Methods and means of electrical measurements. Methods of electrical measurements. There are errors: systematic and random

Energy saving and energy efficiency of industry cannot be imagined without electrical measurements, since it is impossible to save what you do not know how to account for.

Electrical measurements are carried out in one of the following types: direct, indirect, cumulative and joint. The name of the direct type speaks for itself; the value of the required value is determined directly by the device. An example of such measurements is determining power with a wattmeter, current with an ammeter, etc.

Indirect view consists in finding a value based on the known dependence of this value and the value found by the direct method. An example is determining power without a wattmeter. Using the direct method, I, U, phase are found and the power is calculated using the formula.

Aggregate and joint types measurements consist in the simultaneous measurement of several quantities of the same name (cumulative) or not of the same name (joint) quantities. Finding the required quantities is carried out by solving systems of equations with coefficients obtained as a result of direct measurements. The number of equations in such a system must be equal to the number of desired quantities.

Direct measurements As the most common type of measurements, they can be made by two main methods:

direct assessment method
comparison method with measure.

The first method is the simplest, since the value of the desired value is determined on the scale of the device.

This method is used to determine the current strength with an ammeter, the voltage of voltmeters, etc. The advantage of this method is its simplicity, but the disadvantage is its low accuracy.

Measurements by comparison with a measure are performed using one of the following methods: substitution, opposition, coincidence, differential and zero. A measure is a kind of reference value of a certain quantity.

Differential and zero methods– are the basis for the operation of measuring bridges. With the differential method, unbalanced indicating bridges are made, and with the zero method, balanced or zero ones are made.

In balanced bridges, comparison occurs using two or more auxiliary resistances, selected in such a way that with the resistances being compared they form a closed circuit (four-terminal network), powered from a single source and having equipotential points detected by a balance indicator.

The ratio between auxiliary resistances is a measure of the relationship between the quantities being compared. The balance indicator in DC circuits is a galvanometer, and in AC circuits a millivoltmeter.

The differential method is otherwise called the difference method, since the measuring instrument is affected precisely by the difference between the known and desired current values. The zero method is a limiting case of the differential method. For example, in the indicated bridge circuit, the galvanometer shows zero if the equality is met:

R1*R3 = R2*R4;

From this expression it follows:

Rx=R1=R2*R4/R3.

Thus, it is possible to calculate the resistance of any unknown element, provided that the other 3 are exemplary. The direct current source should also be exemplary.

Opposition method- otherwise this method is called compensation and is used for direct comparison of voltage or EMF, current and indirectly for measuring other quantities converted into electrical quantities.

Two counter-directed EMFs, not connected to each other, are switched on to a device that balances the branches of the circuit. In the picture: you need to find Ux. Using an exemplary adjustable resistance Rk, a voltage drop Uk is achieved such that it is numerically equal to Ux.

Their equality can be judged by the readings of a galvanometer. If U and Ux are equal, no current will flow in the galvanometer circuit, since they are oppositely directed. Knowing the resistance and current value, we determine Ux using the formula.

Substitution method– a method in which the desired value is replaced or combined with a known standard value, equal in value to the substituted one. This method is used to determine the inductance or capacitance of an unknown value. An expression that determines the dependence of frequency on circuit parameters:

fo=1/(√LC)

On the left, the frequency f0 is set by the HF generator, on the right side are the values of the inductance and capacitance of the measured circuit. By selecting the resonance frequency, you can determine the unknown values on the right side of the expression.

An indicator of resonance is an electronic voltmeter with a high input resistance, the readings of which will be greatest at the moment of resonance. If the measured inductor is connected in parallel with a reference capacitor and the resonant frequency is measured, then the value of Lx can be found from the above expression. The unknown capacity is located similarly.

First, the resonant circuit, consisting of inductance L and a model capacitor Co, is tuned to resonance at frequency fo; at the same time, the values of fo and the capacitance of the capacitor Co1 are recorded.

