The rectifier ammeter consists the four rectifier elements which arrange in the form of the bridge along with the moving coil ammeter. The circuit diagram of the bridge rectifier elements is shown in the figure below.

In DC moving coil instrument the shunt is used for protecting the moving instrument from the heavy current. But in case of rectifier ammeter, the use of the shunt is not possible because the current passing through the moving coil instrument varies continuously because of the rectifier resistance.

Advantages of the Rectifier Ammeter

The advantages of the rectifier ammeter are explained below in details.

1. The frequency range of the instrument can easily be extended from 20Hz to high audio frequency.
2. The instrument requires very low operating current.
3. It has the uniform scale.
4. The accuracy of the instrument lies between ±5% under normal operating condition.

Factors Affecting the Performance of the Rectifier Ammeter

The following are the factors which affect the performance of the rectifier ammeter.

1. The waveform of the current and voltage affects the working of the rectifier instrument.
2. The element of the rectifier has some resistance which affects the performance of the instrument.
3. The variable temperature also affects the working of the instrument.
4. The rectifier has some capacitance and this capacitance effects the operation of the instrument.
5. The instrument has low sensitivity for ac as compared to dc.

The small size transformer is used in the instrument because of the low burden.

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Three-Phase Wattmeter has two elements. The single element is the combination of the pressure coil and the current coil. The current coils are considered as the fixed coil, and the pressure coils are the moving coil of the Wattmeter.

Working Principle of Three Phase Wattmeter

It works on the principle that the torque develops on the current carrying conductor when it is placed in the magnetic field. The measurand power when passes through the moving coils, the torque develops on the coil. The torque is the type of mechanical force whose effect can deflect the object in circular motion.

In three-phase Wattmeter, the torque develops on both the elements. The value of torque on each element is proportional to the power passes through it. The total torque on the three-phase Wattmeter is the sum of the torque on individual Wattmeter.

Let understand this with the help of the mathematical expressions.

Consider the deflecting torque develops on the coil one is D₁ and the power passes through that element is P₁. Similarly, the torque develops on the coil 2 is D₂ and the power passes through the coil is P₂.

The total torque develops in the coil is expressed as

Connections of three-phase Wattmeter

Consider the circuit has two Wattmeters. The current coil of both the Wattmeter connects across any two phases say R and Y. The pressure coil of both the Wattmeters connects across the third phase say B.

The mutual interference between the elements of the Three-Phase Wattmeter will affect their accuracy. The mutual interference is the phenomena in which the field of two elements interacts each other. In three-phase Wattmeter, the laminated iron shield is placed between the elements. The iron shield reduces the mutual effect of the element.

The mutual effect can compensate by using the Weston method. In Weston method, the adjustable resistors are used. This resistor compensates the mutual interference that occurs between the elements of three phase wattmeter.

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The value of torque/weight ratio of the moving part of the instrument should not be less than 0.1 if the deflecting torque acts as a force on the apparatus and shows the full-scale deflection.

Let understand this with the help of the help of the example. Consider the indicating instrument shown in the figure below.

If the weight of the instrument pointer is small, the instrument has high torque/weight ratio. The high value of the torque-weight ratio shows that even for the small value of deflecting torque, the pointer deflects and shows the measured value.

The frictional torque of an instrument depends on the weight of their moving part. The weight of the moving part is directly proportional to the frictional torque. The frictional torque is a type of rotational force caused by the friction between two objects.

The frictional torque plays an important role in the performance of the instruments. The deflection of the pointer of an instrument depends on the fractional part of the frictional torque. The deflection torque will also depend on the direction in which the frictional torque applies.

If the value of frictional torque is small as compared to the deflecting torque, the deflecting torque is completely neglected.

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The primary windings of the potential transformer are directly connected to the measurand line and their second terminals connect to the meter. The potential transformer converts the high voltage of the measurand line into a fractional value which is determined by the measuring instrument.

The construction of potential transformer and the power transformer are almost same, but they have small differences like

1. The constructional of the potential transformer can be done by considering the cost, efficiency and their regulation. Whereas the potential transformer is designed by keeping in view their performance parameters, i.e., the ratio of the voltage and number of turns remains constant, and the phase difference between the input and output signal becomes small.
2. The temperature rise problem occurs in the power transformer because of overloading. As the output of the potential transformer is small, thereby the problem of overheating not happens in it.

Parts of Potential Transformer

The following are the essential parts of the potential transformer.

1. Core – The core of the potential transformer may be of core type or shell type. In a core type transformer, the windings surrounding the core and in the shell type transformer the core surrounded the winding. The shell type transformer designs for low voltage works while the core type transformer is used for high voltage applications.

