Semester work in metrology on the topic "Measurement of resistance."
Fragments from the abstract
- Introduction
- Ammeter-Voltmeter Method
- Direct assessment method
- Very high resistance measurement
- AC Resistance Measurement
- Immitance Meter
- Measuring line
- conclusions
Introduction
Electrical resistance is the main electrical characteristic of a conductor, a value that characterizes the counteraction of an electric circuit or its section to an electric current. Resistance can also be called a part (it is often called a resistor) that provides electrical resistance to current. Electrical resistance is due to the conversion of electrical energy to other forms of energy and is measured in Ohms.
The resistance (often denoted by the letter R) is considered, within certain limits, a constant value for a given conductor and it can be defined as ...
- R is the resistance;
- U is the electric potential difference at the ends of the conductor, measured in volts;
- I is the current flowing between the ends of the conductor under the influence of the potential difference, measured in amperes.
For practical resistance measurements, many different methods are used, depending on the measurement conditions and the nature of the objects, on the required accuracy and speed of measurements. For example, they distinguish between methods for measuring resistance at direct current and at alternating current, measuring large resistances, resistances of small and ultra-small, direct and indirect, etc.
The aim of the work is to identify the main, most common in practice, methods of measuring resistance.
DC resistance measurement
The main methods for measuring DC resistance are the indirect method, the method of direct evaluation, as well as the bridge method. The choice of measurement method depends on the expected value of the measured resistance and the required measurement accuracy. Of the indirect methods, the most universal method is the ammeter-voltmeter method.
Ammeter-Voltmeter Method
This method is based on measuring the current flowing through the measured resistance and the voltage drop across it. Two measurement schemes are used: measurement of high resistances (a) and measurement of low resistances (b). According to the results of measuring current and voltage, the desired resistance is determined.
For circuit (a), the desired resistance and relative methodological error can be determined by the formulas: ...
where Rx is the measured resistance, and Ra is the resistance of the ammeter.
For circuit (b), the desired resistance and relative methodological measurement error are determined by the formulas: ...
It can be seen from the formula that when calculating the required resistance by an approximate formula, an error occurs, because when measuring currents and voltages in the second circuit, the ammeter also takes into account the current that passes through the voltmeter, and in the first circuit the voltmeter measures voltage in addition to the resistor also on the ammeter .
From the determination of relative methodological errors, it follows that the measurement according to scheme (a) provides a smaller error when measuring large resistances, and the measurement according to scheme (b) - when measuring low resistances. The measurement error by this method is calculated by the expression: ...
“The instruments used in the measurement should have an accuracy class of not more than 0.2. A voltmeter is connected directly to the measured resistance. The current during measurement should be such that the readings are measured on the second half of the scale. In accordance with this, a shunt is used, which is used to measure current with a class 0.2 device. In order to avoid heating the resistance and, consequently, reduce the accuracy of measurements, the current in the measurement circuit should not exceed 20% of the nominal. "
The advantage of the method of measuring with an ammeter and voltmeter is that the same current can be passed through a resistor with measured resistance, as in the condition of its operation, which is important when measuring resistances, the values \u200b\u200bof which depend on the current.
Direct assessment method
The direct assessment method involves measuring the resistance to direct current with an ohmmeter. An ohmmeter is a direct reference measuring device for determining electrical active (active resistances are also called ohmic resistances) resistances. Typically, the measurement is made with direct current, however, in some electronic ohmmeters it is possible to use alternating current. Varieties of ohmmeters: megaohmmeters, teraohmmeters, gigaohmmeters, milliometers, microohmmeters, differing in ranges of measured resistances.
According to the principle of operation, ohmmeters can be divided into magnetoelectric - with a magnetoelectric meter or magnetoelectric logometer (megaohmmeters) and electronic, which are analog or digital.
“The action of a magnetoelectric ohmmeter is based on measuring the current flowing through the measured resistance at a constant voltage of the power source. To measure resistances from hundreds of ohms to several megaohms, the meter and the measured resistance rx are connected in series. In this case, the current strength I in the meter and the deviation of the moving part of the device a are proportional: I \u003d U / (r0 + rx), where U is the voltage of the power source; r0 is the resistance of the meter. At low rx values \u200b\u200b(up to several ohms) the meter and rx are switched on in parallel. ”
The ratiometer megaohmmeter is based on the logometer, to the shoulders of which are connected in different combinations (depending on the measurement limit) exemplary internal resistors and the measured resistance, the reading of the logometer depends on the ratio of these resistances. As a source of high voltage required for such measurements, such devices usually use a mechanical inductor - an electric generator with a manual drive, in some megohmmeters a semiconductor voltage converter is used instead of an inductor.
