electrical measurment

7/31/2019 Electrical Measurment

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Q. 81. Explain:(i) Primary and secondary transducer

(ii) Passive and active transducers

(u) Analog and digital transducers(ii) Transducers and inverse transducers.

Ans. (1) Primary and secondarytransducers. This will be better explained with

the help of Fig. 5.

The Bourden tube acting as a primary detector,

senses pressure (P) and converts it intodisplacement of its free end, which moves the coreof L V D T whose output is voltage proportional tothe pressure Thus there are two stages oftransduction The Bourden tube acts as primarytransducer and the L V D T acts or a secondarytransducer

In most of the cases there is a suitablecombination, where a mechanical device (e gBourden tube) acts as a primary transducer and anelectrical device (e g L V D T) acts as a secondarytransducer2. Passive and active transducer (a) The

passive transducers are those that denve thepower required for transition from an auxilliary


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power source They also derive a part of therequired power from the quantity undermeasurement They are also called Externally

powered transducers The passive transducerscannot function without an external power sourceThe examples of passive transducers are resistive

inductive and capacitive transducers(b) Active transducers are those, that do notrequire an external power source They are calledself generating as they develop their own power

The power reeffect required for production ofoutput power is obtained from the quantity undermeasurementExamples are Taco generators thermocouples,photovoltaic cell, piezo electric crystal etc3. Analog and digital transducers. (a) Analogtransducers are those, that convert the inputquantity into an analog output which is acontinuous function of time

Examples are Strain guage, L V D T thermocouple,thermistor etc(b) Digital transducers are those that convert the

input into an electrical output which is in the form

of pulses.

As a binary number uses only two digits 0 and 1,itcan be easily be represented by opaque and

transparent areas on a glass scale (Fig 6) or bynon-conducting and conducting areas on a metalscale The complete binary number denotingposition is obtained by scanning the pattern

across the scale at a stationary index mark The


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glass scales can be read by means of light sources,an optical system and the photocells The

metal scales are scanned by brushes makingelectrical contact with individual tracks Theresolution depends upon the digits, comprising the

binary number and is n/2 of full scale where n isthe number of digits4. Transducers and Inverse Transducers.Transducers are the devices, which convert a non-electrical quantity into electrical output.Inverse transducers are the devices which convertan electrical quantity into non

electrical output. The examples of inversetransducers are:(i) A piezo electrical transducer: as, when avoltage applied to its surface, it changesits dimensions i.e. it converts the voltage into adisplacement.(ii) A current carrying coil moving in a magnetic

field produces a rotational torque!displacement.(iii) An ammeter or voltmeter. Converts currentinto mechanical displacement.(iv) Data indicating/recording devices such as penrecorder, C.R.O. etc.

The most useful application of inverse transducers

is in Feedback measurement


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system. The Fig. 7 shows a block diagram of afeed back measurement system using

inverse transducers. The firm lines show electrical

devices/signals and dotted linesshow mechanical devices! signals.

In this, the output signal (Usually in electricalform) is fed back and converted by passingthrough an inverse transducer into a non electricalform suitable for comparison with the quantityunder measurement (non electrical). The resultingerror signal is passed through a transducer into

the electrical form and is applied to give outputindication.

Q. 82. Give examples with applications ofactive and passive transducers.

Ans. (a) Active transducers (self-generating-no external power)

Table5

Sr.no Name oftranducers

Application (Thephysical quantitiesmeasured)

1. Thermocouple and

Thermopiles

Temperature, heat

2. Moving coil Velocity, vibrations


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generator

3. Piezoelectrictransducers

Sound, velocity,acceleration,

pressure vibration

4. Photovoltaic cell Phoovoltaic cell

(b) Passive transducers (externally powered)

Sr

no

Name of the

transducers

Application (The

physicalquantities measured)

1.(a) Strain gauge Force, torque,displacement

(b)Hot wire meter Gas pressure

(c) Resistance

thermometerTemperature

(d)Thermistor Temperature

(e)Resistancehygrometer

Humidity

2.(a) Capacitor

pressure gaugeDisplacement,

pressure

(b)

Capacitor

microphone

Speech, music, noise

3.(a) Differentialtransformer(LVDT)

Pressure,displacementvibrations

(b)

Magnetostriction

gauge

Force, pressure,

sound


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4.(a) Hall effect

generatorMagnetic flux,

current

(b)

Photoemissive cell Light

(c) Photomultipliertube

Light

Q. 83. Explain Gauge factor.

Describe working principle and types of wirestrain gaugesWrite about materials used for making wirestrain gauges and applications

Ans (a) Gauge Factor

If a metal conductor (wire) is stretched orcompressed, its dimension (length and crosssectional area) change and due to strain, theresistance of the conductor also angages This isalso called Piezo resistive effect Note thatresistance= p -f-, where p is the resistively, 1 the length and

a is the cross sectional area

If a wire is stretched and its original length L

Let change m the length = &

Strain= change in lengthOriginal length

If the resistance of the conductor wire RDue to strain,, change in the resistance = d R


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New resistance = R +zR . . . (ii)

The gauge factor of a strain gauge is defined as

the ratio of the change in resistance per unitresistance to the change in length per unit length.

