Lecture notes Electrical measurements

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CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION FOR 5TH & 6TH SEMESTER OF ELECTRICAL ENGINEERING & EEE (B.TECH PROGRAMME) DEPARTMENT OF ELECTRICAL ENGINEERING VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY BURLA -768018, ODISHA, INDIA 1 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 DISCLAIMER This document does not claim any originality and cannot be used as a substitute for prescribed textbooks. The matter presented here is prepared by the author for their respective teaching assignments by referring the text books and reference books. Further, this document is not intended to be used for commercial purpose and the committee members are not accountable for any issues, legal or otherwise, arising out of use of this document. 2 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 SYLLABUS ELECTRICAL MEASUREMENTS & INSTRUMENTATION (3-1-0) MODULE-I (10 HOURS) Measuring Instruments: Classification, Absolute and secondary instruments, indicating instruments, control, balancing and damping, constructional details, characteristics, errors in measurement, Ammeters, voltmeters: (DC/AC) PMMC, MI, Electrodynamometer type Wattmeters: Electrodynamometer type, induction type, single phase and three phase wattmeter, compensation, Energymeters: AC. Induction type siqgle phase and three phase energy meter, compensation, creep, error, testing, Frequency Meters: Vibrating reed type, electrical resonance type MODULE-II (10 HOURS) Instrument Transformers: Potential and current transformers, ratio and phase angle errors, phasor diagram, methods of minimizing errors; testing and applications. Galvanometers: General principle and performance equations of D' Arsonval Galvanometers, Vibration Galvanometer and Ballistic Galvanometer. Potentiometers: DC Potentiometer, Crompton potentiometer, construction, standardization, application. AC Potentiometer, Drysdale polar potentiometer; standardization, application. MODULE-III (10 HOURS) DC/AC Bridges :General equations for bridge balance, measurement of self inductance by Maxwell’s bridge (with variable inductance & variable capacitance), Hay’s bridge, Owen’s bridge, measurement of capacitance by Schearing bridge, errors, Wagner’s earthing device, Kelvin’s double bridge. Transducer: Strain Gauges, Thermistors, Thermocouples, Linear Variable Differential Transformer (LVDT), Capacitive Transducers, Peizo-Electric transducers, Optical Transducer, Torque meters, inductive torque transducers, electric tachometers, photo-electric tachometers, Hall Effect Transducer MODULE-IV (10 HOURS) CRO: Block diagram, Sweep generation, vertical amplifiers, use of CRG in measurement of frequency, phase, Amplitude and rise time of a pulse. Digital Multi-meter: Block diagram, principle of operation, Accuracy of measurement, Electronic Voltmeter: Transistor Voltmeter, Block diagram, principle of operation, various types of electronic voltmeter, Digital Frequency meter: Block diagram, principle of operation TEXT BOOKS 1. A Course in Elec. & Electronics Measurements & Instrumentation: A K. Sawhney 2. Modern Electronic Instrumentation and Measurement Techniques: Helfrick & Cooper 3. Electrical Measurement and Measuring Instruments - Golding & Waddis 3 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Model Question Paper: Set-1 Full Marks: 70 Time: 3 hours Answer any six questions including question No. 1 which is compulsory. The figures in the right-hand margin indicate marks. (Answer any six questions including Q.No. 1) 2X10 1. Answer the following questions: (a) Differentiate between the spring control and gravity control. (b) Why an ammeter should have a low resistance value. (c) What are the precautions taken while using a DC voltmeter and DC ammeter. (d) What is the major cause of creeping error in an energy meter (e) What are the errors occurs in instrument transformers. (f) Differentiate the principle of dc potentiometer and ac potentiometer. (g) What are the sources of errors in AC bridge measurement. (h) Differentiate between dual trace and dual beam CRO. (i) What are active and passive transducers? Give examples. (j) What is piezoelectric effect. 2. (a) With a neat diagram explain in detail the construction of PMMC instrument. (b)What are the shunts and multiplier? Derive the expression for both, with reference to meters used in electrical circuits. 