The principle of operation of electronic ohmmeters is based on the conversion of the measured resistance into a voltage proportional to it using an operational amplifier. The measured resistor is connected to the feedback circuit (linear scale) or to the input of the amplifier. The digital ohmmeter is a measuring bridge with automatic balancing. Balancing is performed by a digital control device by the method of selecting precision resistors in the shoulders of the bridge, after which the measurement information from the control device is fed to the display unit.
“When measuring small resistances, an additional error may occur due to the influence of the transition resistance at the connection points. To avoid this, the so-called four-wire connection method is used. The essence of the method is that two pairs of wires are used - one pair of current is supplied to a measured object with a current of a certain force, with the help of another pair a voltage drop proportional to the current strength and object resistance is applied to the device from the object. "The wires are connected to the terminals of the measured two-terminal device so that each of the current wires does not directly touch the voltage wire corresponding to it, and it turns out that the transient resistances at the contact points are not included in the measuring circuit."
DC bridges
Single DC bridges are widely used to measure DC resistance. Single bridges are called four-arm bridges powered by a direct current source. There are a number of designs of these devices with different characteristics. The error of the bridge depends on the measurement limits and is usually indicated in the bridge passport.
Structurally, bridges are designed as portable devices; they are designed to work with their own or external zero indicator. When measuring small resistances, the resistance of the contacts and connecting wires, summed with the measured resistance, has a significant effect on the measurement result. To reduce this effect, special methods of connecting Rx to the bridge are used, for which the bridge has four clamps:
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Measuring line
This is a device for studying the distribution of the electric field along the microwave transmission line. The measuring line is a segment of a coaxial line or waveguide with an indicator moving along it, marking the nodes (antinodes) of the electric field. Using a measuring line, the distribution of the electromagnetic field intensity is studied, from which the standing wave coefficient is determined as the ratio of the wave amplitudes in the antinode and the node and the phase of the reflection coefficient by the node offset. Knowing these parameters, you can find the impedance from the pie chart of the impedances. Measurements are made using a measuring generator as a signal source. As a rule, a galvanometer or a voltage ratio meter is used for reading readings. Measuring lines are used at frequencies from hundreds of megahertz to hundreds of gigahertz.
“The line consists of three main nodes: a segment of the transmission line with a longitudinal narrow slit, a probe head and a carriage with a mechanism for moving the probe head along the line. The probe head is a resonator excited by a probe - a thin wire immersed through a slot in the internal cavity of the waveguide. The immersion depth of the probe in the line is regulated by a special screw located on top of the probe head. A semiconductor detector connected to an indicator device is placed inside the resonator. When moving the probe along a line inside which there is an electromagnetic field, an electromotive force is induced in the probe proportional to the field strength in the cross section of the probe. This e. d.s excites the resonator, creating electromagnetic oscillations in it. To reduce the distorting action of the probe on the electromagnetic field in the line and to increase the sensitivity of the line, the volume resonator of the probe head is tuned to resonance with the frequency of electromagnetic oscillations. "
A device called an impedance meter is also used to measure the impedance of the circuit. Impedance meters have a lower sensitivity than the measuring lines, but they are significantly smaller, especially in the lower part of the frequency range. The coefficient of a standing wave, as in the measuring lines, is determined from the ratio of the readings of the low-frequency indicator at extreme values \u200b\u200bof the signal. The impedance of the object under study is found in a pie chart of the impedances based on the values \u200b\u200bof the standing wave coefficient and phase of the reflection coefficient.
Ultralight Resistance Measurement
In professional and amateur practice, one has to meet the need to measure ultra-small resistance. Among the tasks requiring resistance measurements up to 1 mOhm with a given accuracy, are, for example, manufacturing shunts (including for measuring instruments), measuring the transition resistance of relay contacts, switches, etc. A similar problem also arises if selection is necessary powerful field effect transistors.
conclusions
There are many different methods for measuring resistance. They all differ from each other. And in each case, it is necessary to choose an individual method for measuring. The most common method of indirect resistance measurement is the method of measurements through an ammeter and a voltmeter. It is used in a variety of devices for measuring resistance to both direct and alternating current. However, it is not always possible to use ordinary voltmeters and ammeters to measure voltage and current, since they can give an error, for example, when measuring very small resistances due to the resistance of the connecting wires and contacts. Therefore, for a competent measurement of resistance, it is important to choose a method in which the measurement error will be minimal.