(b) Wire Strain Gauge. This is a device used for

measurement of strain/stress. This is also, used assecondary transducer.

Type of wire strain gauges. They are of thefollowing types:(1) Unbounded wire strain gauge. It consistsof an unbounded wire structure on a platform.These wires have equal length. The four wires

form a Wheatstone bridge. See Figs. 8 (a), (b).When the force (or pressure) to be measured isapplied to the strain gauge, the resistance wire Pand S increase in length while the resistance wiresR and Q decrease in length. This unbalances theWheatstone bridge. The change in the resistance sproportiona1iQtheienth, and the unbalance ridge

causes an ps Ue terminals, the output voltagebeing proportional to the force (or pressure)applied.


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Note that the bridge is balanced, only whenP/Q = R/SThe Fig. 9. shows an unbounded strain gauge.

(ii) Bonded wire strain gauge. It consists offine wire mesh (about 30 m dia.) which is

connected to a thin box of bakelite or paper sheet.The base is bonded to the structure, the bondingmaterial helps in transfer of strain from base to

the wires.Figs. 10 (a to d) show different bonded wire straingauges.


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(c) Material for strain Gauges.

(i) For wire. Table shows the material used for wire

in wire strain gauges and their specifications.Table 7: Materials used for the wire of straingauges

Sr.no

Name ofmaterial

Composition

Resistivity

(Q m)

Max.Permissi

ble ftmp(C)

Gauge

factor

1. Nichrome

Ni 80%Cr20%

100 x10^8

1300 2.5

2. Constant

anNi 50%

Cu50%50 x 10

^8450 2.0

3. Nickel .. 6 x

10^8

1000 -12

4. Platinum .. 9 x

10^81100 5.1

5. Mangnine

Cu 85%

Mn 15%48 x10^8

70 0.48

6. Iron(soft)

.. 75 x10^8

1200 4.3

7. Carbon .. 400 x 3000 2.0


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10^8

(ii) For Base. The material used for the base(carrier) of the wire gauges are:(1) Epoxy-up to 150C(2) Bakelite / cellulose / fibre glass up to 300C.(iii) Adhesive materials. The adhesive (bandingmaterials) used are: ethyl cellulose, cement,epoxy, bakelite, etc. They can work up to 200C.

They are used as binding materials in bondedstrain gauges to bind wire with the base.Applications of Wire Strain Gauges:(a) They are used to analyze stress and strain in

bridges, roads, etc. The strain gauge is used inwheat-stone bridge connections, and the outputcan be displayed on a calibrated C.R.O. and the

stress / strain may be measured. See Fig. 11.

(b) They are also used effectively ta measuretension, torque, force, pressure, etc. in astructure.

Q 84 Write a note an Rosettes


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Ans. The rosettes are a combination of singleelement strain gauges. They are used for specificstress/strain analysis.

An element may be subjected to stresses in anydirection and it is not possible to locate thedirection of the principal stress. It is not possible

to orient the strain gauges along the direction ofprincipal stress, Therefore, necessity was felt tohave strain gauge, which measures the value ofprincipal strain and strains without knowing the

direction.Thereare the following types of rosettes.

i. Two element rosettes. These are used inforce transducers. The elements areconnected in the Wheatstone bridgeconfiguration. The Fig. 12 shows two element

rosette (90) stacked (Foil type) strain guage.

(ii) Three element rosettes. These are usedfor determination of direction and

magnitude of principal strains resulting fromcomplex structural leading.


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Generally the three elements are displaced fromeach other at 45C or 6O. The 45C provide

better angular resolution and are used when thedirection of the principal strain is known, while600 rosettes are used when the direction ofprincipal stress is not known.

Q. 85. Explain construction and

applications of Thermistors.

Ans. (a) Thermistors. These are basicallythermal resistors, their resistance variesnon linearly to the temperature. The Fig. 14shows the characteristic of thermistors.

Infact, these are semi-conductor devices ; withnegative temperature co-efficient of resistance.