2. Windings – The primary and secondary windings are placed coaxially for reducing the leakage reactance of the potential transformer.

Note Leakage Reactance – All the flux from the primary winding of the transformer is not linked with their secondary windings. The small portion of the flux link with any one of the winding. This portion of the flux is known as the leakage flux.

The leakage flux creates the self-reactance in the winding in which they link. The term reactance means the opposition occurs by the circuit element because of the change of the voltage and current. This self-reactance is known as the leakage reactance.

In low voltage transformer, the insulation is placed next to the core for reducing the problems of insulation.The single coil is used as the primary winding of the low potential transformer. But in the large potential transformer, the single coil is subdivided into small parts for reducing the insulation between the layer.

3. Insulation – The cotton tape and the cambric materials are used as insulation between the winding of the potential transformer. The compound insulation is not used in low voltage transformer. The high voltage transformer uses oil as an insulation medium. The transformer having a rating higher than 45kVA uses porcelain material as an insulator.

4. Bushing – The bushing is an insulated device through which the transformer is connected to the external circuit. The bushings of the transformer are made of porcelain material. The transformer which uses the oil as an insulating medium uses the oil filled bushing.

Two bushings transformer is used in the system when the line through which it is connected is not at ground potential.The transformer which connects to the ground neutral uses only one high voltage bushing.

Connection of Potential Transformer

The primary winding of the potential transformer connects to the high voltage transmission line whose voltage needs to be measured. The secondary of the transformer connects to the meter through which the magnitude of the voltage is determined.

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The most significant advantage of this type of instrument is that it measures the high range frequency current more than the Moving Iron and an Electrodynamometer type instrument. At normal frequencies, the electrothermal instrument is used for the accurate voltage measurement.

Classification of Electrothermal Instruments

The Electrothermic effect is used in three ways for the measurement of the current. And according to these ways, the Electrothermic instruments are classified into three categories.

1. Hot Wire Instrument
2. Thermocouple Instrument
3. Bolometer

The pointer of the hot wire, bolometer and the thermocouple instrument depends on the heating effects of the measurand current flows through the coil. These instruments use the thermal impact of a current differently. As the working of the electrothermic devices depends on the heating effect of the current, thus it is used for measuring both the alternating and direct current.

Hot Wire Instrument

The hot wire instruments work on the principle that the current passes through the coil increases the length of the wire. The wire regains its shape with the help of the spring. The expansion and contraction of the wire will deflect the pointer of the meter. The increase in the length of the wire is equal to the square of the current passes through it.

Thermocouple Instrument

Such type of instruments uses the thermocouple which converts the heat energy into electrical energy which is easily measured through the meter. The measurand current passes through the junction of the thermocouples.

The current produces the heats in the heater, which is connected to the thermocouples. The thermocouples convert the heat into an EMF which induces the current to passes through the meter.

Bolometer

The bolometer uses the resistive element whose resistance varies concerning the temperature. The measurand current passes through the resistive element increases their temperature because of which the resistance of the element increases. The variation in resistance determines the magnitude of current passes through it.

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The ideal ammeter has zero internal resistance. But practically the ammeter has small internal resistance. The measuring range of the ammeter depends on the value of resistance.

Symbolic Representation

The capital alphabet A represents the ammeter in the circuit.

Connection of Ammeter in Circuit

The ammeter is connected in series with the circuit so that the whole electrons of measurand current passes through the ammeter. The power loss occurs in ammeter because of the measurand current and their internal resistance. The ammeter circuit has low resistance so that the small voltage drop occurs in the circuit.

The resistance of the ammeter is kept low because of the two reasons.

• The whole measurand current passes through the ammeter.
• The low voltage drop occurs across the ammeter.

Types of Ammeter

The classification of the ammeter depends on their design and the type of current flows through the ammeter. The following are the types of an ammeter regarding construction.

1. Permanent moving coil ammeter.
2. Moving iron ammeter.
3. Electro-dynamometer ammeter.
4. Rectifier type ammeter.

By the current, the ammeter categorises into two types.

• AC ammeter
• DC ammeter

1. PMMC Ammeter – In PMMC instrument the conductor is placed between the pole of the permanent magnet. When the current flows through the coil, it starts deflecting. The deflection of the coil depends on the magnitude of current flows through it. The PMMC ammeter used only for the measurement of the direct current.