5+5 3. (a) Discuss with block diagram, the principle of operation of single phase energy meter. (b) An energy meter is designed to make 100 revolutions of the disc for one unit of energy. Calculate the number of revolutions made by it , when connected to a load carrying 40 A at 230V and 0.4 p.f. for 1 hour. If it actually makes 360 revolutions, find the percentage error. 5+5 4. (a) Derive expression for actual transformation ratio, ratio error and phasor angle error of a P.T. (b) A current transformer with bar primary has 300 turns in its secondary winding. The resistance and reactance of the secondary circuit are 1.5Ω and 1.0 Ω respectively, including the transformer winding. With 5A flowing in the secondary winding, the magnetizing mmf is 100AT and the core loss is 1.2 W. Determine the ratio and phase angle errors. 5+5 5. (a) Derive the equation of balance for Anderson bridge and also draw the phasor diagram. (b) An AC bridge is balanced at 2KHz with the following components in each arm: Arm AB=10KΩ, Arm BC=100µF in series with 100KΩ, Arm AD=50KΩ Find the unknown impendence R±jX in the arm DC, if the detector is between BD. 6. (a) What is transducer? Briefly explain the procedure for selecting a transducer. (b) Derive an expression for gauge factor in terms of Poission’s ration. 5+5 7. (a) With a block diagram, explain the working of CRO (b) With a block diagram, explain in detail the digital frequency meter 5+5 8. Write short notes on (a) Kelvin’s double bridge (b) D- Arsonaval galvanometer 5+5 4 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Model Question Paper: Set-2 Full Marks: 70 Time: 3 hours Answer any six questions including question No. 1 which is compulsory. The figures in the right-hand margin indicate marks. (Answer any six questions including Q.No. 1) 2X10 Q.1 Answer the following questions: (a) Why is damping required for an electromechanical measuring instrument? (b) Why is scale of MI instrument calibrated non- linearly? (c) What is the difference between analog and digital frequency meter? (d) Which instrument can be used to measure non-sinusoidal voltage? (e) What is the major cause of creeping error in an energy meter? (f) What do you mean by active and passive transducer? Give suitable examples. (g) Draw a suitable AC bridge used for measurement of frequency. (h) What are the steps to be taken for minimizing errors in PT? (i) Discuss briefly the role of ordinary galvanometer? (j) What is the function of time base generator in CRO? Q.2 (a) Derive the torque equation of a moving iron instrument? 5 (b) Sketch and explain the working of moving-coil instrument. 5 Q.3 (a) Discuss a method for measurement of low resistance. 5 (b) Explain the operation of a Wagner’s earthing device. 5 Q.4 Derive the errors of CT and PT, and discuss its preventives. 10 Q.5 (a) Discuss about a ac bridge used for measurement of capacitance 5 (b) Discuss about a galvanometer which is used for measurement of frequency. 5 Q.6 (a) How is the voltmeter calibrated with DC potentiometer ? 5 (b) What is the use of LVDT? Discuss its basic principle of operation. 5 Q.7 (a) How are the frequency and phase measured in CRO. 5 (b)Draw the block diagram of an electronic voltmeter and explain its operation. 5 8. Write short notes on any two: 5X2 (a) Owen’s bridge (b)Digital frequency meter (c) Hall-effect transducer 5 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Model Question Paper: Set-3 Full Marks: 70 Time: 3 hours Answer any six questions including question No. 1 which is compulsory. The figures in the right-hand margin indicate marks. (Answer any six questions including Q.No. 1) 2X10 1. Answer the following questions: (k) Why scales of the gravity control instruments are not uniform but are crowded? (l) Why eddy current damping cannot be used for moving iron instrument? (m) What is mean by Phantom Load? (n) Why do we use a multiplier with a voltmeter? (o) What is the major cause of creeping error in an energy meter? (p) Why is dynamometer type instrument chiefly used as a wattmeter? (q) Define gauge factor of a strain gauges how is it related to poisons ratio µ ? (r) Why the secondary of a CT is never left open circuited? (s) Why there are two conditions of balance in ac bridges, where as there is only one for dc bridges? (t) How to prevent the loading of a circuit under test when a CRO is used? 2. (a) Draw the possible methods of connecting the pressure coil of a wattmeter and compare the errors. Explain the meaning of ‘compensating winding’ in a wattmeter and show how they help to reduce the error. 