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5CALCULATION OF THE ERROR IN THE PROCESS OF CONDUCTING EXPERIMENTS ON PHYSICS
1Nurillaev Bobomurot Najmitdinovich, 2Qurbonazarov Ilxom Toxtaevich
1Associate professor of TSPU named after Nizami 2Teacher at TSPU named after Nizami https://doi.org/10.5281/zenodo.7900807
Abstract. This article presents reflections on the errors that arise in the process of conducting experiments on physics, and their accounting. The method of determining the parameters of electrical measuring devices based on the records on their scale is also given
Keywords: direct measurement, indirect measurement, experiment, systematic errors, random errors., gross errors (misses), instrumental error, arithmetic mean, absolute error, relative error, average quadratic measurement error.
INTRODUCTION
Since physics is a science that teaches the reality of the material world, it relies on experiments to study its laws. Experiments are conducted based on the measurement of physical quantities. To measure, it is said to compare the determined physical quantity with the quantity accepted as a unit, that is, to determine how many times it differs from the unit. The purpose of measurement is to obtain the value of physical quantities in the form that is most convenient for use. The main quality of measurement is its accuracy. Assessment of the accuracy of the measurement result is an integral part of the experiment. This assessment can be done by finding measurement errors.
A measuring instrument is a device used to measure a physical quantity. Measuring instruments are used to ensure quality in physical sciences and engineering measurements. Measurement is the activity of obtaining and comparing physical quantities of real-world objects and phenomena. According to the number of experiments, measurements are divided into onetime and multiple measurements. In one-time measurement, only one measurement is made to obtain the value of a certain physical quantity by experiment. If several measurements are made using the same instruments under the same conditions to obtain the value of a physical quantity, this is called multiple measurement. In multiple measurements, the exact value of the quantity is obtained by mathematical processing of the experimental results.
RESEARCH MATERIALS.
There are two types of measurement, they are called direct and indirect measurement. Determining the value of a given physical quantity by comparing it with a unit quantity is called direct measurement. For example, temperature is measured directly with a thermometer, mass scale, conductor resistance with an ohmmeter, length with a ruler or measuring tape, current with an ammeter, and electric current with a voltmeter. For accuracy, the experiment should be repeated several times.
Determining the value of legally, that is, functionally related quantities with directly measured physical quantities is called indirect measurement. An example of this is the methods of determining such quantities as speed, acceleration, energy, volume, conductor resistance. In addition, measurement methods can be divided into contact and non-contact measurement methods. In contact measurement, the surface of the object to be measured and the measuring tool
touch each other (for example, this is the case when measuring the inner diameter of a piston with a caliper). When measuring with a non-contact measurement method, the measured object and the surface of the measuring instrument do not touch each other (for example, the working range of the Testo 830-T2 pyrometric thermometer is from -50oC to + 500oC. The measurement error does not exceed 0.5 or 0.5% of the obtained temperature).
Absolutely accurate measurements cannot be made with any device. The measured value always differs from its true value, and this difference is called error. It is the duty of all measuring equipment manufacturers to ensure that this error is as small as possible. Formation and development of educational experimental competence of future physics teachers depends on their acquisition of competences in working with measuring instruments, knowing the working principles of measuring instruments and accounting for measurement errors.
The main characteristics of measurements are: 1) principle, 2) method, 3) errors, 4) accuracy, 5) correctness 6) reliability of measurement [1]. 1) a measurement principle is a physical phenomenon or a set of physical phenomena that forms the basis of measurement. For example, determination of body mass by weighing method is based on the use of proportionality between mass and gravity; 2) measurement method is a set of principles and the use of measurement tools. The measurement method is a mandatory procedure that determines the type of measurement, regardless of the principle of operation; 3) measurement error is a deviation of the experimental result from the actual value of the measured quantity; 4) accuracy of measurement is a property that reflects measurements. Closeness of the measurement results to the actual value of the measured quantity; 5) correctness of measurements - reflects the quality of measurements. The systematic error should be as small as possible (close to zero); 6) reliability of measurements - indicates the level of confidence in the results of measurements. Measurements in which the probabilistic characteristics of the deviation of the results from the true value are known belong to the reliable category.
Errors can be divided into systematic, random and gross errors. In most cases, systematic error occurs unilaterally as a result of the incorrect indication of the instrument or the imprecise measurement method, and finally, as a result of some continuous external influence (environmental influence). For example, when measuring the current in a circuit, due to the fact that the reading of the ammeter is slightly shifted from zero, until the necessary corrections are made to the measurement results, a systematic error will be made. Also, uneven heating of the balance circuit due to the influence of sunlight or heat from a heat source leads to a systematic error in measuring body mass.
But identifying and correcting these errors remains a challenge. In general, systematic errors appear for objective reasons. It affects the measurement results only one-way, that is, the measurement result may be slightly increased or slightly decreased due to systematic error. Therefore, systematic errors occur due to specific reasons, and its amount may not change in repeated measurements and may change according to a certain law [2]. Instrument error and methodological errors are the main causes of systematic error. The error of the instrument can be explained on the basis of the following: it is impossible to produce two devices that work with exactly the same accuracy; incorrect recording of the arrow pointing due to the fact that the observer's eye does not fall directly on the arrow of the instrument. The accuracy of the measuring instrument is its quality characteristic and reflects the closeness of the error to zero. The
generalized characteristic of this type of measuring instruments is its accuracy class. The smaller the error, the more accurate the measuring instruments.