2. Moving Coil Ammeter (MI) – The MI ammeter measures both the alternating and direct current. In this type of ammeter, the coil freely moves between the poles of a permanent magnet. When the current passes through the coil, it starts deflecting at a certain angle. The deflection of the coil is proportional to the current passes through the coil.

3. Electro-dynamometer Ammeter – It is used for the measurement of both AC and DC. The accuracy of the instrument is high as compared to the PMMC and MI instrument. The calibration of the instrument is same both for AC and DC, i.e. if DC calibrates the instrument then without re-calibration, it is used for AC measurement.

4. Rectifier Ammeter – It is used for measuring the alternating current. The instruments using the rectifying instrument which converts the direction of current and pass it to the PMMC instrument. Such type of instrument is used for measuring the current in the communication circuit.

The instrument which measures the DC is known as the DC ammeter and ammeter which measures AC is known as the AC ammeter,

Ammeter Shunt

The high-value current directly passes through the ammeter which damages their internal circuit. For removing this problem,  the shunt resistance is connected in parallel with the ammeter.

If the large measurand current passes through the circuit, the major portion of the current passes through the shunt resistance. The shunt resistance will not affect the working of the ammeter, i.e., the movement of the coil remains same.

Effect of Temperature in Ammeter

The ammeter is a sensitive device which is easily affected by the surrounding temperature. The variation in temperature causes the error in the reading. This can reduce by swamping resistance. The resistance having zero temperature coefficient is known as the swamping resistance. It connects in series with the ammeter. The swamping resistance reduces the effect of temperature on the meter.

The ammeter has the inbuilt fuse which protects the ammeter from the heavy current. If substantial current flows through the ammeter, the fuse will break. The ammeter is not able to measure the current until the new one does not replace the fuse.

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The main advantage of the resistance box is that the variable resistances are available at one point. If any circuit requires variable resistances, then there is no need of replacing the resistor. The circuit is directly connected to the resistance box, and by changing the rotary switches, the variable resistances are obtained.

The resistance box is of three types. They are

• High resistance Box
• Low Resistance box
• Fractional Resistance Box

The value of the high resistance box lies from 1Ω to 5000Ω or above while the value of the low resistance box is between 1 to 500Ω. In fractional resistance box, the value of resistance is in the form of a fraction. The range of fractional box lies between 0.1Ω to 50Ω.

The construction of the box is simple and cheap. The resistance box is available in different designs. It is also used for testing and designing the circuit in the laboratory.

Simple Resistance Box

The simple resistance box has two copper terminals for connecting the positive and negative terminal of the circuit. The cover of the box on which terminals and knobs are placed is made by ebonite material. The knob is used for adding and removing the resistance from the circuit.

On the second side of the ebonite sheet, the resistances of different value are connected in series with each other. For connecting the resistance across the circuit, the knobs of the particular resistance need to be removed. When all the knob is placed on the air gap then the current pass through the copper stud,  no resistance is connected to the circuit.

The process of using the resistance box.

1. The value of resistance is kept very high so that the less power dissipation occurs in the connecting circuit.
2. Before connecting the box to the circuit, it is essential to set the value of the circuit to minimum resistance. So the less dissipation takes place in the circuit. The resistance of the box is either equal or greater than the resistance of the circuit.
3. The resistance box is always connected to the circuit by the help of the plug connectors.

Decade Resistance Box

In resistance box, the resistor is fixed inside the box. They are arranged in such a manner that the value of resistance varies at every step. The box consists the rotary selector switch. The variable resistances are obtained by rotating the selector switches. The key plug is also used for selecting the resistances but rotary switches are more suitable. Hence it is mostly used in the resistance boxes.

Consider the examples of normal decade resistance box. The normal arrangement of the rotary switches in a decade resistance box is shown below.

• A  range of Switch one – 1 to 10 ohms
• A range of switch two – 10 – 100 ohms
• A range of switch three– 100 – 1000ohms.
• A range of switch four   – 100 ohms and above.

The resistance box contains more than one rotary switch shown above in the figure. The resistance of each of the selector switches varies from few ohms.

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The phantom loading is used for examining the current rating ability of the energy meter. The actual loading arrangement will waste a lot of power. The phantom loading consumes very less power as compared to real loading, and because of this reason, it is used for testing the meter.

In phantom loading, the pressure coil and the current coil are separately excited by the supply source. The pressure coil is energised from the small supply voltage, and the current energises the current coil at very small voltages.

The pressure and current coil circuit have low impedance (less obstruction of movement of the electron) because of which highly rated current is passed through it. The total current supplied for the phantom loading is the sum of the pressure coil current which is supplied at normal voltage and the current of the current coil supply at low voltages.