Then, in parallel with the model capacitor Co, a capacitor Cx is connected by changing the capacitance of the model capacitor to achieve resonance at the same frequency fo; Accordingly, the required quantity is Co2.

Match method– a method in which the difference between the desired and known value is determined by the coincidence of scale marks or periodic signals. A striking example of the application of this method in life is the measurement of the angular velocity of rotation of various parts.

To do this, a mark is applied to the object being measured, for example, a small mark. When a part with a mark is rotated, a strobe light is directed at it, the blinking frequency of which is initially known. By adjusting the frequency of the strobe, you can ensure that the mark stays in place. In this case, the rotation frequency of the part is taken equal to the blinking frequency of the strobe light.

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Electrical measurement methods

Depending on the general methods of obtaining the result, measurements are divided into the following types: direct, indirect and joint.

Direct measurements include those whose results are obtained directly from experimental data. Direct measurement can be conventionally expressed by the formula Y = X, where Y is the desired value of the measured quantity; X is a value directly obtained from experimental data. This type of measurement includes measurements of various physical quantities using instruments calibrated in established units. For example, measuring current with an ammeter, temperature with a thermometer, etc. This type of measurement also includes measurements in which the desired value of a quantity is determined by directly comparing it with the measure. The means used and the simplicity (or complexity) of the experiment are not taken into account when classifying a measurement as direct.

Indirect measurement is a measurement in which the desired value of a quantity is found on the basis of a known relationship between this quantity and the quantities subjected to direct measurements. In indirect measurements, the numerical value of the measured quantity is determined by calculation using the formula

Y = F (Xl, X2 ... Xn),

where Y is the desired value of the measured quantity; X1, X2, Xn are the values of the measured quantities. As an example of indirect measurements, we can point out the measurement of power in DC circuits with an ammeter and a voltmeter.

Joint measurements are those in which the desired values of opposite quantities are determined by solving a system of equations connecting the values of the sought quantities with directly measured quantities. An example of joint measurements is the determination of the coefficients in the formula relating the resistance of a resistor to its temperature:

Rt = R20 (1+b (T1-20)+c(T1-20)).

Depending on the set of techniques for using the principles and means of measurement, all methods are divided into the direct assessment method and comparison methods.

The essence of the direct assessment method is that the value of the measured quantity is judged by the readings of one (direct measurements) or several (indirect measurements) instruments, pre-calibrated in units of the measured quantity or in units of other quantities on which the measured quantity depends. The simplest example of a direct assessment method is the measurement of a quantity with one device, the scale of which is graduated in appropriate units.

The second large group of electrical measurement methods is united under the general name of comparison methods. These include all those methods of electrical measurements in which the measured value is compared with the value reproduced by the measure. Thus, a distinctive feature of comparison methods is the direct participation of measures in the measurement process.

The comparison method is divided into the following: zero, differential, substitution and coincidence.

The zero method is a method of comparing a measured value with a measure, in which the resulting effect of the influence of values on the indicator is brought to zero. Thus, when equilibrium is achieved, the disappearance of a certain phenomenon is observed, for example, the current in a section of the circuit or the voltage on it, which can be recorded using devices that serve this purpose - null indicators. Due to the high sensitivity of null indicators, and also because measures can be carried out with great accuracy, greater measurement accuracy is obtained.

An example of the application of the zero method would be to measure the electrical resistance of a bridge with its complete balancing.

With the differential method, as well as with the zero method, the measured quantity is compared directly or indirectly with the measure, and the value of the measured quantity as a result of the comparison is judged by the difference in the effects simultaneously produced by these quantities and by the known value reproduced by the measure. Thus, in the differential method, incomplete balancing of the measured value occurs, and this is the difference between the differential method and the zero method.

The differential method combines some of the features of the direct assessment method and some of the features of the zero method. It can give a very accurate measurement result, if only the measured quantity and the measure differ little from each other. For example, if the difference between these two quantities is 1% and is measured with an error of up to 1%, then the error in measuring the desired quantity is reduced to 0.01%, if the error of the measure is not taken into account.