Thermistor are manufactured from oxides ofmetals like manganese, nickel, cobalt, copper,

iron, aluminium etc.


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The temperature of thermistor vary at a veryhigh range from several hundred ohms to megaohms. They are available in various shapes such

as discs, rods, beads etc. The various shapes ofthermistor are shown m Fig 15

Applications. (1) The main measurement.application Of thermistors is for temperature

For this, thermistor is connected in series with abattery and a micro ammeter, which may becalibrated m terms of temperature (Fig 16)

(2) The other applications of thermistors are

(z) For control of temperatures(n) To measure difference in temperatures(iii) To measure composition of gas(iv) To measure flow

Q 86 Explain working principle and varioustypes of photo electric transducers


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Ans (a) Photoelectric transducersPrincipal. cThese are used to measure lightintensity examples of Photo electric cells Photo

voltic cells conductive cells Photo diodes andphoto transistors etc These convert thebghtfal1ir them into voltage, which can be

mea4yyoltmeter calibrated in units of(b) Types : Below few photoelectrictransducers have been described:

1.. Photo Emissive Cell (Photo Tube). The

cathode of photo emissive cell emits electrons,when light falls These electrons are accumulatedat its anode or plateThe fig 17(a) shows construction Fig (b) showscharacteristics between negative voltage andleakage current The curves shows electricalintensities in watts per m2 at different currents

The tube is used to measure luminous flux orintensity The circuit arrangement is shown in Fig18


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The voltmeter is calibrated in terms of luminousflux/Intensity. The output voltage may beamplified to drive next stages of measurement.

These devices are stable and do not change

their characteristics with time but theirsensitivity is low2 Photo conductive cells These are also called

Light dependant resistors (LDR) or photoresistors When light falls, their resistancedecreases For making these devic germanium,silicon or cadmium suiplude (CdS) are used Theconstruction (Fig 19a) and symbol (Fig b) isshown

These are used for street light control, andautomatic Iris control of camera and to operaterelays The fig shows its use to control relay

operations When the cell receive light, itsresistance decreases and current is sufficient toenergise the relay When the cell does not get


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light, the current is decreased and the relay isde-energised

3 Photovoltaic cell (Fig 21) A solar cell is themost popular example of photo voltaic cells,

These cells generate electricity, when light fallson them.Solar cells are used to charge batteries ofsatellites. These can also be used for readingpunch cards in an industry.They can also be used as Infra red detectors. Inseries parallel grouping they can act as battery

charger.Their operating range is from - 80 .C to 120CThese do not require any external power sourceand they have a fast frequency response.4 Photo diodes A photodiode is a diode madeof silicon with an opening at Its cover containinga lens, which focusses the light on the diode Aphoto diode with no bias operates as aphotovoltaic cell, and with reverse bias, it acts

as a photo conductive cell


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The photodiodes have fast frequency response

and time constant of 1 gS. These can be usedfor reading punch cards and tape.

5. Photo transistors. The photo transistor is a

device, whose operation depends upon light andnot on the base current. The fig. 23(a) showssymbol of a photo transistor, note that it has nobase lead and (b) shows characteristics. Thecurves show electrical intensity in watt/rn2.

The photo transistor does not have response aslinear as that of junction transistors, i.e.

collector current is not linear to light intensity. A


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photo transistor is much more sensitive than aphoto diode.

Photo transistors find use in the operation of

relay, reading punch cards/tapes and control ofdigital processes.

Q. 87. Explain construction, working,Advantages, Disadvantages and uses

of L.V.D.T.

Ans. LV.D.. (Linear Variable DifferentialTransformer):

1.An L.V.D..is an inductive transducer. Itsworking principle is shown. When a force is

applied to the armature (or core) the are gapchanges and as a result inductance of the coilchanges which is the measure of the appplied,force.


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(b) Construction and Working: An LV.D.T itconsists of a primary winding and two exactlysimilar secondary windings with a magnetic

armature or core m between.When an A.C. signal is connected across theprimary, the voltages induced in two secondary

windings (by transformer action) are V1 and aV2 which are exactly equal in the ideal case andoutput of the secondary is zero. This occurswhen the core is positioned in the centre (null

position).But practically, the coil is not at the centreposition and the output of the transformer isequal to the difference of V1 and V2, as thesecondary are connected in opposition.The differential output voltage of thetransformer (produced by the displacement ofcore) is linear over a considerable range AB asshown. This explains the name L.V.D.T.


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As explained above, when the force (orpressure) to be measured is applied at the inputof the L.V.D.T., the output of the transformer is

the measure of the resultant displacement of

the core and hence of the input.