Measurement method error (or methodological error) results from the imperfection of the adopted measurement method. For example, when determining the strength of the Earth's magnetic field in a university laboratory, the magnetic fields of nearby devices may be affected.
RESEARCH RESULTS:
Electrical measuring devices are devices related to various systems that measure quantities such as current, voltage, charge, frequency, phase difference, current power. They can be based on the mechanical movement of the moving part of the arrow or mirror under the influence of electric or electromagnetic forces. Such devices are called electromechanical devices. Nowadays, electronic devices are taking the place of electromechanical devices. In many cases, electronic and electromagnetic parts are used together in electrical measuring devices. For example, an amplifier is an electronic device, but an electromechanical voltmeter may be fitted to indicate its output voltage [2].
The accuracy class of electrical measuring devices is divided into 8 groups: 0.05; 0.1; 0.2; 0.5; 1.0; 1.5; 2.5; 4.0. Accuracy class 0.05; Instruments with 0.1 are considered control instruments. Accuracy class 0.2; Instruments with 0.5 are used in high-precision laboratory measurements and are called precision instruments. Accuracy class 1.0; 1.5: 2.5 and 4.0 gauges are used in technique and training. Usually, the accuracy class of a measuring instrument is indicated at the bottom of its scale and expressed in %, but without the % sign. If such a symbol is not shown at the bottom of the scale, then the indicated error of this instrument is greater than 4%.
One of the important factors in the development of educational experimental competence of a future physics teacher is to have knowledge about the principle of operation of the measuring instruments used in the course of the lesson. Therefore, we present that it is possible to find out information about its parameters and the principle of operation by looking at the scale of the electrical measuring instrument depicted in the picture below and the symbols shown at the bottom of it (Figure 1).
Measures the constant current voltage
Figure 1. Appearance of the electrical measuring instrument
Figure 1 shows that the given voltmeter is a device in the magnetoelectric system. The measuring
mechanism of such a device consists of a fixed permanent magnet M and a movable 2 coil with a wire winding (Fig. 2). Typically, a thin aluminum frame around which a wire is wound is used as the drive coil. The frame
and the measuring arrow are attached to one (OO!) axle M « k1SNBI (1). The field of the permanent magnet interacts with the magnetic field generated in the current frame and excites 4 arrows. Its turning angle is equal to a. Between the magnetic poles OO! There is 1 solid cylinder with a freely rotating wire around the axis. When a current flows in the opposite direction from the sides of the wire windings parallel to the axis of rotation, double forces act on the sides of the frame, turning it towards the direction of the magnetic induction current. The torque M of the acting pair of forces is directly proportional to the current I, the surface of the wire-wound frame S, the number of windings N, and the permanent magnetic field induction B.
Under the influence of moment M, the frame turns to an angle
a. The deflection angle of the arrow associated with it X = k SNBI (2). Since kj, S, N, B are constant for a given instrument x = k • I (3). Here k = kjSNB (4)
- represents the permanence of this instrument. Constant current strength and voltage magnitudes are measured by means of magnetoelectric devices. DISCUSSION
Depending on the accuracy class of the measuring instrument, it is possible to determine the absolute, relative and quoted errors (Fig. 1):
Figure 2. The structure of
the device in the magnetoelectric system
X -15 10 F-1,5% - absolute error A = ± = ±—^^— = ±0,15 V (5)
100
100%
- relative error S = ±^-100 = ±0,15• 100% (6)
X X
- quoted error Y = ~— •100% = 0— •1 °°% =1,5% (7). Here Xn - measuring limit of
X.
10
the device (10 V in our example), X - indication of the instrument arrow during measurement.
Usually, laboratory practicums for a general physics course are developed and recommended by experienced experimenters. The measurement methodology is developed in such a way that it ensures that systematic errors in the measurement process are minimal. The appropriate methodological instructions suggest the optimal procedure for performing the measurements, indicating the measurement errors for the devices used [3].
Random error has subjective character and does not follow any specific law. The result of each measurement may be more or less. Random error is mainly due to experimenter error, such as seeing the instrument display incorrectly or hearing it incorrectly if it is audible. Random errors, like systematic errors, cannot be completely eliminated. To reduce them, the number of repeated measurements is increased and the average value of the experimental results is obtained. It is also
possible to achieve somewhat accurate results by calculating random errors in measurement using the elements of probability laws.
Gross errors (omissions) are errors that significantly exceed those expected under the measurement conditions. Such errors occur due to operator errors or failure to take into account external influences. They are usually explained by the carelessness of the experimenter. He saw one number but wrote another, for example, he got 6 for 0 when rewriting the result. Or it can occur as a result of a sudden violation of the experimental conditions, such as a strong shaking of the device, a jump of the induced voltage due to a short circuit in an adjacent device, a sudden change in the voltage in the network [4]. Gross errors are immediately noticeable when comparing experimental results or drawing a graph based on the results. It is not so difficult to eliminate them, for example, the experiment can be repeated together with another experimenter or with other devices. Below we will discuss the elements of random error.