Example of Phantom Loading

Consider the DC energy meter having rating voltage 220V and current 9 Ampere. The resistance of the pressure coil and the current coil is 4400Ω and 0.1Ω respectively. The power consumption of the load by direct and indirect phantom is explained below.

Direct Loading Arrangement 

The circuit for direct loading is shown in the figure below. 

The power consumption of the pressure coil circuit is calculated as

Power  = (220)²/ 4400 = 48400/4400 = 11watt

The power consumption of the current circuit is expressed as

Power = 220 Χ 9 = 1980watt

The total power consumed by the pressure and current circuit

Power =  11watt + 1980watt = 1991watt

Phantom Loading Arrangement 

The circuit of the phantom loading is shown in the figure below.

The power consumption of the pressure coil is given below.

P = (220)²/4400 = 11watt

The current coil of the phantom loading arrangement is separately excited by the battery of the 9V. The power of the current coil is measured as

Power = 9 Χ 9 = 81watt

The total power consumed by the phantom loading is expressed as

Total Power = 11watt + 81watt = 92watt

The above example shows that in phantom loading the pressure and the current coil is separately excited by the meter. Hence the power loss is less in phantom loading as compared to direct loading.

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The power factor of the transmission line is measured by dividing the product of voltage and current with the power. And the value of voltage current and power is easily determined by the voltmeter, ammeter and wattmeter respectively. This method gives high accuracy, but it takes time.

The power factor of the transmission line is continuously changed with time. Hence it is essential to take the quick reading. The power factor meter takes a direct reading, but it is less accurate. The reading obtained from the power factor meter is sufficient for many purposes to expect precision testing.

The power factor meter has the moving system called pointer which is in equilibrium with the two opposing forces. Thus, the pointer of the power factor meter remains at the same position which is occupied by it at the time of disconnection.

Types of Power Factor Meter

The power factor meter is of two types. They are

1. Electrodynamometer
   • Single Phase Electrodynammeter
   • Three Phases Electrodynamometer
2. Moving Iron Type Meter
   • Rotating Iron Magnetic Field
   • Number of Alternating Field

The different types of power factor meter are explained below in details.

Single Phase Electrodynamometer Power Factor Meter

The construction of the single phase electrodynamometer is shown in the figure below. The meter has fixed coil which acts as a current coil. This coil is split into two parts and carry the current under test. The magnetic field of the coil is directly proportional to the current flow through the coil.

The meter has two identical pressure coils A and B. Both the coils are pivoted on the spindle. The pressure coil A has no inductive resistance connected in series with the circuit, and the coil B has highly inductive coil connected in series with the circuit.The current in the coil A is in phase with the circuit while the current in the coil B lag by the voltage nearly equal to 90º. The connection of the moving coil is made through silver or gold ligaments which minimize the controlling torque of the moving system.

The meter has two deflecting torque one acting on the coil A, and the other is on coil B. The windings are so arranged that they are opposite in directions. The pointer is in equilibrium when the torques are equal.

Deflecting torque acting on the coil A is given asθ – angular deflection from the plane of reference.
M_max – maximum value of mutual inductance between the coils.

The deflecting torque acting on coil B is expressed as

The deflecting torque is acting on the clockwise direction.

The value of maximum mutual inductance is same between both the deflecting equations.

This torque acts on anti-clockwise direction. The above equation shows that the deflecting torque is equal to the phase angle of the circuit.

Three Phase Electrodynometer Power Factor Meter

The construction of the three phase meter is shown in the figure below. The electrodynamometer is only useful for the balanced load. The moving coil is placed at an angle of 120º. They are connected across different phases of the supply circuit. Both the coil has a series resistance.

The voltage across the coil A is V₁₂ and the current across it I_A1. The circuit of the coil is resistive, and hence the current and voltage are in phase with each other. Similarly, the voltage V₁₃ and the current I_B1 is in phase with each other.

The phasor diagram of the three phase electrodynamic meter is shown in the figure below. Let  Φ – phase angle of the circuit.
θ – angular deflection from the plane of reference.

Torque acting on coil A is Torque acting on coil B is The torque T_A and T_B are acting on the opposite directions. Thus the angular deflection of the coil is directly proportional to the phase angle of the circuit.

 Moving Iron Power Factor Meter

The moving iron instrument is divided into two categories. They are the rotating magnetic field to some alternating fields.

A. Rotating Field Power factor Meter – The following are the essential feature of the rotating magnetic field. The power factor meter has three fixed coils, and their axes are 120º displaced from each other. The axes are intersecting each other. The coils are connected to the three phase supply with the help of the current transformer.