(c) Advantages of L.V.D.T:

(a) The output of L.V.D.T. is more or less linear.A linearity of 0.05% can be obtained.(b) The L.V.D.T. has infinite resolution,practically a resolution of i0 mm can beobtained.(c) It has considerably high output, henceamplification in not much needed.(d) It has a high degree of sensitivity as high as40 V/mm.(e) The power consumption is less than 1 W.

Signal first causes a change in the resistance ofthe wire, then this change is converted into anelectrical output. But in the case of L.V.D.T., the

input is directly converted into the differentialelectrical output. In this respect, L.V.D.T.s aresuperior to the strain gauges.

(d) Disadvantages of L.V.D.T.:


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(a) A relatively high core displacement isneeded for appreciable output.

(b) They need shielding to minimize the effect of

stray magnetic fields. In this respect, these areinferior to the capacitive transducers.(c) They are also affected by vibrations.

(d) Their dynamic response is not good, i.e. ifthe input signal is changing with time, theaccuracy of the result is affected.

Uses of L.V.D.T.s:The L.V.D.T.s can be used, where displacementis from a fraction of a mm to a few xn. They canalso be used to measure force, pressure,weight, etc. But as dynamic response poor, theL.V.D.T.s are not used for dynamic (changingwith time) measurements.

Q. 88. What is R.V.D.T.?

Ans. Rotary Variable DifferentialTransformer (RVDT) : The RVDT can measureangular displacement up to 90. The car diodeshaped core is specifically taken, as it giveshighly linear output.The typical applications of RVDT is

measurement of thickness of hot strip or slab inrolling mills.


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Q. 89. Define sensitivity of LVDT.

Ans. Sensitivity. The value of rms voltage

developed by LVDT for unit displacement iscalled sensitivity.

S = rms output voltage = VDisplacement d

It is usually specified in V/mm voltage inducedin a L.V.D.T. will be given asV =s.d

Q. 90. State laws of thermocouples.

Ans. The thermocouples are governed by thefollowing laws:

(i) Law of homogeneous metals. Accordingto this law a thermoelectric currentcannot be sustained in a circuit single

homogeneous metal byvarying in cross-section and applying heat

alone. In simple words, a


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thermocouple can be made only of twodissimilar metals.

(ii) Law of intermediate metals. According tothis law, a homogeneous metal can always beadded to a thermocouple circuit and this has no

effect on the emf athe circuit.

For example, there is no harm if in athermocouple made of platinum and platinumrhodium alloy with both copper leads or one of

copper and other of aluminium lead I used dueto heavy cost of platinum (See Fig. 28).

Q. 91. Write note on:1. Thermocouple 2. Seebeck effect 3.Peltier effect 4. Thomson effect

Ans. 1. Thermocouple. This is a simplest

device for measurement of temperature. Itconsists of two dissimilar metals A and Binsulated from each other but welded or brazedat their ends making two junctions.


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When one end is kept in the fumance whosetemperature is to be measured, the meterconnected at the other end gives temperature ofthe fumance.

2. Seebeck effect. This operation of athermocouple is based on the seeback effect. Itstates that when two wires of dissimilar metalsare joined together at each and end form acomplete electric circuit, then a current flowsthrough the circuit when the two junctions arekept at different temperatures.

The current is caused by the potential differencebetween two thermoelectric emfs

e1 and e2 induced at the two ends. The amountof potential difference only depends upon the

metals of the device and is independent of otherfactors like size of wires, are a of contact etc.


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3. Peltier effect. This is just reverse ofSeeback effect, i.e. when an electric current is

made to flows across a junction of two dissimilarmetals the heat is either generated berated) orabsorbed depending upon the direction of flow

of current (Fig. 31).When the current flows in the same direction asthe See beck current, heat is absorbed at thehot junction and liberated at cold junction. In

this case, if thermocouple voltage is measuredwith potentiometer no current flows and heatingand cooling are not present but if the voltage ismeasured by a milli voltmeter, current flows andheat is absorbed at the cold junction and heat isliberated at hot junction, however heating andcooling is negligible. This principle is used Ininstrument amplifier.

