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**Chapter 5 **

**MEASUREMENT ERRORS**

1. Ablosute Error. The difference between the measured value Am and the true alue A of the unknown quanity if known as the abloute error of measurement* δA* **i.e.**d**A* =* A** _{m} *-

2. Relative Error is the ratio of absolute error to the true value of the quantity to be measured i.e.

∈_{r} =*δA* /* A* =∈_{0} / *A* = absolute error/true value.

3. Gross Errors. In this category, errors occur because of mistakes in reading or using instruments and in recording and computing measurement results. these errors are usually because of human mistakes and may be of any magnitude can cannot be subjected to mathematical treatment.

4. Systematic Errors. Such error remain constant of change according to a definite law on repeated measurement of a given quantity. Such errors cab be evaluated and their influence on the measurement results a can be eliminated by introducing proper corrections. These errors are of two types namely

(a) instrumental errors

(b) environmental errors.

Instrumental errors are inherent in the measuring instruments because of their mechanical structure and calibration or operation of the apparatus used. Environmental errors are introduced due to use of an instrument in different environmental conditions than in which it was assembled and calibrate. these errors are much more troublesome as these change with time in an unpredictable manner.

5. Random (or accidental) Errors. These error are of variable magnitude and sign and do not obey and known law. Presence of random errors becomes evident when different results are obtained on repeated measurements of one and the same quantity.

**Determination of Maximum systematic Error **

1. Sum of Two or More Quantities. Let the final result y be the sum of measured quantities u, v, and z, each of which is subjected to possible systematic error ±* δu*, ±*δv and* ± *δz* r sp ectively, corres ponding limiting error *δy* is given by

2. Difference of two Quantities, Let y=u–v

3. Product of Two Quantities, Let y = u.v.z

4. Quotient of Two Quantities.

5. Power of factor. Ley y = u^{n} where n may be + ve or -ve, integral of fractional

6. Composite Factor. Let y = u^{n} v^{m}

**Resolution and Sensitivity **The resolution of discrimination of an instrument is the smallest change in the input signal (quantity under measurement) which can be detected by the instrument. it may be expressed as an actual value or as a fraction of percentage may be expressed as an actual value or as a fraction of percentage of the fullscal value.

The sensitivity is defined as the ratio of output signal or response of the instrument to a change of input signal or the quantity under measurement.

Accuracy and Precision Accuracy is a closeness with which the instrument reading approaches the true value of the variable under measurement while precision is a measure of the reproducibility of the measurement i.e. precision is a measure of the degree to which successive measurements differ from one another. significant figures An indication of the precision of the measurement is obtained from the number of significant figures in which result is expressed. More the significant figures, greater the precision of measurement.

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