Homework on Sensors
March 2001
PART - 1
Multiple Choice Questions:
1) Wheat-stone bridge with DC excitation voltage is needed in displacement measurements
using:
a) Thermistors;
b) Capacitive transducers;
c) Piezoelectric crystals;
d) Strain gage.
2) Which one of the following transducers needs a phase sensitive demodulator?
a) Thermistor;
b) Strain gage;
c) LVDT;
d) Piezoelectric crystal.
3) The effect of temperature on a strain gage displacement transducer can be best
compensated by using a:
a) Thermistor;
b) Second strain gage at a reference temperature;
c) Thermocouple;
d) Second strain gage at the same temperature as the measuring one.
4) In piezoelectric transducers which of the following is primarily related to the velocity?
a) Current coming out of it;
b) Voltage across it;
c) Impedance of it;
d) Charge on it.
5) A strain gage type displacement transducer has a gage factor of 40 and unstrained
resistance of 120.The Poisson coefficient is 0.4.
a) How much of the gage factor is due to piezoresistive effect?
 38;
 39;
 35;
 None. It is....
b) An external strain causes 6 change in the resistance. The percentage change in
dimension is:  1;
 0.5;
 0.125;
 2.
6) In the following configuration Rx is a strain gage with an unstrained resistance of 100
ohms and a gage factor of 50 at 25C. The change in Rx due to a displacement, which
causes 0.1% change in the length, is:  1 ohm;  5 ohms;
 10 ohms;
 0.5 ohm.
7) In the above problem assume that the value
of Rx is reduced by 3 ohms. The output
voltage becomes about:  1 Volt;  70 mV;
 37 mV;
 500 mV.
8) The zero power resistance of a thermistor is
the value obtained at:
a) -273C;
b) Current passing through it is zero;
c) Current passing through it is below the self-heating value;
d) A reference temperature.
9) A thermocouple is used for temperature measurement. The reference junction is kept at
0C and the measured temperature is 80C. a=50V/C and b=0.1V/C.
a) The electromotive force E is:  2.125mV;  4.32 mV;  0.22 V;  2mV.
b) The sensitivity is:  45V/C;  58V/C;  0.04mV/C;  None.
PART - 2 : Solve the Following Questions in Detail.
1) A Wheatstone bridge is used for converting the change in the resistance into voltage for a
resistance transducer. Draw the bridge with a 10 volts DC supply, three arms with
resistance of 1K and one arm with 0.99K. The bridge output is measured using a digital
voltmeter. Find the voltage that will appear on meter’s display.
2) Suppose four strain gage transducers are used to detect the
Q
displacement of a cantilever beam:
a) Place the transducers on the cantilever and form a
Wheatstone Force bridge to obtain maximum possible
sensitivity;
R2
R4
R1 R3
W
b) Suppose the unstrained resistance of each strain gage is
120 ohms at 25C and the gage factor is 25. The bridge is excited by a 8 Volts DC
Cantilever source. Find the output voltage if the displacement causes 1% change in the
dimension (length) of each gage;
c) Discuss the effect of temperature on the output for the above configuration.
d) Define the piezoresistance.
3) Draw the output voltage with respect to time for a LVDT when the displacement varies
linearly with time. Explain why the LVDT needs AC excitation voltage.
4) A strain gage type displacement transducer has a gage factor of 25 and the unstrained
resistance of 120 at 25C. The poisson coefficient is 0.35. The sensitivity of the strain
gage to temperature is +1%/C.
a) How much of the gage factor is due to the piezoresistive effect?
b) An external strain causes 3 changes in the resistance at 25C. What is the percentage
change in the dimension?
c) An external strain causes 0.1% change in the dimension at 0C. What is the new value
of the resistance of the strain gage?
d) How can you compensate the effect of temperature in measurements involving strain
gages?
5) Discuss shortly how a thermocouple converts temperature into voltage. What is the
thermoelectric sensitivity and is it linear? What is the cold junction compensation and
how it is managed?