4. Thomson effect. According to Thomsoneffect, when current flows through a conductorhaving a temperature gradient (and thus a heat

flow) along its length, heat is liberated

(generated) at any point where the current flowis in the direction as the heat flow, while theheat is absorbed at any point, where these are

opposite (i e, the current flow and heat flow areopposite (or in reverse direction to each otherThe effect is not observed if potentiometer isused to measure the thermocouple voltages, If


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even a milli voltmeter is used the effect isnegligible

In this way, the Thomson effect speaks about

the temperatures of the conductors betweenJunctions rather the Junctions itself

The total emf set up in a thermocouple is partlydue to Peltier effect which is localized at eachjunction and is proportional to the difference injunction temps and parily due to Thomsoneffect, which is distributed along each conductorbetween the junclions and is proportional to thesquare of difference in junction temperatures. If

E = Total thermoelectric emf set up in athermocoupleWe can writeT1 absolute temperature of hot junctionT2 = absolute temperature of cold junction


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The a and j3 are constants whose valuesdepend upon the two metals used in thethermocouple.

Q. 92. Describe how thermocouple outputis measured..

Ans. The measurement of thermocouple outputinvolves two steps:

1.To maintain the cold junction temperatureconstant. While using a thermocouple tomeasure temperature (or emf), one junctionis kept in the furnace whose temperature is tobe measured, the meter calibrated in terms of

temperature or in volts is connected at theother (cold) junction gives the output value

directly; For this, foremost condition is thattemperature of the cold junction should bemaintained constant.

Following methods are used to maintainconstant temperature.

1.The cold junction of the thermocouple may beimmersed in ice water (Fig. 33)


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1.The temperature of the cold junction may be

controlled by automatic temperature controldevice placed away from hot junction. Notethe arrangement carefully. (Fig. 33)

(2) To measure the thermocouple output. Thevarious methods are:

(a) By millivoitmeter. This is simplestmethod. In this a sensitive millivoitmeter isused. A high resistance may be connected inseries with the instrument. This will give asufficient current through the meter and will

reduce the errors. This method is not veryaccurate. This causes loading error and also

errors due to variation of resistance.


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1.By potentiometer. This method is widelyused as it gives high accuracy, and does notcause any loading error because it does not

draw any current from the thermocouple. Theproblem due to variation of resistance are alsoeliminated.

A secondary transducer senses the magnitudeand direction of unbalance current and moves,

a slider to eliminate it the same by employing a

servomotor to the null balance position.


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(c) Electronic method

In this method,. I.C. technology is employed.

Art amplifier amplifies the thermocouple outputemf and feeds to the meter. This method is freefrom errors but needs an extra power source.

Q. 93. Write note on Thermocouplepyrometer with advantages, disadvantages

and applications.

Ans. (a) Thermocouple Pyrometer (RadiationPyrometer). Thermocouples are also

employed for making pyrometers which canmeasure very high temperature, e.g.temperature of furnace and also of the sun.

Along with thermoelectric effects thesepyrometers are also based on the principleof radiations that all objects emit radiations athigh temperatures. This produces two effects(a) The object appears bright.(b) There is change in the colour of the light dueto change in the wavelength.

(b) Construction: A thermocouple (radiation)pyrometer is shown. It consists of a

highly polished concave mirror C which can bemoved to and fro along the axis of the tube bymeans of screw S.

In the tube, thermocouple (T.C.) is also keptwhich is connected to a milli voltmeter


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calibrated in the temperature scale. For thepurpose of focussing an eye-piece (E.P.) is alsoprovided in the opening of the mirror.

1.Working :

Suppose the temperature of afurnance is to be measured The eyepiece of thepyrometer is kept near the eyes and the otheren4 towards the furnace. The radiations from

the furnace after reflection from C are focusedat one junction of the thermocouple (T.C.)whereas the other junction is shielded fromradiations. Now the temperature of the furnaceis read directly on the millivoltmeter calibrated

in degrees Centigrade.

(d) Advantages of thermocouples(i) The thermocouples are small and rugged mconstruction

(ii) These are cheaper than resistancethermometers


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(iii) The temperature range of thermocouples isabout 1400C

(iv) These have a time constant of 10 us

(e) Disadvantages of thermocouples(i) These axe less accurate than resistance

thermometers(ii) Compensation is to be provided for referencejunction

Applications(1) Pyrometers can used for measurement at anumber of points.(ii) Thermocouples can indicate rapid change intemperature.(iii) They can measure surface temp.

Q. 94. Write note on Piezoelectrictransducer.

Ans (a) PIEZOELECRIC TRANSDUCERAccording to the piezoelectric effect, if apiezoelectric material is subjected to a pressure,an e.m.f appears across its surfaces.Conversely, if an alternating voltage is appliedacross the crystal, it will change the dimensions

of the crystal, i e crystal will be deformedThe materials which exhibit this effect areRochelle salt, quartz, lithium sulphate, ceramics,

barium titanate, etc. The crystal of these


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materials are used in piezoelectric transducers,which can measure force, pressure, etc.