Arithmetic average value: if we want to get a result close to its real value while measuring physical quantity a, we have to increase the number of measurements, for example n times. Let
the results al5 a2? an? of measuring physical quantity a n times be recorded. If we add
these values and divide by the number of measurements, we will create the arithmetic average value of the quantity being measured
a + a2 + a3+ •••• + a i "n
<a> =-= a (8)
n n t!
Absolute error: the difference between the average arithmetic value of the measured quantity and the result of each individual measurement gives the absolute error made during the
measurement. It is defined as Aa. Let's say the absolute errors in the first, second, etc.
measurement:
n
Aa = < a > —a Aa = < a > —a Aa =
2
2
< a > —a
(9) The
arithmetic mean of these absolute errors is called the arithmetic mean error:
Aa + Aa +Aa +.... + Aa 1
< Aa > -2-3-n = -'^Aaf (10)
n n tT
Taking into account that the actual value of the measured quantity may be greater or less than its average arithmetic value, we can write the result of the measurements as follows:
a = < a > ± < Aa > (11)
Relative error: It should be noted that the absolute error does not always fully describe the quality of the measurement. Therefore, in addition to the absolute error, it is important to know the error called the relative error in order to describe the level of accuracy of the measurement results. The relative error is determined by the ratio of the average value of the absolute errors (10) to the arithmetic average value of the experimental results (8) and is expressed as a percentage:
< Aa >
£ = '1(12). In cases where very accurate measurement is not required, a relative
error of 5-7% is allowed.
Mean squared and most probable errors: Sometimes the mean arithmetic error in the
measurement of the quantity a can be < Aa > = 0, but there is a quantity called the mean squared error, the value of which is never equal to zero. Therefore, in order to increase the
accuracy limit of the results in the measurement of quantities, concepts and quantities called mean square error are used as the most probable error. Mean squared error of each measurement is
considered the quantity
S„ =
1
Z (Aa, )2
1=1
(13). When the number of measurements is very
n • (n -1)
large, that is n ^ œ , Sn tends to a constant value G . G can be called statistical threshold value of Sn, that is G = lim Sn (14).
Essentially, this threshold value is the root mean squared error. However, in practical work, we always calculate not G , but its approximate value Sn. The larger n is, the closer Sn is to G .
Student's coefficient: If the number of measurements n is finite, then the coefficient ta (n) called Student's coefficient is used to calculate the error, its numerical value depends on
the probability a and the number of measurements n. the value of the most probable error in measuring a physical quantity a is calculated using the following expression:
r = ta (")
1
Z (Aa , )2
i=1
(15). Thus, taking into account the above errors, the actual value of the
n • (n -1)
measured quantity a can be written as follows: ahaq = ^ a ^ ± r (16).
Based on the above considerations, we can describe the process of performing physical measurements in the form of the following scheme:
Figure 3. Scheme reflecting the process of physical measurements
Here are some examples of tests and assignments designed to monitor the level of development of future teachers' competence in working with measuring instruments:
Test №1. A millivoltmeter with a scale of 50 mV has an accuracy class of 0.5. What is the absolute error of this instrument?
A. ± 0,25 mV ; b. ± 0,5 mV ; c. ± 0,05 mV ; d. ± 0,2 mV
Test №2. The accuracy class of the voltmeter is 1.5. The upper limit of the scale is 100 V. The reading of the instrument is 50 V. What is the absolute error of this instrument?
A. ± 1,5 V ; B. ± 0,5 V ; C. ± 0,15 V ; D. ± 0,25 V
Test №3. The reading of the voltmeter is 50 V. Its absolute error is 1.5 V. What is the relative error of the instrument?
A. 3% ; B. 5 % ; C. 1,5 % ; D. 2,5 %
Test №4. The upper limit of the voltmeter scale is 100 V. Its absolute error is 1.5 V? What is the quoted error of the instrument?
A. 1,5%; B. 0,15 % ; C. 3 % ; D. 2,5 %
Assignment for students №1
№
1.
The content of the assignment
How much and what kind of current is the amperemeter shown in the picture designed to measure?
How many divisions is the given amperemeter scale divided into?
Determine the division value of the amperemeter scale.
Determine the absolute error of the given amperemeter.
If the amperemeter needle indicates a current of 2A, determine the relative error of the instrument.
Determine the quoted error of the given amperemeter.
U1 1 1 VI V111VIV1 .
In what system is this amperemeter an electrical measuring instrument?
Measuring instrument
Amperemeter [5]
CONCLUSION. As a conclusion, we can note that the information and comments presented in this article can be used as a methodical instruction in the process of conducting experiments by pupils and teachers of secondary general education and vocational schools and academic lyceums, as well as, future teachers studying in pedagogic higher education institutions and physics teachers working in higher education institutions.
REFERENCES
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