5 (b) Sketch and explain the working of moving-coil instrument. 5 3. (a) What are the different testing conducted on a single phase energy meter? 5 (b)The meter constant of 230V, 10A energy meter is 1700. The meter is tested under half load and rated voltage at unity p.f. The meter is found to make 80 revolutions in 138 sec. Find % error. 5 4. Differentiate between a C.T. and P.T. Discuss the theory of a P.T with phasor diagrams. Derive expression for actual transformation ratio, ratio error and phasor angle error of a P.T. 10 5. (a) Describe how an AC potentiometer, can be used for the calibration of wattmeter? 5 (b)Explain how LVDT can be used for measurement of displacement. 5 6. (a) Derive the equation of balance of a Schering Bridge. Draw the phasor diagram under null conditions and explain how loss angle of capacitor can be calculated. 5 (b) Describe the general working principle of a D’ Arsonval Galvanometer. 5 7. (a) Explain the use of CRG in the measurement of frequency. 5 (b)Draw the block diagram of an electronic voltmeter and explain its operation. 5 8. Write short notes on: 5X2 (a) Thermo couple (b)Peizo-Electric Transducers. 6 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Model Question Paper: Set-4 Full Marks: 70 Time: 3 hours Answer any six questions including question No. 1 which is compulsory. The figures in the right-hand margin indicate marks. (Answer any six questions including Q.No. 1) 1. Answer the following questions: 2 x 10 (a) What are the parameters on which the critical damping of galvanometer depends? Why critical damping is important? (b) The current flowing through a resistance of 10.281 kΩ is measured as 1.217 mA. Calculate the voltage drop across the resistor to the appropriate number of significant errors. (c) What are the main advantages and disadvantages of PMMC instruments? (d) Why an electrodynamometer type instrument is called a “Universal Instrument”? (e) Write the working principle of resonance type frequency meter. (f) What are the advantages of electronic voltmeter over electro – mechanical type voltmeter? (g) Why Maxwell Bridge is limited to the measurement of medium – Q coils? (h) What will happen in a current transformer, if the secondary circuit is accidentally opened while the primary winding is energized? (i) Suggest a transducer for the measurement of displacement in the order of one – tenth of millimeter and write the basic principle of measurement. (j) What is the function of delay line in oscilloscope? Q. 2. 5 + 5 a) The coil of a measuring instrument has a resistance of 1 Ω and the instrument has a full scale deflection of 250 V when a resistance of 4999 Ω is connected with it. Find the current range of the instrument when used as an ammeter with the coil connected across a shunt of (1/499) Ω and the value of the shunt resistance for the instrument to give a full scale deflection of 50 A. b) Distinguish between gross error, systematic error and random error with examples. What are the methods for their elimination/reduction? Q. 3. 5 + 5 a) Draw the circuit diagram of Schering Bridge. Derive the conditions for balancing the bridge and draw the phasor diagram during balanced condition. b) Describe the theory and method of measurement of low resistance using Kelvin’s double Bridge. How the effect of thermo – electric emf is taken into account during measurement? 7 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Q. 4. 10 A single range student type potentiometer has 20 step dial switch where each step represents 0.1 V. The dial resistors are 20 Ω. The slide wire of the potentiometer is circular and has 10 turns and a resistance of 10 Ω each. The slide wire has 200 divisions and interpolation can be done to one fourth of a division. The working battery has a voltage of 10 V and negligible internal resistance. Draw the circuit diagram and calculate i) The measuring range of potentiometer ii) The resolution iii) Working current iv) Resistance of series rheostat Q. 5. 5 + 5 a) What is the requirement of “Screening of bridge components”? Draw the circuit diagram of Wagner’s earthing device and explain its operation. b) Define the sensitivity of a strain gauge. Draw the circuit for measurement of strain and derive the expression of output voltage in terms of strain. Q. 6. 