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Here we are interested in electrical measuring instruments so we will discuss about them in detail. Electrical instruments measure the various electrical quantities like

Electrical Measurements

Basically there are three types of measuring instruments and they are

(a) Electrical measuring instruments

(b) Mechanical measuring instruments.

(c) Electronic measuring instruments.

electrical power factor, power, voltage and electric current etc. All analog electrical instruments use mechanical system for the measurement of various electrical quantities but as we know the all mechanical system has some inertia therefore electrical instruments have a limited time response.

Now there are various ways of classifying the instruments. On broad scale we can categorize them as:

Absolute Measuring Instruments

These instruments give output in terms of physical constant of the instruments. For example Rayleigh’s electric current balance and Tangent galvanometer are absolute instruments.

Secondary Measuring Instruments

These instruments are constructed with the help of absolute instruments. Secondary instruments are calibrated by comparison with an absolute instruments. These are more frequently used in measurement of the quantities as compared to absolute instruments, as working with absolute instruments is time consuming.

Another way of classifying the electrical measuring instruments depends on the way they produce the result of measurements. On this basis they can be of two types:

Deflection Type Instruments

In these types of instruments, pointer of the electrical measuring instrument deflects to measure the quantity. The value of the quantity can be measured by measuring the net deflection of the pointer from its initial position. In order to understand these types of instruments let us take an example of deflection type permanent magnet moving coil ammeter which is shown below:

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Deflection type Permanent Magnet Moving Coil Ammeter

The diagram shown above has two permanent magnets which are called the stationary part of the instrument and the moving part which is between the two permanent magnets that consists of pointer. The deflection of the moving coil is directly proportion to the current. Thus the torque is proportional to the electric current which is given by the expression Td = K.I, where Td is the deflecting torque. K is proportionality constant which depends upon the strength of the magnetic field and the number of turns in the coil. The pointer deflects between the two opposite forces produced by the spring and the magnets. And the resulting direction of the pointer is in the direction of the resultant force. The value of electric current is measured by the deflection angle θ, and the value of K.

Null Type Instruments

In opposite to deflection type of instruments, the null or zero type electrical measuring instruments tend to maintain the position of pointer stationary. They maintain the position of the pointer stationary by producing opposing effect. Thus for the operation of null type instruments following steps are required:

(1) Value of opposite effect should be known in order to calculate the value of unknown quantity.

(2) Detector shows accurately the balance and the unbalance condition accurately.

The detector should also have the means for restoring force.

Let us look at the advantages and disadvantages of deflection and null type of measuring instruments:

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(1) Deflection type of instruments is less accurate than the null type of instruments. It is because, in the null deflecting instruments the opposing effect is calibrated with the high degree of accuracy while the calibration of the deflection type instruments depends on the value of instrument constant hence usually not having high degree of accuracy.

(2) Null point type instruments are more sensitive than the Deflection type instruments.

(3) Deflection type instruments are more suitable under dynamic conditions than null type of instruments as the intrinsic responses of the null type instruments are slower than deflection type instruments.

Following are the important three functions of the electrical measuring instruments.

Indicating Function

These instruments provide information regarding the variable quantity under measurement and most of the time this information are provided by the deflection of the pointer. This kind of function is known as the indicating function of the instruments.

Recording Function

These instruments usually use the paper in order to record the output. This type of function is known as the recording function of the instruments.

Controlling Function

This is function is widely used in industrial world. In this these instruments controls the processes.

Now there are two characteristics of electrical measuring instruments and measurement systems. They are written below:

Static Characteristics

In these type of characteristics measurement of quantities are either constant or vary slowly with the time. Few main static characteristics are written below:

(1) Accuracy: It is desirable quality in measurement. It is defined as the degree of the closeness with which instrument reading approaches the true value of the quantity being measured. Accuracy can be expressed in three ways (a) Point accuracy (b) Accuracy as the percentage of scale of range. (c) Accuracy as percentage of true value.

(2) Sensitivity: It is also desirable quality in the measurement. It is defined as the ratio of the magnitude response of the output signal to the magnitude response of the input signal.

