Bachelor of Applied Technology
ETEC: 6419 – Control Engineering
These tutorial questions should be printed out at the end of class 1.
Tutorial questions
Problems
Attempt these tutorial questions prior to lecture 3. Solutions will be provided during
lecture 3. Research the solutions for the roots of a quadratic equation, additionally
material has been left on the student directory in this folder to assist you with a solution!.
Tutorial
1. Write down the formula for calculating Vout from a voltage divider.
2. What is the alternative name for this kind of circuit?
3. Does the resistance of the LDR go down or up in bright light? Explain your answer.
4. Calculate Vout for the circuit shown below, assuming the LDR has a resistance of 2
kΩ.
• 5. In this circuit, does Vout increase or decrease in bright light?
5. How could you reverse the action of the circuit?
Thermistors
6. How could you make a sensor circuit for use in a fire alarm?
7. You want a circuit which will deliver a HIGH voltage when hot conditions are
detected.
8. You need a voltage divider with the ntc thermistor in the Rtop position
9. How could you make a sensor circuit to detect temperatures less than 4°C to warn
motorists that there may be ice on the road?
10. You want a circuit which will give a HIGH voltage in cold conditions.
11. You need a voltage divider with the thermistor in place of Rbottom
12. How to estimate the resistance of the thermistor at T °C ?
13. It is possible to calculate an approximate value for the resistance of the thermistor
at any particular temperature
Using the equation for NTC thermister
R = Ro exp( Beta/T - Beta/To)
where
R
Thermistor resistance at T (K)
T
Thermistor temperature (K)
Ro
Nominal resistance at To (K)
To
Temperature where Ro is measured
Beta
Thermistor material constant
14. Aassuming you purchased a thermistor that measures Ro = 10k at To = 25 and has
a material constant Beta = 3548. The device should measure resistances across a 15 to 65 deg C range that look like
T (deg C)
T (K)
= T(deg C) + 273
R (Ohms)
-15
258
?
+25
298
?
+65
338
?
15. Assuming the thermistor in 14above reads 9000 ohms what is the temperature in
C and K?
16. Distinguish between ntc and ptc thermistors. What happens to the resistance of each
type as temperature increases?
17. A greenhouse fan is to start automatically if the temperature exceeds 40°C. Estimate
the thermistor resistance at 40°C from the characteristic curve:
RESISTANCE TYPE SENSORS
These work on the principle that the electrical resistance of a conductor change with
temperature. If a constant voltage is applied to the conductor then the current flowing
through it will change with temperature. The resistivity of the conductor change with
temperature. This usually means the resistance gets bigger as the conductor gets hotter.
The following law relates the resistance and temperature.
R = Ro(1 + )
(1)
is the temperature coefficient of resistance. Ro is the resistance at 0°C. Sometimes the
equation is given as
R = Ro(1 - 2)
(2)
A basic temperature sensor is made by winding a thin resistance wire into a small sensor
head. The resistance of the wire then represents the temperature. This has an advantage
over a thermocouple in that it is unaffected by the temperature of the gauge end. The
main type of wire used is PLATINUM. The sensors are usually manufactured to have a
resistance of 100 at 0C and the value of is 0.00385 to 0.00390. A typical operating
range is - 200 to 400C
18. A Platinum resistance thermometer has a resistance of 100 at 0C and the value
of is 0.00385. In operation the resistance is 101 . Calculate the temperature
using equation (1).
SOLUTION
Hint - Rearrange the formula to make the subject and evaluate.
19. A thermocouple produces an e.m.f. in mV according to the temperature difference
between the sensor tip 1 and the gauge head 2 such that e = (1-2) + (12-22)
= 3.5 x 10-2 and = 8.2 x 10-6 The gauge head is at 20C. The mV output is 12
mV. Calculate the temperature from the sensor using the equation provided in
question 2 i.e. e = (1-2) + (12-22)
SOLUTION
Hint - This is a quadratic type equation, rearrange the equation provided in 2) and find
the solution using the roots of a quadratic equation use the value 12 in the calculations
not 12x10-3
20. A thermocouple produces an e.m.f. in mV according to the temperature
difference between the sensor tip 1 and the gauge head 2 such that e = (1-2)
+ (12-22)
Given = 3.5 x 10-2 and = 8.2 x 10-6 determine the mV output when the tip is at 220C
and the gauge head at 20C.
(Answer 7.394 mV)
21. State two reasons why instrument systems use standard transmission signals of
either 4 - 20 mA or 0.2 – 1 bar.
22. A strain gauge is glued to a structure. It has a gauge factor of 2.1 and a resistance
of 120.2 . The structure is stressed and the resistance changes to 120.25 .
Calculate the strain and convert this into stress.
Take E = 205 GPa