MEASURING ELECTRICAL RESISTANCE
General information
Electrical resistance to direct current is the main parameter of resistors. It also serves as an important indicator of the serviceability and quality of action of many other elements of radio circuits - connecting wires, switching devices, various kinds of coils and windings, etc. The possible values \u200b\u200bof resistances, the need for measurement of which arises in radio engineering practice, lie in a wide range - from thousandths ohm or less (resistance of conductor segments, contact transitions, shielding, shunts, etc.) up to thousands of megohms or more (insulation resistance and leakage of capacitors, surface and volume resistance of electrical insulating materials, etc.). Most often it is necessary to measure the resistance of average values \u200b\u200b- from about 1 ohm to 1 megohm.
The main methods for measuring DC resistance are: indirect method (using voltage and current meters); direct assessment method using ohmmeters and megohmmeters; bridge method. When conducting measurements on alternating current, the impedance of electrical circuits or their elements will be determined, containing the active and reactive components. If the frequency of the alternating current is not large (low frequency region) and the resistance elements prevail in the circuit under test, then the measurement results may be close to those obtained when measuring with direct current.
In the absence of special devices, an approximate idea of \u200b\u200bthe order of electrical resistance of circuits and elements can be obtained using the simplest indicator devices - electrical probes.
If the measurement of the resistances of resistors (or other parameters of electrical components) is carried out directly in the installation of any installation, you must first make sure that the power sources are turned off, the high-voltage capacitors are discharged, and other elements that can affect the measurement results are not connected in parallel with the part being checked.
Electrical resistance measurement
Measurement by ammeter and voltmeter. The resistance of any electrical installation or section of the electrical circuit can be determined using an ammeter and voltmeter, using Ohm's law. When turning on the devices according to the scheme of Fig. 339, and not only the measured current I x passes through the ammeter, but also the current I v flowing through the voltmeter. Therefore resistance
R x \u003d U / (I - U / R v) (110)
where R v - resistance of the voltmeter.
P when turning on the devices according to the scheme of Fig. 339, b voltmeter will measure not only the voltage drop Ux at a certain resistance, but also the voltage drop in the winding of the ammeter U A \u003d IR A. Therefore
R x \u003d U / I - R A (111)
where R A - resistance of the ammeter.
In those cases when the resistances of the devices are unknown and, therefore, cannot be taken into account, it is necessary to use the circuit in fig. 339, a, and when measuring large resistances - the circuit of Fig. 339, b. In this case, the measurement error, determined in the first circuit by the current I v, and in the second one by the voltage drop UA, will be small compared to the current I x and voltage U x.
Resistance measurement by electric bridges. The bridge circuit (Fig. 340, a) consists of a power source, a sensitive device (galvanometer G) and four resistors included in the shoulders of the bridge: with unknown resistance R x (R4) and known resistance R1, R2, R3, which can be measured change. The device is included in one of the diagonals of the bridge (measuring), and the power source in the other (power).
Resistances R1 R2 and R3 can be selected such that when the contact B is closed, the readings of the device will be zero (in
Fig. 339. Schemes for measuring resistance by the method of ammeter and voltmeter
com case it is customary to say that the bridge is balanced). In this case, the unknown resistance
R x \u003d (R 1 / R 2) R 3 (112)
In some bridges, the shoulder ratio R1 / R2 is fixed, and the balance of the bridge is achieved only by selecting the resistance R3. In others, on the contrary, the resistance R3 is constant, and the equilibrium is achieved by selecting the resistances R1 and R2.
The resistance measurement by the DC bridge is as follows. To terminals 1 and 2 they attach an unknown resistance R x (for example, the winding of an electric machine or apparatus), a galvanometer to terminals 3 and 4, and a power source (dry galvanic cell or battery) to terminals 5 and 6. Then, by changing the resistances R1, R2 and R3 (which are used resistance stores switched by the corresponding contacts), they achieve equilibrium of the bridge, which is determined by the zero reading of the galvanometer (with contact B closed).
There are various designs of DC bridges, the use of which does not require calculations, since the unknown resistance R x is counted on the scale of the device. The resistance shops mounted in them allow you to measure resistance from 10 to 100,000 ohms.