An example of the application of the differential method is the measurement with a voltmeter of the difference between two voltages, of which one is known with great accuracy, and the other is the desired value.

The substitution method consists of alternately measuring the desired quantity with a device and measuring with the same device a measure that reproduces a homogeneous quantity with the measured quantity. Based on the results of two measurements, the desired value can be calculated. Due to the fact that both measurements are made by the same instrument under the same external conditions, and the desired value is determined by the ratio of the instrument readings, the error of the measurement result is significantly reduced. Since the instrument error is usually not the same at different points on the scale, the greatest measurement accuracy is obtained with the same instrument readings.

An example of the application of the substitution method can be the measurement of a relatively large electrical resistance at direct current by alternately measuring the current flowing through a controlled resistor and a reference one. The circuit during measurements must be powered from the same current source.

The coincidence method is a method in which the difference between the measured quantity and the value reproduced by the measure is measured using the coincidence of scale marks or periodic signals. This method is widely used in the practice of non-electrical measurements. An example would be measuring length with a vernier caliper. In electrical measurements, an example is measuring the rotational speed of a body with a strobe light. Let us also indicate the classification of measurements based on changes in time of the measured value. Depending on whether the measured quantity changes over time or remains unchanged during the measurement process, static and dynamic measurements are distinguished. Static measurements are measurements of constant or steady values. These include measurements of effective and amplitude values of quantities, but in a steady state.

If instantaneous values of time-varying quantities are measured, then the measurements are called dynamic. If, during dynamic measurements, measuring instruments allow you to continuously monitor the values of the measured quantity, such measurements are called continuous. It is possible to measure a quantity by measuring its values at certain times t1, t2, etc. As a result, not all values of the measured quantity will be known, but only the values at selected times. Such measurements are called discrete.

measurement electrical electrical engineering

Standardization of methods and measuring instruments plays an important role in science and technology because it is impossible to imagine our life in the 21st century without the objects and things that surround us, and after all, when they were created, they were all measured by someone and somehow. In order for anyone to make these measurements and methods, it is of course necessary to standardize them.

The essence of measurement is to determine the numerical value of a physical quantity. This process is called measurement conversion, emphasizing the connection of the measured physical quantity with the resulting number.

List of sources used

1. “Electrical engineering and electronics”, ed. prof. B.I. Petlenko M. 2003

2. “Metrology, Standardization, Certification and Electrical Measuring Equipment, edited by K.K. Kima 2006

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Basic terms and definitions in the field of metrology. Classification of measurements: direct, indirect, cumulative, etc. Classification of measurement tools and methods. Errors of measuring instruments. Examples of accuracy class designation. Types of measuring instruments.

The indirect type consists in finding a value based on the known relationship between this value and the value found by the direct method. An example is determining power without a wattmeter. Using the direct method, I, U, phase are found and the power is calculated using the formula.

Cumulative and joint types of measurements involve the simultaneous measurement of several quantities of the same name (cumulative) or not of the same name (joint). Finding the required quantities is carried out by solving systems of equations with coefficients obtained as a result of direct measurements. The number of equations in such a system must be equal to the number of desired quantities.

Direct measurements, as the most common type of measurement, can be made by two main methods: the method of direct assessment and the method of comparison with a measure. The first method is the simplest, since the value of the desired value is determined on the scale of the device.

This method is used to determine the current strength with an ammeter, the voltage of voltmeters, etc. The advantage of this method is its simplicity, but the disadvantage is its low accuracy.

Differential and zero methods are the basis for the operation of measuring bridges. With the differential method, unbalanced indicating bridges are made, and with the zero method, balanced or zero ones are made.

The differential method is otherwise called the difference method, since the measuring instrument is affected precisely by the difference between the known and desired current values. The zero method is a limiting case of the differential method. So, for example, in the indicated bridge circuit, the galvanometer shows zero if the equality is met:

From this expression it follows:

Thus, it is possible to calculate the resistance of any unknown element, provided that the other 3 are exemplary. The direct current source should also be exemplary.

