Engleză

A. EXPERIMENTAL DATA PROCESSING

I. ELEMENTS OF ERROR CALCULATIONS

Any experimental measurement is affected by errors. Depending on their cause, they can be divided into 3 categories: systematic, random and rough errors.

1. The systematic errors have three possible sources:

a) Observation errors. If, for instance, the observer reads the indications of the measurement device while looking at it in an oblique way, all of his readings will be higher or smaller than the real values. These errors can be completely eliminated by correcting the observer's working method.

b) Device errors. Any measurement device has a scale (for the digital display devices, we can consider the scale as implicit). No reading made on this scale can be more accurate than half of the smallest scale division. These errors can be reduced (by replacing the used device with a more accurate one), but they cannot be completely eliminated.

c) Method errors. During the process of measuring, the system that is measured interacts with the measurement device, and this interaction modifies the results of the measurement. For instance, in order to measure a resistance, we can use the upstream or the downstream methods. In the first case the value obtained is bigger than the real one ( ), and in the second one it is smaller ( ). We can eliminate these errors if we know the internal resistances of the measurement devices (which means to measure other resistances), or if we replace this method with a bridge one, which compares the unknown resistance with other ones, assumed as known (this implies, again, measuring other resistances). Therefore, these errors can be reduced, but they cannot be completely eliminated.

Whatever the causes of systematic errors may be, they share one feature: the value of an individual measurement is the same every time we repeat the measuring, therefore the error is also the same. For this reason, the calculation of errors for indirect measurements is done in the same way for all systematic errors.

The absolute error of a measured quantity x represents the modulus of the maximum possible difference between the measured and the real value. The relative error is expressed by the ratio between the absolute error and the modulus of the real value (under the condition that the denominator is non-null).

Then, if an indirectly determined value results from the relation

(1)

its absolute error is (2)

while if the value results from the relation (3)

its relative error is (4)

2. The random errors are due to statistical reasons.

Referatele in engleza de la laborator