The P is the fixed coil connected in series with the high resistance circuit across the phases 2 and 3. There is an iron cylinder across coil P. The two iron vanes are fixed to the cylinder. The spindles also carry damping vanes and pointer.

The phasor diagram of the power factor meter is shown in the figure. The total torque of the meter is zero for steady state deflection.

The coil P and the iron cylinders generate the alternating flux which interacts with the flux of the fixed coils. The interaction of the coil generates the moving system which determined the phase angle of the current. The vanes of the power factor meter are magnetized by the current of the moving coil which is in phase with the system line voltage.

Advantages of Moving Iron power Power Factor

1. The meter requires large working force as compared to the electrodynamometer type meter.
2. The coils of the moving iron instruments are fixed permanently.
3. The range of the scale extends up to 360º.
4. The construction of the meter is robust and simple.
5. The moving iron instrument is cheap as compared to electrodynamic meter.

Disadvantages of moving iron instrument

1. The loss occurs in the iron part of the meter. The losses depend on the load and the frequency of the meter.
2. The meter has low accuracy.
3. The calibration of the meter is affected because of the variation in supply frequencies, voltage and waveforms etc.

The power factor meter is used for measuring the power factor of the balanced load.

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The piezo transducer converts the physical quantity into an electrical voltage which is easily measured by analogue and digital meter.

The piezoelectric transducer uses the piezoelectric material which has a special property, i.e. the material induces voltage when the pressure or stress applied to it. The material which shows such property is known as the electro-resistive element.

The word piezoelectric means the electricity produces by the pressure. The Quartz is the examples of the natural piezoelectric crystals, whereas the Rochelle salts, ammonium dehydration, phosphate, lithium sulphate, dipotassium tartrate are the examples of the man made crystals. The ceramic material is also used for piezoelectric transducer.

The ceramic material does not have the piezoelectric property. The property is developed on it by special polarizing treatment. The ceramic material has several advantages. It is available in different shapes and sizes. The material has the capability of working at low voltages, and also it can operate at the temperature more than 3000ºC

Piezoelectric Effect

The EMF develops because of the displacement of the charges. The effect is changeable, i.e. if the varying potential applies to a piezoelectric transducer, it will change the dimension of the material or deform it. This effect is known as the piezoelectric effect.

The pressure is applied to the crystals with the help of the force summing devices for examples the stress is applied through mechanical pressure gauges and pressure sensors, etc. The deformation induces the EMF which determines the value of applied pressure.

Theory of Piezo-Electric Transducer

A piezoelectric crystal is shown in the figure below. 

The polarity of the charge depends on the direction of the applies forces. 

Where, d – charge sensitivity of the crystals
F – applied force in Newton

The force changes the thickness of the crystals. 

Where A – area of crystals in meter square
t – the thickness of crystals in meter
E –  Young’s modulus N/m²

The young modulus is, 

where ω – width of crystals in meter
l – the length of crystals in meter

On substituting the value of force in the equation of charge, we get

The output voltage is obtained because of the electrode charges.

The g is the voltage sensitivity of the crystals. 

Where E₀ – electric field strength, V/m

The voltage sensitivity of the crystals is expressed by the ratio of the electric field intensity and pressure.

When the mechanical deformation occurs in the crystals, it generates charges. And this charge develops the voltages across the electrodes.

The Piezoelectric crystal is direction sensitive. The polarity of the voltage depends on the direction of the force which is either tensile or compressive. The magnitude and the polarity of the charges depend on the magnitude and the direction of the applied force.

Modes of Operation of Piezo-Electric Crystal

The Piezoelectric crystals are used in many modes likes, thickness shear, face shear, thickness expansion, Transverse expansion, etc. The figure of the fear shear is shown in the figure below. 

Properties of Piezo Electric-Crystal

The following are the properties of the Piezoelectric Crystals.

1. The piezoelectric material has high stability.
2. It is available in various shapes and sizes.
3. The piezoelectric material has output insensitive to temperature and humidity.

Uses of Piezoelectric Crystal

The following are the uses of the Piezoelectric transducers.

1. The piezoelectric material has high stability and hence it is used for stabilizing the electronic oscillator.
2. The ultrasonic generators use the piezoelectric material. This generator is used in SONAR for underwater detection and in industrials apparatus for cleaning.
3. It is used in microphones and speakers for converting the electric signal into sound.
4. The piezoelectric material is used in electric lighter.

The transducer has low output, and hence external circuit is associated with it.

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