(3) Reproducibility: It is again a desirable quality. It is defined as the degree of the closeness with which a given quantity may be repeatedly measured. High value of reproducibility means low value of drift. Drift are of three types (a) Zero drift (b) Span drift (c) Zonal drift.

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Dynamic Characteristics

These characteristics are related with the rapidly changing quantities therefore in order to understand these types of characteristics we are required to study the dynamic relations between the input and the output.

True Value

ERRORS IN MEASUREMENT

In order to understand the concept of errors in measurement, we should know the two terms that defines the error and these two terms are written below:

It is not possible to determine the true of quantity by experiment means. True value may be defined as the average value of an infinite number of measured values when average deviation due to various contributing factor will approach to zero.

Measured Value

It may be defined as the approximated value of true value. It can be found out by taking means of several measured readings during an experiment, by applying suitable approximations on physical conditions.

Now we are in a position to define static error. Static error is defined as the difference of the measured value and the true value of the quantity. Mathematically we can write an expression of error as, dA = Am - At where dA is the static error Am is measured value and At is true value.

It may be noted that the absolute value of error cannot be determined as due to the fact that the true value of quantity cannot be determined accurately.

Let us consider few terms related to errors.

Limiting Errors or Guarantee Errors

The concept of guarantee errors can better clear if we study this kind of error by considering one example. Suppose there is a manufacturer who manufacture an ammeter, now he should promises that the error in the ammeter he is selling not greater the limit he sets. This limit of error is known as limiting errors or guarantee error.

Relative Error or Fractional Error

It is defined as the ratio of the error and the specified magnitude of the quantity. Mathematically we write as,

Where dA is the error and A is the magnitude.

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Now here we are interested in computing resultant limiting error under the following cases:

(a) By taking the sum of two quantities: Let us consider two measured quantities a1 and a2. The sum of these two quantities can be represented by A. Thus we can write A = a1 + a2. Now the relative incremental value of this function can be calculated as

Separating the each term as shown below and by multiplying and dividing a1 with the first term and a2 with the second term we have

From the above equation we can see that the resultant limiting error is equal to the sum of products formed by multiplying the individual relative limiting errors by the ratio of each term to the function. Same procedure can be applied to calculate the resultant limiting error due to summation of more than two quantities. In order to calculate the resultant limiting error due to difference of the two quantities just change the addition sign with subtraction and rest procedure is same.

(b) By taking the product of two quantities: Let us consider two quantities a1 and a2. In this case the product of the two quantities are expressed as A = a1.a2. Now taking log both sides and differentiating with respect to A we have resultant limiting errors as

From this equation we can see that the resultant error is summation of relative errors in measurement of terms. Similarly we can calculate the resultant limiting error for power of factor. Hence the relative error would be n times in this case.

Types of Errors

Basically there are three types of errors on the basis; they may arise from the source.

Gross Errors

This category of errors includes all the human mistakes while reading, recording and the readings. Mistakes in calculating the errors also come under this category. For example while taking the reading from the meter of the instrument he may read 21 as 31. All these types of error are come under this category. Gross errors can be avoided by using two suitable measures and they are written below:

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(i) A proper care should be taken in reading, recording the data. Also calculation of error should be done accurately. (ii) By increasing the number of experimenters we can reduce the gross errors.

If each experimenter takes different reading at different points, then by taking average of more readings we can reduce the gross errors.

Systematic Errors

In order to understand these kinds of errors, let us categorize the systematic errors as

(i) Instrumental Errors

These errors may be due to wrong construction, calibration of the measuring instruments. These types of error may be arises due to friction or may be due to hysteresis. These types of errors also include the loading effect and misuse of the instruments. Misuse of the instruments results in the failure to the adjust the zero of instruments. In order to minimize the gross errors in measurement various correction factors must be applied and in extreme condition instrument must be re-calibrated carefully.