When force F to be measured is applied, to thetransducer, it converts it into voltage Vo, whichcan be easil9 measured by a voltmetercalibrated in Newton (Fig. 38).

(Ii) The equivalent circuit of the transducer can

be drawn as shown.

In Fig. 39 (a) C is the capacitance of the crystal,R is the leakage resistance of the crystal and Qis the charge generated by the crystal.

Now Q/C = V


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So, the equivalent circuit can also be drawn asshown in the Fig. (b), in which Q has beenreplaced by a voltage source V.

(c) Advantages of Piezo Electric transducers(1) These are small, compact in size and light inweight.

(ii) These are active transducers and do notneed any external source of power(iii) They have a temperature range from 1500 to 3000 C

(iv) They have a good frequency response from1 Hz to 30 KHz

(d) Disadvantages(i) Though leakage resistance of the transduceris very high (1012 ohm). But the chargegenerated leaks through the leakage resistancevery rapidly, when a voltmeter is connectedacross its terminals for measurement This

creates problems in measurement of staticdisplacements.(ii) The output voltage is affected by

temperature variations.

(e) V Uses of Piezoelectric Transducers:(a) They are more used for dynamic

measurements, such as surface roughness etc.(b) They are also used in SONAR (soundnavigation and ranging)

(c). They are used to measure force, pressure,

deformation etc.


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(d) They can also be used t measuretemperatures. The crystal can give a very linearrelation between its resonant frequency and

temperature of the order of 1 kHz per second.

Q 95 Provide analytical explanation, howforce can be measured by a piezo crystaltransducer

Ans The fig 40 (a) shows a piezo electric crystalused for measurement of force (F) The fig.. (b)shows usually adopted axis numbering systemfor the crystal. Note that a crystal has six axes.

A crystal used for converting mechanical motiondeformation to electrical signal may be taken asa Charge generator and a capacitor. Themechanical deformation generates a charge and

this charge appears as a voltage across theelectrodes.The piezo electric effect is direction sensitive.

A tensile force generates a voltage of onepolarity and a compressive force generates a


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voltage of opposite polarity. The magnitude andpolarity of the charge are proportional to themagnitude and direction of the applied force. In

the same way application of electric field maydeform the crystal to contract or to expand,depending upon the polarity of the electric field.

As told above, the magnitude and polarity of theinduced surface changes are proportional to themagnitude and direction of the applied force, wecan write down:

Q = d.F, where is the charge in coulombs and Fis the force. Also, d is a constant is called charge sensitivity of the crystal incoulombs per Newton; and is constant for agiven crystal cut.The force F causes a change in thickness equalto zt (in meters) and so,

where A is area of crystal in m2, E is the youngmodulus of elasticity and t is the thickness ofthe crystal.The charge at electrodes generates an outputvoltage V0 which can be expressed as

where C is the capicatance between the

electrodes with crystal is an insulation betweentwo conductor electrodes hence, behaves as acrystal].


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where, e is the absolute permittivity (8854x1042) and er is the relative permattivatySo we can write down by putting the values of Q

from e.g. (i) and value of C from eg (ii)

Where note that g is called voltagesensitivity of the crystal and P= F/A is thepressure in pascals applied an the crystal.The e.g. (i.ii) can be rewritten as

Q. 96. (a) Write a note on materials usedfor piezoelectric transducers.(b) Explain equivalent circuit of piezoelectric transducer along with analysis.

Ans. (a) the piezoelectric transducermaterials are of three types:

(i) Natural crystals. Such an Quartz andRochelle salt.The natural Quartz is the most suitable material; it has lower lower temperature sensitivity andhigher receptivity (about 1012 2/rn3) It gives


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large time constant and allows staticcalibration. It exhibits linearity over wide rangeof stress level with very low hysterisis.

The Rochelle salts performance is affected, ifhumidity rises above 80% or falls below 30%and so requires a wax coating for protection.

The quartz is most stable but its output is small,on the other head, the trochee salt provideshighest output but its highest workingtemperature is 45C and needs a protection

against humidity told above.

i. Polarized ferroelectric ceramics. Such asBarium Titanate etc.

The ferroelectric ceramics, as artificially

polarized by applying a strong field as thematerials, simultaneously, the material isheated to an temperature above curiepoint where it looses the perro electricproperties.

Then it is cooled down with the field, stillapplied. Now removing the electric field a

remnant polarization is retained and thematerial exihibits piezoelectric effect.

As compared to Quartz, piezo electricceramics have higher sensitivity but havepoor temperature characteristics.

Barium titanate can be made in any shapeand size and it has also a high

permittivity.