5 + 5 a) Derive the torque equation of moving iron instrument and comment on the shape of the scale. b) Prove that for electrodynamometer type wattmeter true power = cos Φ / cos Φ cos (Φ – β x actual wattmeter reading Where cos Φ = power factor of the circuit -1 β = tan (ωL/R) where L and R are the inductance and resistance of the pressure coil of the circuit. Q. 7. 5 + 5 a) Describe the construction and principle of operation of D’ Arsonval type Galvanometer. b) Discuss the major sources of errors in current transformer. What are the means to reduce errors in CT? Explain design and constructional feature to reduce the error. Q. 8. 6 + 4 a) Describe the measurement of frequency, phase angle and time delay using oscilloscope with suitable diagrams and mathematical expressions. b) With block diagram explain the operation of “Ramp type’ digital voltmeter. 8 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 MEASURING INSTRUMENTS 1.1 Definition of instruments An instrument is a device in which we can determine the magnitude or value of the quantity to be measured. The measuring quantity can be voltage, current, power and energy etc. Generally instruments are classified in to two categories. Instrument Absolute Instrument Secondary Instrument 1.2 Absolute instrument An absolute instrument determines the magnitude of the quantity to be measured in terms of the instrument parameter. This instrument is really used, because each time the value of the measuring quantities varies. So we have to calculate the magnitude of the measuring quantity, analytically which is time consuming. These types of instruments are suitable for laboratory use. Example: Tangent galvanometer. 1.3 Secondary instrument This instrument determines the value of the quantity to be measured directly. Generally these instruments are calibrated by comparing with another standard secondary instrument. Examples of such instruments are voltmeter, ammeter and wattmeter etc. Practically secondary instruments are suitable for measurement. Secondary instruments Indicating instruments Recording Integrating Electromechanically Indicating instruments 9 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 1.3.1 Indicating instrument This instrument uses a dial and pointer to determine the value of measuring quantity. The pointer indication gives the magnitude of measuring quantity. 1.3.2 Recording instrument This type of instruments records the magnitude of the quantity to be measured continuously over a specified period of time. 1.3.3 Integrating instrument This type of instrument gives the total amount of the quantity to be measured over a specified period of time. 1.3.4 Electromechanical indicating instrument For satisfactory operation electromechanical indicating instrument, three forces are necessary. They are (a) Deflecting force (b) Controlling force (c)Damping force 1.4 Deflecting force When there is no input signal to the instrument, the pointer will be at its zero position. To deflect the pointer from its zero position, a force is necessary which is known as deflecting force. A system which produces the deflecting force is known as a deflecting system. Generally a deflecting system converts an electrical signal to a mechanical force. Fig. 1.1 Pointer scale 10 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 1.4.1 Magnitude effect When a current passes through the coil (Fig.1.2), it produces a imaginary bar magnet. When a soft-iron piece is brought near this coil it is magnetized. Depending upon the current direction the poles are produced in such a way that there will be a force of attraction between the coil and the soft iron piece. This principle is used in moving iron attraction type instrument. Fig. 1.2 If two soft iron pieces are place near a current carrying coil there will be a force of repulsion between the two soft iron pieces. This principle is utilized in the moving iron repulsion type instrument. 1.4.2 Force between a permanent magnet and a current carrying coil When a current carrying coil is placed under the influence of magnetic field produced by a permanent magnet and a force is produced between them. This principle is utilized in the moving coil type instrument. Fig. 1.3 1.4.3 Force between two current carrying coil When two current carrying coils are placed closer to each other there will be a force of repulsion between them. If one coil is movable and other is fixed, the movable coil will move away from the fixed one. This principle is utilized in electrodynamometer type instrument. 