(ii) Environmental Errors

This type of error arises due to conditions external to instrument. External condition includes temperature, pressure, humidity or it may include external magnetic field. Following are the steps that one must follow in order to minimize the environmental errors:

(A)Try to maintain the temperature and humidity of the laboratory constant by making some arrangements. (B)Ensure that there should not be any external magnetic or electrostatic field around the instrument.

Observational Errors

As the name suggests these types of errors are due wrong observations. The wrong observations may be due to PARALLAX. In order to minimize the PARALLAX error highly accurate meters are required, provided with mirrored scales.

Random Errors

After calculating all systematic errors, it is found that there are still some errors in measurement are left. These errors are known as random errors. Some of the reasons of the appearance of these errors are known but still some reasons are unknown. Hence we cannot fully eliminate these kinds of error.

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PERMANENT MAGNET MOVING COIL INSTRUMENT

The permanent magnet moving coil instrument or PMMC type instrument uses two permanent magnets in order to create stationary magnetic field. These types of instruments are only used for measuring the dc quantities as if we apply ac electric current to these type of instruments the direction of electric current will be reversed during negative half cycle and hence the direction of torque will also be reversed which gives average value of torque zero. The pointer will not deflect due to high frequency from its mean position showing zero reading. However it can measure the direct electric current very accurately.

Let us move towards the constructions of permanent magnet moving coil instruments. We will see the construction of these types of instruments in five parts and they are described below:

(a) Stationary part or magnet system: In the present time we use magnets of high field intensities, high coercive force instead of using U shaped permanent magnet having soft iron pole pieces. The magnets which we are using nowadays are made up of materials like alcomax and alnico which provide high field strength.

(b) Moving coil: The moving coil can freely moves between the two permanent magnets as shown in the figure given below. The coil is wound with many turns of copper wire and is placed on rectangular aluminium which is pivoted on jeweled bearings.

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(c) Control system: The spring generally acts as control system for PMMC instruments. The spring also serves another important function by providing the path to lead electric current in and out of the coil.

(d) Damping system: The damping force hence torque is provided by movement of aluminium former in the magnetic field created by the permanent magnets.

(e) Meter: Meter of these instruments consists of light weight pointer to have free movement and scale which is linear or uniform and varies with angle.

Let us derive a general expression for torque in permanent magnet moving coil instruments or PMMC instruments. We know that in moving coil instruments the deflecting torque is given by the expression:

Td = NBldI where N is number of turns,

B is magnetic flux density in air gap,

l is the length of moving coil,

d is the width of the moving coil,

And I is the electric current.

Now for a moving coil instruments deflecting torque should be proportional to current, mathematically we can write Td = GI. Thus on comparing we say G = NBIdl. At steady state we have both the controlling and deflecting torques are equal. Tc is controlling torque, on equating controlling torque with deflection torque we have GI = K.x where x is deflection thus electric current is given by

Since the deflection is directly proportional to the electric current therefore we need a uniform scale on the meter for measurement of current.

Now we are going to discuss about the basic circuit diagram of the ammeter. Let us consider a circuit as shown below:

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Basic Ammeter Circuit

The electric current I is shown which breaks into two components at the point A. The two components are Is and Im. Before I comment on the magnitude values of these currents, let us know more about the construction of shunt resistance. The basic properties of shunt resistance are written below,

The electrical resistance of these shunts should not differ at higher temperature, it they should posses very low value of temperature coefficient. Also the resistance should be time independent. Last and the most important property they should posses is that they should be able to carry high value of electric current without much rise in temperature. Usually manganin is used for making dc resistance. Thus we can say that the value of Is much greater than the value of Im as resistance of shunt is low. From the we have,

Where Rs is resistance of shunt and Rm is the electrical resistance of the coil.

From the above two equations we can write,

Where m is the magnifying power of the shunt.

Errors in Permanent Magnet Moving Coil Instruments

There are three main types of errors: (a) Errors due to permanent magnets: Due to temperature effects and aging of the magnets the

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magnet may lose their magnetism to some extent. The magnets are generally aged by the heat and vibration treatment.