“SchemeMethod of opposition - otherwise this method is called compensation and is used for direct comparison of voltage or EMF, current and indirectly for measuring other quantities converted into electrical ones.

Their equality can be judged by the readings of a galvanometer. If Uк and Uх are equal, no current will flow in the galvanometer circuit, since they are oppositely directed. Knowing the resistance and current value, we determine Ux using the formula.

Substitution method is a method in which the desired value is replaced or combined with a known standard value, equal in value to the substituted one. This method is used to determine the inductance or capacitance of an unknown value. An expression that determines the dependence of frequency on circuit parameters:

“ResonanceThe resonance indicator is an electronic voltmeter with a high input resistance, the readings of which will be greatest at the moment of resonance. If the measured inductor is connected in parallel with a reference capacitor and the resonant frequency is measured, then the value of Lx can be found from the above expression. The unknown capacity is located similarly.

Then, in parallel with the model capacitor Co, a capacitor Cx is connected and by changing the capacitance of the model capacitor, resonance is achieved at the same frequency fo; Accordingly, the required quantity is Co2.

The coincidence method is a method in which the difference between the desired and known value is determined by the coincidence of scale marks or periodic signals. A striking example of the application of this method in life is the measurement of the angular velocity of rotation of various parts.

Error of measuring instruments and accuracy class

Measurement accuracy is the quality of a measurement, reflecting the closeness of its results to the true value of the measured value. High measurement accuracy corresponds to low error.

The error of a measuring device is the difference between the readings of the device and the true value of the measured value.

The result of a measurement is the value of a quantity found by measuring it.

With a single measurement, the instrument reading is the result of the measurement, and with multiple measurements, the measurement result is found by statistically processing the results of each observation. According to the accuracy of the measurement results, they are divided into three types: full-time (precision), the result of which must have a minimum error; control and verification tests, the error of which should not exceed a certain specified value; technical, the result of which contains an error determined by the error of the measuring device. As a rule, accurate and control measurements require multiple observations.

According to the method of expression, the errors of measuring instruments are divided into absolute, relative and reduced.

Absolute error DA is the difference between the reading of instrument A and the actual value of the measured quantity A.

Relative error - the ratio of the absolute error YES to the value of the measured quantity A, expressed as a percentage:

Reduced error (in percent) - the ratio of the absolute error of the aircraft to the standard value:

For instruments with a zero mark at the edge or outside the scale, the standard value is equal to the end value of the measuring range. For instruments with a double-sided scale, that is, with scale marks located on both sides of zero, it is equal to the arithmetic sum of the final values of the measurement range. For instruments with a logarithmic or hyperbolic scale, the normalizing value is equal to the length of the entire scale.

Table 1 - Accuracy classes* of measuring instruments

Instruments for measuring electrical quantities must satisfy the following basic requirements (PUE):

1) the accuracy class of measuring instruments must be no worse than 2.5;
2) accuracy classes of measuring shunts, additional resistors, transformers and converters must be no worse than those given in table. 1.;
3) the measurement limits of instruments must be selected taking into account the possible largest long-term deviations of the measured values from the nominal values.

Accounting for active electrical energy should ensure the determination of the amount of energy: generated by ES generators; consumed per s. n. and economic needs (separately) of ES and PS; supplied to consumers via lines extending from the ES buses directly to consumers; transmitted to or received from other energy systems; released to consumers from the electrical network. In addition, accounting for active electrical energy should provide the ability to: determine the flow of electrical energy into electrical networks of different voltage classes of the power system; compiling balances of electrical energy for self-supporting units of the energy system; monitoring compliance by consumers with their specified consumption regimes and balance of electrical energy.

Accounting for reactive electrical energy should provide the ability to determine the amount of reactive electrical energy received by the consumer from the power supply organization or transferred to it only if these data are used to make calculations or monitor compliance with the specified operating mode of compensating devices.

Classification of electrical appliances

Electrical devices (EA) are electrical devices for controlling energy and information flows, operating modes, monitoring and protecting technical systems and their components.