When measuring small resistances with conventional bridges, the resistances of the connecting wires and contact joints introduce large errors in the measurement results. To eliminate them, double DC bridges are used (Fig. 340, b). In these bridges, the wires connecting the resistor with the measured resistance R x and some model resistor with the resistance R0 with other bridge resistors, and their contact connections are connected in series with the resistors of the corresponding arms, the resistance of which is set to at least 10 Ohms. Therefore, they practically do not affect the measurement results. The wires connecting resistors with resistances R x and R0 enter the power circuit and do not affect the equilibrium conditions of the bridge. Therefore, the accuracy of measuring low resistances is quite high. The bridge is made so that when adjusting it the following conditions are met: R1 \u003d R2 and R3 \u003d R4. In this case
R x \u003d R 0 R 1 / R 4 (113)
Dual bridges allow you to measure resistance from 10 to 0.000001 Ohms.
If the bridge is not balanced, then the arrow in the galvanometer will deviate from the zero position, since the current of the measuring diagonal at constant values \u200b\u200bof the resistances R1, R2, R3 and e. d.s the current source will depend only on a change in resistance R x. This allows you to calibrate the galvanometer scale in units of resistance R x or any other units (temperature, pressure, etc.) on which this resistance depends. Therefore, an unbalanced DC bridge is widely used in various devices for measuring non-electric quantities by electrical methods.
Various AC bridges are also used, which make it possible to measure inductance and capacitance with high accuracy.
Measurement with an ohmmeter. An ohmmeter is a milliammeter 1 with a magnetoelectric measuring mechanism and is connected in series with the measured resistance R x (Fig. 341) and an additional resistor R D into the DC circuit. With unchanged e. d.s the source and resistance of the resistor R D the current in the circuit depends only on the resistance R x. This allows you to calibrate the scale directly in ohms. If the output terminals of device 2 and 3 are short-circuited (see the dashed line), then the current I in the circuit is maximum and the arrow of the device deviates to the right by the largest angle; on the scale this corresponds to a resistance of zero. If the circuit of the device is open, then I \u003d 0 and the arrow is at the beginning of the scale; this position corresponds to resistance equal to infinity.
The device is powered by a dry galvanic cell 4, which is installed in the device. The device will give correct readings only if the current source has a constant e. d.s (same as when calibrating the instrument scale). Some ohmmeters have two or more measuring ranges, for example from 0 to 100 ohms and from 0 to 10,000 ohms. Depending on this, a resistor with a measured resistance R x is connected to various terminals.
Measurement of large resistances by megohmmeters.To measure insulation resistance, megaohmmeters of a magnetoelectric system are most often used. As a measuring mechanism, they used a logometer 2 (Fig. 342), the readings of whichhorn
Independent of the voltage of the current source supplying the measuring circuits. The coils 1 and 3 of the device are located in the magnetic field of a permanent magnet and are connected to a common power source 4.
In series with one coil, an additional resistor R d is included, and a resistor with resistance R x is included in the circuit of the other coil.
A small DC generator 4, called an inductor, is usually used as a current source; the generator armature is rotated by a handle connected to it through a gearbox. Inductors have significant voltages from 250 to 2500 V, so that large resistances can be measured with a megohmmeter.
When the currents I1 and I2 flowing through the coils interact with the magnetic field of a permanent magnet, two oppositely directed moments M1 and M2 are created, under the influence of which the moving part of the device and the arrow will occupy a certain position. As shown in § 100, the position of the movable
parts of the logometer depends on the ratio I1 / I2. Therefore, when R x changes, will the angle? deflection arrows. The megaohmmeter scale is graduated directly in kiloomes or megaohms (Fig. 343, a).
To measure the insulation resistance between the wires, it is necessary to disconnect them from the current source (from the network) and connect one wire to terminal L (line) (Fig. 343, b), and the other to terminal 3 (ground). Then, rotating the handle of the inductor 1 megohmmeter, determine the insulation resistance on the scale of the logometer 2. The switch 3 included in the device allows changing the measurement limits. The voltage of the inductor, and therefore the speed of its handle, theoretically does not affect the measurement results, but it is practically recommended to rotate it more or less evenly.
When measuring the insulation resistance between the windings of an electric machine, they are disconnected from each other and one of them is connected to clamp A and the other to clamp 3, after which, by rotating the handle of the inductor, the insulation resistance is determined. When measuring the insulation resistance of the winding relative to the housing, it is connected to terminal 3, and the winding to terminal L.
The main methods for measuring DC resistance are:
- indirect method;
- direct assessment method;
- bridge method.
Fig. 1.7. Test transformer switching circuit for tgδ measurement.
1 - circuit breaker; 2 - adjusting autotransformer; 3 - voltmeter; 4-pole polarity switch test transformer 5.
Fig. 1.8. Arrangement of devices during measurement.