(b) Error may appear in PMMC Instrument due to the aging of the spring. However the error caused by the aging of the spring and the errors caused due to permanent magnet are opposite to each other, hence both the errors are compensated with each other.

(c) Change in the resistance of the moving coil with the temperature: Generally the temperature coefficients of the value of coefficient of copper wire in moving coil is 0.04 per degree celsius rise in temperature. Due to lower value of temperature coefficient the temperature rises at faster rate and hence the resistance increases. Due to this significant amount of error is caused.

Advantages of Permanent Magnet Moving Coil Instruments

(1)The scale is uniformly divided as the electric current is directly proportional to deflection of the pointer. Hence it is very easy to measure quantities from these instruments.

(2)Power consumption is also very low in these types of instruments.

(3)Higher value of torque is to weight ratio.

(4)These are having multiple advantages, a single instrument can be used for measuring various quantities by using different values of shunts and multipliers.

Instead of various advantages the permanent magnet moving coil instruments or PMMC Instrument posses few disadvantages.

Disadvantages of Permanent Magnet Moving Coil Instruments

(1) These instruments cannot measure ac quantities.

(2) Cost of these instruments is high as compared to moving iron instruments.

Whenever a piece of iron is placed nearer to a magnet it would be attracted by the magnet. The force of this attraction depends upon the strength said

MOVING IRON INSTRUMENT

This instrument is one of the most primitive forms of measuring and relay instrument. Moving iron type instruments are of mainly two types. Attraction type and repulsion type instrument.

magnetic field. If the magnet is electromagnet is electromagnet then the magnetic field strength can easily be increased or decreased by increasing or decreasing electric current through its coil. Accordingly the attraction force acting on the piece of iron would also be increased and decreased. Depending upon this simple phenomenon attraction type moving iron instrument was developed.

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Whenever two pieces of iron are kept side by side and a magnet is brought nearer to them the iron pieces will repulse each other. This repulsion force is due to same magnetic poles induced in same sides the iron pieces due external magnetic field. This repulsion force increases if field strength of the magnet is increased. Like case if the magnet is electromagnet, then magnetic field strength can easily be controlled by controlling input electric current to the magnet. Hence if the electric current increases the repulsion force between the pieces of iron is increased and it the electric current decreases the repulsion force between them is decreased. Depending upon this phenomenon repulsion type moving iron instrument was constructed.

Construction of Moving Iron Instrument

Attraction type moving iron instrument

The basic construction of attraction type moving iron instrument is illustrated bellow A thin disc of soft iron is eccentrically pivoted in front of a coil. This iron tends to move inward that is from weaker magnetic field to stronger magnetic field when electric current flowing through the coil. In attraction moving instrument gravity control was used previously but now gravity control method is replaced by spring control in relatively modern instrument. By adjusting balance weight null deflection of the pointer is achieved. The required damping force is provided in this instrument by air friction. The figure shows a typical type of damping system provided in the instrument, where damping is achieved by a moving piston in an air syringe.

Theory of Attraction Type Moving Iron Instrument

Suppose when there is no electric current through the coil, the pointer is at zero, the angle made by the axis of the iron disc with the line perpendicular to the field is φ. Now due electric current I and corresponding magnetic field strength, the iron piece is deflected to an angle θ. Now component of H in the direction of defected iron disc axis is Hcos{90 - (θ + φ) or Hsin(θ + φ). Now force F acting on the disc inward to the coil is thus proportional to H2sin(θ + φ) hence the force is also proportional to I2sin(θ + φ) for constant permeability. If this force is acting on the disc at a distance l from the pivot, then deflection torque,

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Working of Moving Iron Instrument

Since l is constant.

Where k is constant.

Now, as the instrument is gravity controlled, controlling torque will be

Where k' is constant.

At steady state condition,

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Where K is constant.