Electrical devices, depending on the element base and operating principle, are divided into three groups:

electromechanical;

The main feature of electromechanical devices is the presence of moving parts in them. For many types of electromechanical devices, one of the moving parts is a contact system that switches the electrical circuit.

static;

Static devices are made on the basis of electronic components (diodes, thyristors, transistors, etc.), as well as controlled electromagnetic devices (magnetic amplifiers, saturation chokes, etc.). Devices of this type, as a rule, belong to power electronic devices, since they are usually used to control the flow of electrical energy, rather than information.

hybrid.

They are a combination of electromechanical and static devices.

Main types of electrical devices

Electrical devices can be classified according to various criteria, for example:

by voltage: low (up to 1000 V) and high voltage from units to thousands of kilovolts;

current value: low-current (up to 5 A) and high-current (from 5 A to hundreds of kiloamperes);

type of current: direct and alternating;

power supply frequency: with normal (up to 50 Hz) and increased (from 400 Hz to 10 kHz) frequency;

the type of functions performed: switching, regulating, monitoring, measuring, limiting current or voltage, stabilizing;

design of the switching element: contact and non-contact (static), hybrid, synchronous, arcless.

The variety of classification types is determined by the areas of application: in automatic and non-automatic control circuits of various electrical equipment; in devices for automatic regulation, stabilization, control and measurement of electrical energy distribution and power supply systems for electrical enterprises and many other industries related to the use of electrical energy.

High voltage electrical apparatus (AVN)

According to their functional characteristics, AVNs are divided into the following types:

switching devices (switches, load switches, disconnectors);

measuring devices (current and voltage transformers, voltage dividers);

limiting devices (fuses, reactors, arresters, nonlinear surge suppressors);

compensating devices (controlled and uncontrolled shunt reactors);

complete distribution devices.

Low voltage electrical control and switchgear

Control devices are designed to control the operating mode of electrical equipment and are divided into the following types:

contactors;

starters;

controllers;

electrical control relays;

command devices;

switches;

control electromagnets;

electrically controlled clutches.

Switchgear devices are designed to protect electrical equipment in various emergency modes (overload and short circuit currents, unacceptable voltage reduction, leakage currents to ground when insulation is damaged, reverse currents, etc.). These devices are divided into circuit breakers and low-voltage fuses.

Structurally complete electrical components: electrical connectors (socket, plug), lighting control gears, special pulse generators. forms, control units for mains voltage parameters, etc.

Electrical automation devices

To implement electrical automation devices, various physical principles are used. By purpose they are classified as follows:

primary converters (sensors);

distributors (switches);

adders, logic elements, regulators;

actuators (electrical automation relays, electric hydraulic valves, electric hydraulic valves, electric valves, magnetic supports and suspensions, valves, pushers, etc.);

electrical automation relays (sealed magnetically controlled contacts (reed switches), etc.).

relay devices with mechanical control (input) and electrical output (buttons, keys, keyboards, toggle switches, microswitches).

Voltage, current and power measurement

When studying electrical engineering, one has to deal with electrical, magnetic and mechanical quantities and measure these quantities.

To measure an electrical, magnetic or any other quantity means to compare it with another homogeneous quantity taken as a unit.

This article discusses the classification of measurements that are most important for. This classification includes the classification of measurements from a methodological point of view, i.e. depending on the general techniques for obtaining measurement results (types or classes of measurements), the classification of measurements depending on the use of principles and measuring instruments (measurement methods) and the classification of measurements depending on the dynamics of the measured quantities.

Types of electrical measurements

Depending on the general methods of obtaining the result, measurements are divided into the following types: direct, indirect and joint.

Towards direct measurements include those whose results are obtained directly from experimental data. Direct measurement can be conditionally expressed by the formula Y = X, where Y is the desired value of the measured quantity; X is a value directly obtained from experimental data. This type of measurement includes measurements of various physical quantities using instruments calibrated in established units.