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The crystal axis can be obtained as perrequirement by selecting the direction ofpolarization. It is a polycrystalline and has

a higher dielectric constant.

i. Synthetic materials. Such as Lithiumsulphate, ammunium hydrogen phosphate etc.These have in general a higher voltagesensitivity.

1.Equivalent circuit of Piezo electric

transducer along with analysis. Thepiezoelectric effect can cause mechanicaldeformation of the material in many modes.

Such as thickness expansion, transverseexpansion, thickness shear and face shearmode. But the common mode is thicknessexpansion the mode depends upon thefactors:- Such as shape and orientation of thebody w.r.t. crystal axis, and location of

electrodes. The electrodes are metallic

materials and the crystal is an insulator, sowhen the electrodes are plated on the crystal

the arrangement acts as a capacitor/chargegenerator. A charge produced to mechanicaldeformation results in definite voltageappearing across the electrodes and is given

by V0 = Q/C, where Q is the charge produced


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and C is the capacitance of the piezo electricelement.

The equivalent circuit of a piezoelectrictransducer (charge generator) is shown in Fig.42. In this, charge is generated by the crystalacorss its capacitance C and leakage resistance.R.

The charge generator can be replaced by an

equivalent voltage source having a voltage V mseries with a capacitance C and resistance R(Fig. 43).


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1.Analysis. Let the transducer be

loaded. The load has a capacitance CL and

resistance RL. The CL! Loading effect is thecombination of capacitance of the load,capacitance of the cable and the stray

capacitance. The fig. 44 shows the loaded

transducer.

The value of leakage resistance R of the crystal

is very large (about 1011 ). The value of loadresistance R1 is comparatively smaller than R,So the leakage resistance R can be dropped.Note that due to high leakage current resistance

R, the leakage i.e. power loss will be negligibleand the equivalent circuit can be reduced to asshown in Fig. 45.


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Impedence of Load,

Total impedence offered to the voltage source

The voltage output of the loaded transducer.

Putting value of V = Q = dF , where F is theforce

C C

The equation (i) becomes:


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The eq. (ii) is the output voltage V0 of thetransducer with applied force F.At medium and high frequencies,

This is the expression for output voltage of thetransducer at medium and high frequencies. Theoutput voltage V0 is independent of frequencybut depends upon the load capacitance CL Itcan be observed that under steady state, force F

i.e. when w 0, the transducer provides nooutput, while the high frequency is imposed bythe mechanical resonance of the piezo electricdevice and the mountings (electrodes).

Q. 97. Explain Capacitive transducers.

Ans. (a) CAPACITIVE TRANSDUCERS: Theprinciple used is same as in capacitivemicrophones which respond to the soundpressure falling on their diaphragm andconverting the sound Into electrical pulsesaccording to the pressure of the sound.


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The capacitive transducers can, otherwise, beused to measure a force as explained below:

The capacitance of a parallel plate capacitor is

given by:

Where A is the area of each plate and d isdistance between the plates.

Therefore any variation in distance d betweenthe plates will vary the capacitance of thecapacitor.The force F to be measured is applied at the

diaphragm of the transducer.

(b) Construction : The diaphragm icts as one

plate and the static plate act as cont plate ofthe capacitor. By applying force, the diaphragmshows deflection and the distance betweendiaphragm and the static plate decreases. Thedistance decreases Further with increase in theforce.The resulting change in the capacitance can be

measured by an A.C. bridge and the appliedforce can be accordingly calculated.

Note that the diaphragm and the staticplate are separated by a dielectric forms acapacitor; hence the name capacitive

transducer.


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Fig. 46 (a) shows construction and Fig. (b)shows equivalent electric circuit for a capacitivetransducer.

(c) Advantages of Capacitive Transducers:(a) They re very sensitive.(b) They have a good frequency response upto60 kHz.

(c) Their resolution is of the order of 2 x mm.(d) They need very small power to operate.

Disadvantages of CapacitiveTransducers:(a) Sometimes they shown a non-linearbehaviour.(b) They have high output impedance and henceshow some loading effect.

(c) Their metallic parts are to be properlyearthed.

Uses of Capacitive Transducers:

(a) The capacitive microphones andloudspeakers are available.


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(b) They can be used to measure linear as wellas angular displacement may 1 small up to 10mm and large up to 30 mm

(c) They can be used to measure force andpressure.(d) They can effectively measure humidity

(e) When used along with mechanical modifiersthey can be used to measure volume weight anddensity.

Q. 98. Why the gauge factor of a metallicstrain gauge is approximately equal to forthe most of the cases?

Ans G = I + 2 v, Where v is the Poisson ratio,which is 05 for most of the metals,

G = 1 + 2 (0.5) 2. This is the reason the Gaugefactor, for most of the metallic stress guages isapproximately 2.