Working Principle of Electrostatic Type Instruments

ELECTROSTATIC TYPE INSTRUMENTS

As the name suggests the electrostatic type instrument use static electrical field to produce the deflecting torque. These types of instrument are generally used for the measurement of high voltages but in some cases they can be used in measuring the lower voltages and powers of a given circuit. Now there are two possible ways in which the electrostatic force can act. The two possible conditions are written below,

Construction of Electrostatic Type Instruments

(a) When one of the plates is fixed and other plate is free to move, plates are oppositely charged in order to have attractive force between them. Now due this attractive force movable plate will move towards the stationary or fixed plate till the moving plate stored maximum electrostatic energy.

(b) In other arrangement there may be force of attraction or repulsion or both, due to some rotary of plate.

Force & Torque Equation of Electrostatic Type Instrument

Now let us derive force equation for the linear electrostatic type instruments. Let us consider two plates as shown in the diagram given below.

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Linear Electrostatic Instrument

Plate A is positively charged and plate B is negatively charged. As mentioned above as per the possible condition (a) we have linear motion between the plates. The plate A is fixed and plate B is free to move. Let us assume there exists some force F between the two plates at equilibrium when electrostatic force

becomes equal to spring force. At this point, the electrostatic energy stored in the plates is Now suppose we increase the applied voltage by an amount dV, due to this the plate B moves towards the plate A by a distance dx. The work done against the spring force due to displacement of the plate B be

F.dx. The applied voltage is related to electric current as From this value of electric current the input energy can be calculated as

From this we can calculate the change in the stored energy and that comes out to b By neglecting the higher order terms that appears in the expression. Now applying the principle of energy conservation we have input energy to the system = increase in the stored energy of the system + mechanical work done by the system. From this we can write,

From the above equation the force can be calculated as

Now let us derive force and torque equation for the rotary electrostatic type instruments. Diagram is shown below,

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Rotary Type Electrostatic Instruments

In order to find out the expression for deflecting torque in case of rotary type electrostatic instruments, just replace the in the equation (1) F by Td and dx by dA. Now rewriting the modified equation we have

deflecting torque is equals to . Now at steady state we have controlling torque is given

by the expression Tc = K*A. The deflection A can be written as From this expression we conclude that the deflection of the pointer is directly proportional to the square of the voltage to be measured hence the scale will be non uniform. Let us now discuss about Quadrant electrometer. This instrument is generally used in measuring the voltage ranging from 100V to 20 kilo volts. Again the deflecting torque obtained in the Quadrant electrometer is directly proportional to the square of the applied voltage; one advantage of this is that this instrument can used to measure both the ac and dc voltages. One advantage of using the electrostatic type instruments as voltmeters is that we can extend the range of voltage to be measured. Now there are two ways of extending the range of this instrument. We will discuss them one by one.

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(a) By using resistance potential dividers: Given below is the circuit diagram of this type of configuration.

The voltage which we want to measure is applied across the total resistance r and the electrostatic capacitor is connected across the portion of the total resistance which is marked as r. Now suppose the applied voltage is dc, then we should make one assumption that the capacitor which is connected is having infinite leakage resistance. In this case the multiplying factor is given by the ratio of electrical resistance r/R. The ac operation on this circuit can also be analyzed easily again in case of ac operation we multiplying factor equal to r/R.

(b) By using capacitor multiplier technique: We can increase the range of voltage to be measured by placing a series of capacitors as shown in the given circuit.

Let us derive the expression for multiplying factor for the circuit diagram 1. Let us mark the capacitance of the voltmeter be C1 and series capacitor be C2 as shown in the given circuit diagram. Now the series combination of these capacitor be equal to

Which is the total capacitance of the circuit. Now the impedance of the voltmeter is equal to Z1 = 1/jωC1 and thus total impedance will be equal to

Now the multiplying factor can be defined as the ratio of Z/Z1 which is equal to 1 + C2 / C1.

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Similarly the multiplying factor can also be calculated. Hence by this way we can increase the range of voltage to be measure.

Advantages of Electrostatic Type Instruments

Now let us look at some advantages of electrostatic type instruments.

(a) The first and the most important advantage is that we can measure both ac and dc voltage and the reason is very obvious the deflecting torque is directly proportional to the square of the voltage. (b) Power consumption is quite low in these types of instruments as the electric current drawn by these instruments is quite low.

