Download Sheet Ec732

Automated Measurements
Sheet EC- 732
Automated Measurements
Resistive Position Transducer (R.D.T)
1. A resistive displacement transducer with a shaft stroke of 5 inch
and the total resistance 120  , the applied voltage 10v. what is the
displacement indicated by each of the voltage readings 2V, 4V , 6V
sketch the relation between volt and displacement
2. A resistive position detector transducers has the total resistance of
500 k  and the total length of shaft stroke is 5 inch the wiper to
the position 2 inch from B. find the value of the resistance relative
to the wiper position, and find the o/p voltage,
3. If the o/p voltage is measured by the avometer has the internal
resistance of 200 k  find the o/p voltage which is measured by
avometer, calculate the percentage error in the output voltage.
Strain Gauge Transducer
1. A thin circular wire of soft iron has a gauge factor of 3.8.
Determine the poisson’s ratio of soft iron.
2. The wire in a strain gauge is 0.1 m long and has an initial
resistance of 120  . On application of force, the wire length
increases by 0.1mm and resistance increases by 0.21  . Determine
the gauge factor of the device.
3. A strain gauge having a resistance of 500  and a gauge factor 3 is
bonded on to a member of structure under tensile stress. Determine
the percentage strain suffered by the member, if the change in
resistance of the gauge is accurately measured as 1.5  .
4. A resistance strain gauge is used to measure stress on steel. The
steel is stressed to 1400 kg /cm2. Assume Young’s modulus of steel
2.1 *106 kg /cm2. Calculate the percentage change of resistance of a
strain gauge assuming gauge factor equal to2.
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5. A strain gauge with gauge factor of 2 is fastened to a metallic
member subjected to a stress of 1000 kg/cm2. the modulus of
elasticity of the metal is 2× 106 kg /cm2. Calculate the percentage
change in resistance of the strain gauge what is the value of
poisson’s ratio?
6. A single electrical resistance strain gauge of resistance 150  and
gauge factor 2 is bonded to steel having an elastic limit stress of
400 MN/m2 and modulus of elasticity 200 GN/m2.
Determine the resistance changes in these cases
1. Due to a stress to be reduced to one- tenth.
2. Due to temperature variation of 20C and the material of wire is
advance alloy with temperature coefficient is 0.2 × 10-4 /C.
3. Due to temperature coefficient of linear expansion for advance
alloy and steel are 1.6 × 10-5 / C and 1.2 × 10-5 /C respectively.
Calculate the total change in resistance due to changes in
temperature and stress.
7. A strain gauge having a resistance of 200  and gauge factor 2.5 is
connected in series with a blast resistance of 400  across a 24v.
Determine the change in the output voltage when a stress of 140
MN/m2 is applied the modulus of elasticity is 200 GN/m2.
R= 200 
RB= 400 
24v
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Hall Effect Transducer
1. A hall element used for measuring a magnetic field strength gives
an output voltage of 10.5mv. The element is made of silicon and is
2.5mm thick and carries of a current of 4A. The Hall coefficient for
4.1 * 10-6 Vm/A- wb/m2.
2. A Hall Effect element used for measuring a magnetic field strength
gives the o/p voltage = 20mv. The thickness is 5mm thick and
carries current of 5A. The magnetic flux density is 2 Wb/m2. Find
the type of metal and the concentration of carrier.
Inductive Transducer
1. A LVDT produces a rms output voltage of 2.6V for displacement
of 0.4  m. Calculate the sensitivity of LVDT.
2. A LVDT has a secondary voltage of 5v for a displaced of 
12.5mm. Determine the output voltage for a core displacement
8mm from its central position.
3. A LVDT is used for measuring the defection of a bellows. The
sensitivity of LVDT is 40v /mm. The bellows is defected 0.125mm
by a pressure of 0.8 ×106 N/m2. Find the sensitivity of the LVDT in
V/N/m2 of the pressure when the o/p voltage is 3.5.
4. LVDT has the following data:
Vi/p = 6.3 volt, vo/p = 5.2 volt.
Range of Displacement =  0.5 inch form the center. Plot the
output volt versus core position for a core movement from 0.45 to –
0.3 inch.
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Temperature Transducers
1. A platinum resistance thermometer has a resistance of 120  at
25c. Determine its resistance at 75c. The temperature coefficient
of resistance of platinum at 25c is 0.00392  /c. In case of the
thermometer is found to be 180  , Determine the temperature.
Sketch the relation between the resistance and temperature.
2. A copper resistor haring resistance of 15  at 20c, is used to
indicate the temperature of bearings of a machine Determine the
limiting value of resistance if the max temperature of the bearing is
not to exceed 175c. The temp coefficient of resistance of copper at
20c is 0.00425.
3. A thermistor has a temperature coefficient of resistance of 0.05
over a temperature range of 25c to 50c. Find the resistance of
thermistur at 40C if the resistance of the thermistor at 25c is
120  .
4. A thermistor has A resistance of 4000  at 0c and 800  at 40c.
the resistance relationship is given by
R1 = R0  CB/T
1. Determine constants  and B.
2. Determines the range of resistance to be measured in case
the temperature rises from 50c to 100 c.
5. The output relationship for thermistor transducer is
1 1 
R=R  e  T  To 
B
T in Kelvin
R at ref temp. ‘
T unknown temp
For To = 300k, B = 3420, R = lk  , R= 2K 
Calculate the value of T. Find the sensitivity S=
transducer at a given operating point
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R
T
of the
6. A copper- constantan thermocouple has  = 37.5  v/c and B=
0.0045  v/c. Determine emf developed by the thermocouple
when its hot junction is at 200c and cold junction is kept in ice in
Kelvin.
Piezoelectric Transducer
1. A piezoelectric crystal has a thickness of 2.5mm and a voltage
sensitivity of 0.05 Vm/N. Determine the output voltage when it is
subjected to a pressure of 1.6 * 106 N/m2.
2. A barium titanate (Batio3) piezoelectric has dimensions of 6mm 
6mm  1.5mm and a voltage sensitivity of 0.012 Vm/N. Determine
the voltage developed when a force of 0.8 kg is applied to it. Find
the charge sensitivity if the relative permittivity of the barium
titanate is 1400.
3. A piezo electric crystal having dim 5mm  5mm  2mm and a
voltage sensitivity of 0.05 Vm/N is employed for measuring, force,
find the force required to develop a voltage of 150v.
4. A barium titanate piezoelectric transducer has dim of 6mm 
6mm 1.5m and voltage sensitivity of 0.012 Vm/N. The relative
permittivity of barium titanate is 1400, and modulus of elasticity is
12  1010 N/m2
Find:
1. The o/p voltage.
2. Charge sensitivity.
3. Strain.
4. Charge generated.
5. The Capacitance.
The force is applied to a transducer is 10N.
5. A piezoelectric pressure transducer having a charge sensitivity of
2* 10-12 C/N is connected to a charge amplifier, the gain being set
to 5 mN/pc. The amplifier output is connected to an ultraviolet
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chart recorder, whose sensitivity is set to 25mm per volt.
Determine the overall sensitivity and the deflection of the chart due
to a pressure of 200 N.
6. For the pressure transducer, convert the following control signals:1- 25% to pneumatic and electronic.
2- 15 mA to percentage and pneumatic.
3- 12 psi to electronic and percentage.
Given that the ideal inputs and outputs for pressure transducer are:
3
15 psi
Pressure
0.2
1 bar
Transducer
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1
4
5 VOLT
20 mA