1. Measurement and Instrumentation

2. Statistical Analysis A mathematical analysis of the
various measurements. It helps to
determine analytically the
uncertainty of the final test
results

3. Statistic Analysis -result-

4. Statistical Analysis -Examples-
Arithmetic Mean and Median
Average Deviation
Standard Deviation
Variance

5. Mean Most value of the set of measured variable value
𝑥 = 𝑥 1 + 𝑥 2 + 𝑥 3 + ……….+ 𝑥 𝑛 𝑛 = 𝑛=1 𝑛 𝑥 𝑛 𝑛
mean
nth reading taken
total number of readings

6. Median A set of n measurements written down in
the ascending order of magnitudes
𝑥 𝑜𝑑𝑑= 𝑥 𝑛+1 2
𝑥 𝑒𝑣𝑒𝑛= 𝑥 6 + 𝑥 7 2

7. Average/Mean Deviation
The difference between a given reading and
the arithmetic mean of the data set
𝐷 = 𝑑 𝑖 𝑛
𝑑 𝑖 = 𝑥 𝑖 − 𝑥
Deviation of ith reading
Arithmetic mean
Value of ith reading

8. Standard Deviation It is a root mean square deviation
-Less the value of standard deviation,
More accurate in the measurement -
𝜎= 𝑑 𝑑 ……….+ 𝑑 𝑛 2 𝑛 = 𝑑 2 𝑛
𝜎= 𝑑 𝑑 ……….+ 𝑑 𝑛 2 𝑛−1 , 𝑛<20

9. Variance It is a mean square deviation
𝑉= 𝜎 2 = 𝑑 𝑑 2 2 +…….+ 𝑑 𝑛 2 𝑛
𝑉= 𝜎 2 = 𝑑 𝑑 2 2 +…….+ 𝑑 𝑛 2 𝑛−1 , 𝑛<20

10. Example In a survey of 15 owners of a certain
model of car, the following figures are
for average petrol consumption were reported
Calculate mean value, median value, standard
Deviation and the variance

11. Indicating Instrument
Analog Instruments Electronic Instruments Digital Instrument
DC Ammeter
DC Voltmeter
Ohm Meter
Energy Meter
Rectifier Instrument
Multimeter
Power Factor Meter
Deflecting
Controlling
Damping
PMMC MI
EDy

12. Permanent Magnet Moving Coil Instrument

13. Permanent Magnet Moving Coil Instrument

14. Permanent Magnet Moving Coil Instrument

15. Permanent Magnet Moving Coil Instrument

16. Permanent Magnet Moving Coil Instrument
Example: A PMMC instrument has a coil of dimensions
10 mm X 8 mm. The flux density in the air gap is 0.15
Wb/m2. If the coil is wound for 100 turns, carrying a
current of 5 mA then calculate the deflecting torque.
Calculate the deflection if the spring constant is 0.2 x 10-6
Nm/deg

17. Moving Iron Instrument -Attraction Type-

18. Moving Iron Instrument -Repulsion Type-

19. Moving Iron Instrument -Deflection Torque-

20. Moving Iron Instrument -Deflection Torque-

21. Moving Iron Instrument -Deflection Torque-

22. Moving Iron Instrument -Example-
The inductance of a moving iron instrument is
given by
L = (12 + 6 - 2) H
where  is the deflection in radians from zero
position. The spring constant is 12 x 10-6 Nm/radians.
Calculate the deflection for a current of 8 A

23. Electrodynamometer Type Instruments

24. Electrodynamometer Type -Ammeter, Voltmeter, Wattmeter-

25. Electrodynamometer Type -Torque Equation-

26. DC Ammeter Rm
Rsh

27. DC Ammeter -Theory-

28. DC Ammeter -Theory-

29. DC Ammeter -Theory-

30. DC Ammeter -Example-
A 2 mA meter with an internal resistance of 100 Ω is to be converted to mA ammeter. Calculate the value of the shunt resistance required.
A moving coil ammeter has fixed shunt of 0.01Ω. With a coil resistance of 750Ω and a voltage drop of 400 mV across it, the full scale deflection is obtained.
a) Calculate the current through shunt
b) Calculate the resistance of meter to give full scale
deflection if the shunted current is 50 A

31. DC Ammeter -Multirange-
R1 = Rm/m1 -1
R2 = Rm/m and so on

32. DC Ammeter -Multirange-
Example: Design a multirange dc ammeter with a basic meter having a resistance 75 Ω and full scale deflection for the current of 2 mA. The required ranges are 0-10 mA, 0-50 mA and mA.

33. DC Voltmeter Rs

34. DC Voltmeter -Theory-

35. DC Voltmeter -Theory-

36. DC Voltmeter -Example-
A moving coil instrument gives a full scale deflection with a current of a 40 A, while the internal resistance of the meter is 500 Ω. It is to be used as a voltmeter to measure a voltage range of 0 – 10 V. Calculate the multiplier resistance needed.
A moving coil instrument gives a full scale deflection for a current of 20 mA with a potential difference of 200 mV across it. Calculate I) Shunt required to use it as an ammeter to get a range of 0 – 200 A and ii) Multiplier required to use it as a voltmeter of range 0 – 500 V

37. DC Voltmeter -Multirange-

38. DC Voltmeter -Practical Multirange-

39. DC Voltmeter -Practical Multirange-

40. DC Voltmeter -Example-