(c) We can measure high value of voltage.

Disadvantages of Electrostatic Type Instruments

Instead of various advantages, electrostatic instruments posses few disadvantages and these are written below.

(a) These are quite costly as compared to other instruments and also these have large size. (b) The scale is not uniform.

(c) The various operating forces involved are small in magnitude.

Before we study the internal construction of electrodynamometer wattmeter, it very essential to know the principle of working of electrodynamometer type wattmeter. Dynamometer type wattmeter works on very simple principle and this principle can be stated as "when any

ELECTRODYNAMOMETER TYPE WATTMETER

electric current carrying conductor is placed inside a magnetic field, it experiences a mechanical force and due this mechanical force deflection of conductor takes place".

Construction and Working Principle of Electrodynamometer Type Wattmeter

Now let us look at constructional details of electrodynamometer. It consists of following parts There are two types of coils present in the electrodynamometer. They are :

(a) Moving coil : Moving coil moves the pointer with the help of spring control instrument. A limited amount of electric current flows through the moving coil so as to avoid heating. So in order to limit the electric current we have connect the high value resistor in series with the moving coil. The moving is air cored and is mounted on a pivoted spindle and can moves freely. In electrodynamometer type wattmeter, moving coil works as pressure coil. Hence moving coil is connected across the voltage and thus the electric current flowing through this coil is always proportional to the voltage.

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(b) Fixed coil: The fixed coil is divided into two equal parts and these are connected in series with the load, therefore the load electric current will flow through these coils. Now the reason is very obvious of using two fixed coils instead of one, so that it can be constructed to carry considerable amount of electric current. These coils are called the electric current coils of electrodynamometer type wattmeter. Earlier these fixed coils are designed to carry the electric current of about 100 amperes but now the modern wattmeter are designed to carry electric current of about 20 amperes in order to save power.

(c) Control system: Out of two controlling systems i.e.

(1) Gravity control

(2) Spring control, only spring controlled systems are used in these types of wattmeter. Gravity controlled system cannot be employed because they will appreciable amount of errors.

(d) Damping system: Air friction damping is used, as eddy electric current damping will distort the weak operating magnetic field and thus it may leads to error.

(e) Scale: There is uniform scale is used in these types of instrument as moving coil moves linearly over a range of 40 degrees to 50 degrees on either sides.

Now let us derive the expressions for the controlling torque and deflecting torques. In order to derive these expressions let us consider the circuit diagram given below:

Electrodynamometer Type Wattmeter

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We know that instantaneous torque in electro dynamic type instruments is directly proportional to product of instantaneous values of currents flowing through both the coils and the rate of change of flux linked with the circuit.

Let I1 and I2 be the instantaneous values of currents in pressure and electric current coils respectively. So the expression for the torque can be written as:

where x is the angle. Now let the applied value of voltage across the pressure coil be

Assuming the electrical resistance of the pressure coil be very high hence we can neglect reactance with respect to its resistance. In this the impedance is equal to its electrical resistance therefore it is purely resistive. The expression for instantaneous electric current can be written as I2 = v / Rp where Rp is the resistance of pressure coil.

If there is phase difference between voltage and electric current, then expression for instantaneous electric current through electric current coil can be written as

As electric current through the pressure coil in very very small compare to electric current through electric current coil hence electric current through the electric current coil can be considered as equal to total load current.

Hence the instantaneous value of torque can be written as

Average value of deflecting torque can be obtained by integrating the instantaneous torque from limit 0 to T, where T is the time period of the cycle.

Controlling torque is given by Tc = Kx where K is spring constant and x is final steady state value of deflection.

Advantages of Electrodynamometer Type Wattmeter

Following are the advantages of electrodynamometer type wattmeters and they are written as follows: (a) Scale is uniform up to certain limit.

(b) They can be used for both to measure ac as well dc quantities as scale is calibrated for both.

Errors in Electrodynamometer Type Wattmeter

Following are the errors in the electrodynamometer type wattmeters:

(a) Errors in the pressure coil inductance.