11 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Fig. 1.4 1.5 Controlling force To make the measurement indicated by the pointer definite (constant) a force is necessary which will be acting in the opposite direction to the deflecting force. This force is known as controlling force. A system which produces this force is known as a controlled system. When the external signal to be measured by the instrument is removed, the pointer should return back to the zero position. This is possibly due to the controlling force and the pointer will be indicating a steady value when the deflecting torque is equal to controlling torque. T =T (1.1) d c 1.5.1 Spring control Two springs are attached on either end of spindle (Fig. 1.5).The spindle is placed in jewelled bearing, so that the frictional force between the pivot and spindle will be minimum. Two springs are provided in opposite direction to compensate the temperature error. The spring is made of phosphorous bronze. When a current is supply, the pointer deflects due to rotation of the spindle. While spindle is rotate, the spring attached with the spindle will oppose the movements of the pointer. The torque produced by the spring is directly proportional to the pointer deflection . θ T ∝θ (1.2) C The deflecting torque produced T proportional to ‘I’. WhenT =T , the pointer will come to a d C d steady position. Therefore θ ∝ I (1.3) 12 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Fig. 1.5 Since, θ and I are directly proportional to the scale of such instrument which uses spring controlled is uniform. 1.6 Damping force The deflection torque and controlling torque produced by systems are electro mechanical. Due to inertia produced by this system, the pointer oscillates about it final steady position before coming to rest. The time required to take the measurement is more. To damp out the oscillation is quickly, a damping force is necessary. This force is produced by different systems. (a) Air friction damping (b) Fluid friction damping (c) Eddy current damping 1.6.1 Air friction damping The piston is mechanically connected to a spindle through the connecting rod (Fig. 1.6). The pointer is fixed to the spindle moves over a calibrated dial. When the pointer oscillates in clockwise direction, the piston goes inside and the cylinder gets compressed. The air pushes the piston upwards and the pointer tends to move in anticlockwise direction. 13 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Fig. 1.6 If the pointer oscillates in anticlockwise direction the piston moves away and the pressure of the air inside cylinder gets reduced. The external pressure is more than that of the internal pressure. Therefore the piston moves down wards. The pointer tends to move in clock wise direction. 1.6.2 Eddy current damping Fig. 1.6 Disc type An aluminum circular disc is fixed to the spindle (Fig. 1.6). This disc is made to move in the magnetic field produced by a permanent magnet. 14 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 When the disc oscillates it cuts the magnetic flux produced by damping magnet. An emf is induced in the circular disc by faradays law. Eddy currents are established in the disc since it has several closed paths. By Lenz’s law, the current carrying disc produced a force in a direction opposite to oscillating force. The damping force can be varied by varying the projection of the magnet over the circular disc. Fig. 1.6 Rectangular type 1.7 Permanent Magnet Moving Coil (PMMC) instrument One of the most accurate type of instrument used for D.C. measurements is PMMC instrument. Construction: A permanent magnet is used in this type instrument. Aluminum former is provided in the cylindrical in between two poles of the permanent magnet (Fig. 1.7). Coils are wound on the aluminum former which is connected with the spindle. This spindle is supported with jeweled bearing. Two springs are attached on either end of the spindle. The terminals of the moving coils are connected to the spring. Therefore the current flows through spring 1, moving coil and spring 2. Damping: Eddy current damping is used. This is produced by aluminum former. Control: Spring control is used. 15 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Fig. 