Accuracy and Errors in Measurement Physics Notes
Accuracy and Errors in Measurement:
The measuring process is essentially a process of comparison. To measure any physical quantity, we compare it with a standard (unit) of that quantity. No measurement is perfect as the errors involved in the process cannot be removed completely. Hence, in spite of our best effort, the measured value of a quantity is always somewhat different from its actual value, or true value.
Measurement error: The measurement error is defined as the difference between the true or the actual value and the measured value
i. e., the error is quantity = (True value – measurement value) of the quantity.
Types of errors in measurement:
The errors may arise from the different sources and are usually classified into the following types. These types are:
1. Systematic errors
2. Random errors
3. Gross errors
Their types are explained below in detail.
(A) Systematic errors: Systematic errors are those which occur according to a definite pattern. These errors affect the measurement alike i. e., in the same way. The causes of systematic errors are known. Therefore, such errors can be minimized.
Some of the sources of systematic errors are:
1. Instrumental errors: These errors mainly arise due to the three reasons:
(a) Inherent shortcomings of the instrument: Such types of errors are inbuilt in the instruments because of their mechanical structure. They are due to the manufacturing, calibration or operation of the device. These errors may cause the error to read too low or too high.
For example: If the instrument uses the weak spring then it gives the high value of measuring quantity. The error occurs in the instrument because of the friction or hysteresis loss.
(b) Misuse of the instrument: The error occurs in the instrument because of the fault of the operator. A good instrument used in an unintelligent way may give an enormous result.
For example: The misuse of the instrument may cause the failure to adjust the zero of instruments, poor initial adjustment, using leads of high resistance. These improper practices may not cause permanent damage to the instrument, but all the same, they cause errors.
(c) Loading effect: It is the most common type of error which is caused by the instrument in the measurement work. For example, when the voltmeter is connected to the high resistance circuit it gives a misleading reading, and when it is connected to the low resistance circuit, it gives the dependable reading. This means the voltmeter has a loading effect on the circuit.
2. Natural errors: These errors are due to the external conditions of the measuring devices. Such types of errors mainly occur due to the effect of temperature, humidity, dust, vibration or because of the magnetic or electrostatic field. The corrective measures employed to eliminate or to reduce these undesirable effects are:
The arrangement should be made to keep the conditions as constant as pcoiible.
Using the equipment which is free from these effects.
By using the techniques which eliminate the effect of these disturbances.
By applying the computed corrections.
3. Observation error: Such type of errors are due to the wrong observation of the reading. There are many sources of observational error. For example, the pointer of a voltmeter reset slightly above the surface of the scale. Thus, an error occurs unless the line of vision of the observer is exactly above the pointer. To minimise the parallax error highly accurate meters are provided with mirrored scales.
(B) Random errors: These errors are due to the unknown causes and are sometimes termed as chance errors. In an experiment, even the same person repeating an observation may get different reading every time. For example, measuring diameter of a wire with a screw gauge, one may get different readings in different observations. It may happen due to many reasons. For example due to non-uniform area of cross-section of the wire at different places, the screw might have been tightened unevenly in different observation, etc. In such a case, it may not be possible to indicate which observation is most accurate. However, if we repeat the observation a number of times, the arithmetical mean of all the reading is found to be most accurate or very close to the most accurate reading for that observation. That is why, for an experiment it is recommended to repeat an observation a number of times and then to take their arithmetical mean.
If a1, a2, a3………., an are the n different readings in an experiment, their arithmetic mean is given by.
(C) Gross errors: This error occurs because of human mistakes. For example consider the person using the instrument takes the wrong reading, or they can record the incorrect data. Such type of error comes under the gross error. The gross error can only be avoided by taking the reading carefully.
Example: The experimenter reads the reading 31.5°C as while the actual reading is 21.5°C. This happens because of the oversights. The experimenter takes the wrong reading and because of which the error occurs in measurement.
Such type of errors are very common in measurement. The complete elimination of such type of errors is not possible. Some of the gross errors are easily detected by the experimenter but some of them are difficult to find out.
Two methods can be used to remove the gross error:
- The reading should be taken out very carefully.
- Two or more readings should be taken of the measurement quantity. The readings are taken by the different experimenter and at a different point to remove the errors.