is calibrated.
  • There may be some error due to the rectifier circuit as we are not included the resistance of the rectifier bridge circuits in both the case. The nonlinear characteristics of a bridge may distort the current and voltage waveform.
  • There may variation in the temperature due to which the electrical resistance of the bridge changes hence in order to compensate this kind of errors we should apply multiplier resistor with a high temperature coefficient.
  • Effect of the capacitance of the bridge rectifier: Bridge rectifier has imperfect capacitance thus due to this it byp asses the high-frequency currents. Hence there is a decrement in the reading.

The sensitivity of Rectifier type instruments is low in case of ac input voltage.

Advantages of Rectifier Type Instruments

Following are the advantages of the rectifier type of instruments:

  • The accuracy of rectifier type instrument is about 5 percent under normal operating condition.
  • The frequency range of operation can be extended to high value.
  • They have uniform scale on the meter.
  • They have low operating value of current and voltages.

The loading effect of an ac rectifier voltmeter in both the cases (i.e. half wave diode rectifier and full wave diode rectifier) is high as compared to the loading effects of DC voltmeters as the sensitivity of the voltmeter either using in half wave or full wave rectification is less than the sensitivity of DC voltmeters.

Thermocouple Instrument



The Seebeck effect is fairly linear; that is, the voltage produced by a heated junction of two wires is directly proportional to the temperature. This means that the temperature of the metal wire junction can be determined by measuring the voltage produced. Thus, the Seebeck effect provides for us an electric method of temperature measurement.

When a pair of dissimilar metals are joined together for the purpose of measuring temperature, the device formed is called a thermocouple. Thermocouples made for instrumentation use metals of high purity for an accurate temperature/voltage relationship.

  • The thermocouple instruments are more delicate than the rectifier type of instruments.

    Seebeck voltages are quite small, in the tens of millivolts for most temperature ranges. This makes them somewhat difficult to measure accurately. Also, the fact that any junction between dissimilar metals will produce temperature-dependent voltage creates a problem when we try to connect the thermocouple to a voltmeter.

  • Two thermocouple junctions can be connected in opposition to each other to generate a voltage signal proportional to differential temperature between the two junctions. A collection of junctions so connected for the purpose of generating electricity is called a thermopile.
  • When electrons flow through the junctions of a thermopile, heat energy is transferred from one set of junctions to the other. This is known as the Peltier Effect.
  • Multiple thermocouple junctions can be connected in parallel with each other to generate a voltage signal representing the average temperature between the junctions. “Swamping” resistors may be connected in series with each thermocouple, to maintain equality between the junctions, so the resultant voltage will be more representative of a true average temperature.

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