1.7 Principle of operation When D.C. supply is given to the moving coil, D.C. current flows through it. When the current carrying coil is kept in the magnetic field, it experiences a force. This force produces a torque and the former rotates. The pointer is attached with the spindle. When the former rotates, the pointer moves over the calibrated scale. When the polarity is reversed a torque is produced in the opposite direction. The mechanical stopper does not allow the deflection in the opposite direction. Therefore the polarity should be maintained with PMMC instrument. If A.C. is supplied, a reversing torque is produced. This cannot produce a continuous deflection. Therefore this instrument cannot be used in A.C. Torque developed by PMMC Let T =deflecting torque d T = controlling torque C θ = angle of deflection K=spring constant b=width of the coil 16 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 l=height of the coil or length of coil N=No. of turns I=current B=Flux density A=area of the coil The force produced in the coil is given by F = BIL sinθ (1.4) ° θ = 90 When For N turns, (1.5) F = NBIL Torque produced T =F×⊥ distance (1.6) d r T = NBIL×b=BINA (1.7) d T =BANI (1.8) d T ∝I (1.9) d Advantages  Torque/weight is high  Power consumption is less  Scale is uniform  Damping is very effective  Since operating field is very strong, the effect of stray field is negligible  Range of instrument can be extended Disadvantages  Use only for D.C.  Cost is high  Error is produced due to ageing effect of PMMC  Friction and temperature error are present 17 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 1.7.1 Extension of range of PMMC instrument Case-I: Shunt A low shunt resistance connected in parrel with the ammeter to extent the range of current. Large current can be measured using low current rated ammeter by using a shunt. Fig. 1.8 Let R =Resistance of meter m R =Resistance of shunt sh I = Current through meter m I =current through shunt sh I= current to be measure ∴V =V (1.10) m sh I R =I R m m sh sh I R m sh = (1.11) I R sh m Apply KCL at ‘P’ I =I +I (1.12) m sh n Eq (1.12) ÷ by I m I I sh =1+ (1.13) I I m m 18 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 I R m = 1+ (1.14) I R m sh   R m   ∴I = I 1+ (1.15) m   R  sh   R  m   1+ is called multiplication factor   R  sh  Shunt resistance is made of manganin. This has least thermoelectric emf. The change is resistance, due to change in temperature is negligible. Case (II): Multiplier A large resistance is connected in series with voltmeter is called multiplier (Fig. 1.9). A large voltage can be measured using a voltmeter of small rating with a multiplier. Fig. 1.9 Let R =resistance of meter m R =resistance of multiplier se V =Voltage across meter m V = Voltage across series resistance se V= voltage to be measured I =I (1.16) m se V V m se = (1.17) R R m se V R se se ∴ = (1.18) V R m m 19 CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015 Apply KVL, V =V +V (1.19) m se n Eq (1.19) ÷V m   V V R se se =1+ =1+  (1.20)   V V R m m  m    R se   ∴V =V 1+ (1.21) m   R  m   R  se   1+ → Multiplication factor   R  m  1.8 Moving Iron (MI) instruments One of the most accurate instrument used for both AC and DC measurement is moving iron instrument. There are two types of moving iron instrument. • Attraction type • Repulsion type 1.8.1 Attraction type M.I. instrument Construction: The moving iron fixed to the spindle is kept near the hollow fixed coil (Fig. 1.10). The pointer and balance weight are attached to the spindle, which is supported with jeweled bearing. Here air friction damping is used. Principle of operation The current to be measured is passed through the fixed coil. As the current is flow through the fixed coil, a magnetic field is produced. By magnetic induction the moving iron gets magnetized. The north pole of moving coil is attracted by the south pole of fixed coil. Thus the deflecting force is produced due to force of attraction. Since the moving iron is attached with the spindle, the spindle rotates and the pointer moves over the calibrated scale. But the force of attraction depends on the current flowing through the coil. Torque developed by M.I Let ‘θ ’ be the deflection corresponding to a current of ‘i’ amp Let the current increases by di, the corresponding deflection is ‘θ +dθ ’ 20

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