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(b) Errors may be due to pressure coil capacitance.

(c) Errors may be due to mutual inductance effects.

(d) Errors may be due connections.(i.e. pressure coil is connected after electric current coil)

(e) Error due to Eddy currents.

(f) Errors caused by vibration of moving system.

(g) Temperature error.

(h) Errors due to stray magnetic field.

Before we introduce various types of power factor meters it is very essential to understand what are the needs of power factor meter? Why we do not directly calculate power factor in an a.c. circuit just by dividing the power with product of

POWER FACTOR METERS

electric current and voltage as these readings can be easily obtained from wattmeter, ammeter and voltmeter. Obviously there various limitations of using this method as it may not provide high accuracy, also chances of increment of error is very high. Therefore this method is not adopted in industrial world. Measurement of power factor accurately is very essential everywhere. In power transmission system and distribution system we measure power factor at every station and electrical substation using these power factor meters. Power factor measurement provides us the knowledge of type of loads that we are using, helps in calculation of losses happening during the power transmission system and distribution. Hence we need a separate device for calculating the power factor accurately and more precisely. General construction of any power factor meter circuit include two coils pressure coil and electric current coil. Pressure coil is connected across the circuit while electric current coil is connected such it can carry circuit electric current or a definite fraction of current, by measuring the phase difference between the voltage and electric current the electrical power factor can be calculated on suitable calibrated scale. Usually the pressure coil is splits into two parts namely inductive and non-inductive part or pure resistive part. There is no requirement of controlling system because at equilibrium there exist two opposite forces which balance the movement of pointer without any requirement of controlling force. Now there are two types of power factor meters.

(1) Electrodynamometer type and (2) Moving iron type.

Let us study electrodynamometer type first.

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In electrodynamometer type power factor meter there are further two types on the basis of supply voltage

(1) Single phase (2) Three phase.

Now the pressure coil is spitted into two parts one is purely inductive another is purely resistive as shown in the diagram by resistor and inductor. At present the reference plane is making an angle A with coil 1. And the angle between both the coils 1 and 2 is 90°. Thus the coil 2 is making an angle (90°+A) with the reference plane. Scale of the meter is properly calibrated shown the value values of cosine of angle A. Let us mark the electrical resistance connected to coil 1 be R and inductor connected to coil 2 be L. Now during measurement of power factor the values of R and L are adjusted such that R=ωL so that both coils carry equal magnitude of current. Therefore the electric current passing through the coil 2 is lags by 90° with reference to electric current in coil 1 as coil 2 path is highly inductively in nature.

The general circuit diagram of single phase electrodynamometer power factor meter is given below.

Single Phase Power Factor Meter

Let us derive an expression for deflecting torque for this power factor meter. Now there are two deflecting torques one is acting on the coil 1 and another is acting on the coil 2. The coil winding are arranged such that the two torques produced, are opposite to each other and therefore pointer will take a position where the two torques are equal. Let us write a mathematical expression for the deflecting torque for coil 1-

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Where M is the maximum value of mutual inductance between the two coils, B is the angular deflection of the plane of reference.

Now the mathematical expression for the deflecting torque for coil 2 is-

At equilibrium we have both the torque are equal thus on equating T1=T2 we have A=B. From here we can see that the deflection angle is the measure of phase angle of the given circuit. The phasor diagram is also shown for the circuit such that the electric current in the coil 1 is approximately at an angle of 90° to electric current in the coil 2.

Given below are some of the advantages and disadvantages of use electro dynamic type power factor meters.

Advantages of Electro dynamic Type Power Factor Meters

(1) Losses are less because of minimum use of iron parts and also give less error over a small range of frequency as compared to moving iron type instruments.

(2) They high torque is to weight ratio.

Disadvantages of Electro dynamic Type Power Factor Meters

(1) Working forces are small as compared to moving iron type instruments.

(2) Scale is not extended over 360°.

(3) Calibration of electrodynamometer type instruments are highly affected by the changing the supply voltage frequency.

(4) They are quite costly as compared to other instruments.