For example, measuring current with an ammeter, temperature with a thermometer, etc. This type of measurement also includes measurements in which the desired value of a quantity is determined by directly comparing it with the measure. The means used and the simplicity (or complexity) of the experiment are not taken into account when classifying a measurement as direct.

Indirect measurement is a measurement in which the desired value of a quantity is found on the basis of a known relationship between this quantity and quantities subjected to direct measurements. In indirect measurements, the numerical value of the measured value is determined by calculating using the formula Y = F(Xl, X2 ... Xn), where Y is the desired value of the measured value; X1, X2, Xn - values of measured quantities. As an example of indirect measurements, we can point out the measurement of power in DC circuits with an ammeter and a voltmeter.

Joint measurements are called those in which the desired values of opposite quantities are determined by solving a system of equations connecting the values of the sought quantities with directly measured quantities. An example of joint measurements is the determination of the coefficients in the formula relating the resistance of a resistor to its temperature: Rt = R20

Electrical measurement methods

Depending on the set of techniques for using the principles and means of measurement, all methods are divided into the direct assessment method and comparison methods.

Essence direct assessment method lies in the fact that the value of the measured quantity is judged by the readings of one (direct measurements) or several (indirect measurements) instruments, pre-calibrated in units of the measured quantity or in units of other quantities on which the measured quantity depends.

The simplest example of a direct assessment method is the measurement of a quantity with one device, the scale of which is graduated in appropriate units.

The second large group of electrical measurement methods is united under the general name comparison methods. These include all those methods of electrical measurements in which the measured value is compared with the value reproduced by the measure. Thus, a distinctive feature of comparison methods is the direct participation of measures in the measurement process.

Comparison methods are divided into the following: zero, differential, substitution and coincidence.

An example of the application of the zero method would be to measure the electrical resistance of a bridge with its complete balancing.

At differential method, as well as with zero, the measured quantity is compared directly or indirectly with the measure, and the value of the measured quantity as a result of comparison is judged by the difference in the effects simultaneously produced by these quantities and by the known value reproduced by the measure. Thus, in the differential method, incomplete balancing of the measured value occurs, and this is the difference between the differential method and the zero method.

For example, if the difference between these two quantities is 1% and is measured with an error of up to 1%, then the error in measuring the desired quantity is reduced to 0.01%, if the error of the measure is not taken into account. An example of the application of the differential method is the measurement with a voltmeter of the difference between two voltages, of which one is known with great accuracy, and the other is the desired value.

Substitution method consists in alternately measuring the desired quantity with a device and measuring with the same device a measure that reproduces a homogeneous quantity with the measured quantity. Based on the results of two measurements, the desired value can be calculated. Due to the fact that both measurements are made by the same instrument under the same external conditions, and the desired value is determined by the ratio of the instrument readings, the error of the measurement result is significantly reduced. Since the instrument error is usually not the same at different points on the scale, the greatest measurement accuracy is obtained with the same instrument readings.

An example of the application of the substitution method would be to measure a relatively large one by alternately measuring the current flowing through a controlled resistor and a reference one. The circuit during measurements must be powered from the same current source. The resistance of the current source and the device measuring the current must be very small compared to the variable and reference resistances.

Match method is a method in which the difference between the measured value and the value reproduced by the measure is measured using the coincidence of scale marks or periodic signals. This method is widely used in the practice of non-electrical measurements.

An example is the measurement of length. In electrical measurements, an example is measuring the rotational speed of a body with a strobe light.

Let us also indicate classification of measurements based on changes in time of the measured value. Depending on whether the measured quantity changes over time or remains unchanged during the measurement process, static and dynamic measurements are distinguished. Static measurements are measurements of constant or steady values. These include measurements of effective and amplitude values of quantities, but in a steady state.

It is possible to measure a quantity by measuring its values at certain times t1, t2, etc. As a result, not all values of the measured quantity will be known, but only the values at selected times. Such measurements are called discrete.

Question

Electric field

Electric charges interact with each other, that is, like charges repel each other, and opposite charges attract. The forces of interaction between electric charges are determined by Coulomb's law and are directed along a straight line connecting the points at which the charges are concentrated.

