Measurement and Instrumentation

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

Statistic Analysis -result-

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

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

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

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

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

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

Example In a survey of 15 owners of a certain model of car, the following figures are for average petrol consumption were reported 25.5 30.3 31.1 29.6 32.4 28.9 30.0 39.4 33.3 31.4 29.5 30.5 31.7 33.0 29.2 Calculate mean value, median value, standard Deviation and the variance

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

Permanent Magnet Moving Coil Instrument

Permanent Magnet Moving Coil Instrument

Permanent Magnet Moving Coil Instrument

Permanent Magnet Moving Coil Instrument

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

Moving Iron Instrument -Attraction Type-

Moving Iron Instrument -Repulsion Type-

Moving Iron Instrument -Deflection Torque-

Moving Iron Instrument -Deflection Torque-

Moving Iron Instrument -Deflection Torque-

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

Electrodynamometer Type Instruments

Electrodynamometer Type -Ammeter, Voltmeter, Wattmeter-

Electrodynamometer Type -Torque Equation-

DC Ammeter Rm Rsh

DC Ammeter -Theory-

DC Ammeter -Theory-

DC Ammeter -Theory-

DC Ammeter -Example- A 2 mA meter with an internal resistance of 100 Ω is to be converted to 0-150 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

DC Ammeter -Multirange- R1 = Rm/m1 -1 R2 = Rm/m2 -1 and so on

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 0-100 mA.

DC Voltmeter Rs

DC Voltmeter -Theory-

DC Voltmeter -Theory-

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

DC Voltmeter -Multirange-

DC Voltmeter -Practical Multirange-

DC Voltmeter -Practical Multirange-

DC Voltmeter -Example-