Q. 99. Define a transducer and distinguishbetween a sensor and a transducer.

Ans. Transducer is a device that converts oneform of energy into other form.Sensor is a part of transducer, it senses andsends signal to the transduction element.


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Q. 100. Why strain guage is passivetransducer ? Define sensitivity of strainguage.

Ans. Because in strain guage, the electricalparameters change with change. in the input

signal, so the strain guage is a passivetransducer, moreover it needs an externalpower source for the operation.

Sensitivity of a strain guage is the lowest

change in the input, which can be detected/sensed by the strain gauge.

Q. 101. Why the secondary windings ofLVDT are connected in series opposition?

Ans. The secondary windings of L.V.D.T. (Linearvariable differential transformer) are connectedin series opposition, so that the output voltageis the difference (or differential) of the twosecondary voltages.

Q. 102. What is the basic principle of straingauge based measurements?

Ans. In strain gauge based measurements, themechanical elongation/compression

is converted into the change of resistance. Theend device is accordingly calibrated to measurethe input


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Q. 103. Name materials used for wire foil

guages.

Ans. (i) Nic1ome(ii) Coustantor(iii) Nickel(iv) Platinum

Q. 104. Define Poission ratio.

Ans. The poission ratio is the ratio of lateralstrain and longitudinal strain.

It is negative and approximate value is 0.3.

Q. 105. Why are Strain Gauges called piezoresistive strain gauges?

Ans. If a metal conductor is stretched, there is

change of resistively of the conductor due tochange in its dimensions. This is called piezoresistive effect. This is the reason, that straingauges are also called as piezo resistivegauges.


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Q. 106. Why piezoelectric transducerscannot be used for static displacementmeasurements?

Ans. As the voltage developed by application ofstrain is not held under static conditions, so the

piezoelectric transducer cannot be used forstatic measurements.

Q. 107. Explain the measurement ofdisplacement using LVDT.

Ans. The displacement is converted into

electrical voltage by LVDT, which isproportional to the displacement of the core.This electrical voltage can be measured by a

voltmeter calibrated in terms of displacement.

Q. 108. What do you understand bypiezoelectric effect ? How it can be used tomeasure pressure?

Ans. When a mechanical pressure is appliedbetween two phases of a piezo electric crystal(such as quartz), the output is an electricalsignal. The phenomenon is reversible. This iscalled Piezo electric effect.

When pressure is applied across the crystal, weget electrical voltage as output. This electrical


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voltage can be measured by an instrumentcalibrated in terms of pressure.

Q. 109. How capacitive transducers aresuperior to other transducers?

Ans. (i) They can be used in smallest systems.(ii) They are exteremely sensitive.(iii) They have a good frequency response.

(iv) A resolution of 2.5 x i0 mm can beobtained.

NUMERICALPROBLEMS

Problem 1. The wire of a strain gauge is 0.1m long has initial reistance of 120 Q.On applying force, the length of the wire

increases by 0.1 mm and resistance increasesby 0.

Q. 1 Find gauge factor.

Sol. 1 0.1 m = 100 mm


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& 0.1m=100mm

R =120QzR =0.2W

Gauge factor

= 1.75Ans.

Problem 2. A strain gauge with gauge factorof 2 is fastened to a metal and is subjected toa stress of 1000 kg,fcm2. The Youngs

modulus of the metal is2 x io Kg/cm2. Find percentage change in theresistance of the strain gauge.

Sol.

Percentage change in the resistance of the strain

gauge


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Problem 3. A thermistor has a temp. coeff. ofresistance as 0.5 for temperature range of25C to 50C. Find the resistance of the

thermister at 40C, if its resistance at25C is 120i

Sol:

Problem 4. A strain gauge is bonded to asteel beam of 0.lm length and 4 cm2

cross section. The modulus of beam material(steel) is 207 x i0 N/rn2. The strainguage has initial resistance of 240 and agauge factor of 2.2. When a load is appliedthe resistance of the strain gauge changes by0.013 Q.Calculate (i) change in the length of the beamand (ii) force applied to the beam.

Sol.


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Change in length. 2.46x10 m. Ans

(ii)

Force on the beam

Problem 5. A thermistor has a resistance

temp. coeff. of 5% over a temperaturerange of 25C to 50C. If resistance of thethermistor at 25C is 100Q, Find itsresistance at 35C.

Sol. Resistance at 35C .100 [1 -0.05(35 25)j

50 Ans.

electrical measurment

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