According to Coulomb's law, the force of interaction between two point electric charges is directly proportional to the product of the amounts of electricity in these charges, inversely proportional to the square of the distance between them and depends on the environment in which the charges are located:

Question

Potential- A quantity characterizing the energy reserve of a body located at a given point in the field (electric, magnetic).

Electric field strength- a vector physical quantity that characterizes the electric field at a given point and is numerically equal to the ratio of the force acting on a stationary point charge placed at a given point in the field to the magnitude of this charge

Question

Electric field- one of two components of the electromagnetic field, which is a vector field that exists around bodies or particles with an electric charge.

Conductors

Conductors include all metals and their alloys, as well as electrical coal
Liquid conductors include: water, solutions of salts, acids and alkalis.
Gaseous gases include ionized gases.
Electric current in solid conductors is the directed movement of free electrons under the influence of emf.
Conductor properties: Electrical, Physical, Mechanical, Chemical.

Dielectrics

They do not allow electric current to pass through. Dielectrics have high resistivity. Used to protect the conductor from moisture, mechanical damage, and dust.

Dielectrics are: solid - all non-metals; liquid - oils, synthetic fluids SOVOL, SOVTOL; gaseous - all gases: air, oxygen, nitrogen, etc.

Dielectric properties: Electrical properties, Physico-chemical properties, Chemical, Mechanical.

Question

Types of electrical measurements. Direct measurements include those whose results are obtained directly from experimental data. Direct measurement can be conventionally expressed by the formula Y = X. This type of measurement includes measurements of various physical quantities using instruments calibrated in established units. This type of measurement also includes measurements in which the desired value of a quantity is determined by direct comparison of it with the measure

Indirect is a measurement in which the desired value of a quantity is found on the basis of a known relationship between this quantity and quantities subjected to direct measurements. In indirect measurements, the numerical value of the measured quantity is determined by calculating using the formula Y = F (Xl, X2 ... Xn). As an example of indirect measurements, we can point to the measurement of power in DC circuits with an ammeter and voltmeter.

Joint measurements are called those in which the desired values of opposite quantities are determined by solving a system of equations connecting the values of the sought quantities with directly measured quantities. An example of joint measurements is the determination of the coefficients in the formula relating the resistance of a resistor to its temperature: Rt = R20

Electrical measurement methods

Null method- this is a method of comparing a measured value with a measure, in which the resulting effect of the influence of values on the indicator is brought to zero. Thus, when equilibrium is achieved, the disappearance of a certain phenomenon is observed, for example, the current in a section of the circuit or the voltage on it, which can be recorded using devices that serve this purpose - null indicators. Due to the high sensitivity of null indicators, and also because measures can be carried out with great accuracy, greater measurement accuracy is obtained. An example of the application of the zero method would be to measure the electrical resistance of a bridge with its complete balancing.

At differential method, as well as with zero, the measured quantity is compared directly or indirectly with the measure, and the value of the measured quantity as a result of comparison is judged by the difference in the effects simultaneously produced by these quantities and by the known value reproduced by the measure. Thus, in the differential method, incomplete balancing of the measured value occurs, and this is the difference between the differential method and the zero method.

Substitution method consists in alternately measuring the desired quantity with a device and measuring with the same device a measure that reproduces a homogeneous quantity with the measured quantity. Based on the results of two measurements, the desired value can be calculated. Due to the fact that both measurements are made by the same instrument under the same external conditions, and the desired value is determined by the ratio of the instrument readings, the error of the measurement result is significantly reduced. Since the instrument error is usually not the same at different points on the scale, the greatest measurement accuracy is obtained with the same instrument readings.

Match method is a method in which the difference between the measured value and the value reproduced by the measure is measured using the coincidence of scale marks or periodic signals. This method is widely used in the practice of non-electrical measurements. An example is measuring length with a vernier caliper. In electrical measurements, an example is measuring the rotational speed of a body with a strobe light.