OI - object of measurement; C - reference capacitor; T - test transformer; M - bridge; PAT-regulation autotransformer; 0 - portable fence.
The choice of measurement method depends on the expected value of the measured resistance and the required accuracy.
The most universal of indirect methods is the method of an ammeter voltmeter.
Ammeter-voltmeter method. It is based on measuring the current flowing through the measured resistance and the voltage drop across it. Two measurement schemes are used: the measurement of high resistances (Fig. 1.9, a) and the measurement of low resistances (Fig. 1.9, b). According to the results of measuring current and voltage, the desired resistance is determined.
For the circuit of Fig. 1.9, and the desired resistance and relative methodological measurement error are determined
where RX is the measured resistance; Ra - ammeter resistance.
For the circuit of Fig. 1.9.6 the desired resistance and the relative methodological measurement error are determined
where Rv is the resistance of the voltmeter.
From the definition of relative methodological errors it follows that the measurement according to the scheme of Fig. 1.9, a provides a smaller error in the measurement of large resistances, and the measurement according to the scheme of Fig. 1.9.6 - when measuring low resistances.
The measurement error by this method is calculated by the expression
where γв, γа, are accuracy classes of the voltmeter and ammeter; U „, I limits of measurement of the voltmeter and ammeter.
The instruments used in the measurement should have an accuracy class of not more than 0.2. A voltmeter is connected directly to the measured resistance. The current during measurement should be such that the readings are measured on the second half of the scale. In accordance with this, a shunt is used, which is used to measure current with a class 0.2 device. In order to avoid heating the resistance and, accordingly, reducing the accuracy of measurements, the current in the measurement circuit should not exceed 20% of the nominal.
Fig. 1.9. Scheme for measuring large (a) and small (b) resistances using the ammeter-voltmeter method.
When measuring resistance in circuits with high inductance, the voltmeter should be connected after the current in the circuit is established, and disconnected before the current circuit breaks. This must be done in order to exclude the possibility of damage to the voltmeter from the EMF of self-induction of the measurement circuit.
Direct assessment method. It involves measuring the resistance to direct current with an ohmmeter. Measurements with an ohmmeter give significant inaccuracies. For this reason, this method is used for approximate preliminary measurements of resistances and for testing switching circuits. In practice, ohmmeters of the type M57D, M4125, F410 and others are used. The range of measured resistances of these devices lies in the range from 0.1 Ohm to 1000 kOhm.
To measure small resistances, for example, the resistance of the rations of the anchor windings of DC machines, microohmmeters of the type M246 are used. These are ratiometric instruments with an optical pointer, equipped with special self-cleaning probes.
Also, for measuring small resistances, for example, the transient resistances of the contacts of switches, contact meters have been used. Mosenergo contact meters have measurement limits of 0 - 50,000 μOhm with an error of less than 1.5%. Contactors KMS-68, KMS-63 allow measurements within the range of 500-2500 μOhm with an error of less than 5%.
To measure the resistance of the windings of power transformers, generators with fairly high accuracy, DC potentiometers of the type PP-63, KP-59 are used. These devices use the principle of compensation measurement, i.e., the voltage drop across the measured resistance is balanced by a known voltage drop.
Bridge method. Two measurement schemes are used - a single bridge scheme and a double bridge scheme. The corresponding measurement schemes are presented in Fig. 1.10.
To measure resistances in the range from 1 ohm to 1 megohm, single DC bridges of the type ММВ, Р333, МО-62, etc. are used. The measurement error with these bridges reaches 15% (MMV bridge). In single bridges, the measurement result takes into account the resistance of the connecting wires between the bridge and the measured resistance. Therefore, resistances less than 1 Ohm cannot be measured with such bridges due to a significant error. An exception is the P333 bridge, with which it is possible to measure high resistances using a double-clamp circuit and low resistances (up to 5 10 Ohms) using a four-clamp circuit. In the latter, the influence of the resistance of the connecting wires is almost eliminated, since two of them are included in the galvanometer circuit, and the other two are in the resistance circuit of the bridge arms having relatively large resistances.
Fig. 1.10. Schemes of measuring bridges.
a - a single bridge; b - double bridge.
The shoulders of single bridges are made from resistance stores, and in some cases (for example, MMV bridge), the shoulders of R2, R3 can be made of calibrated wire (rechord) along which an engine connected to a galvanometer moves. The equilibrium condition of the bridge is determined by the expression Rx \u003d R3 (R1 / R2). Using R1, the ratio R1 / R2 is established, usually a multiple of 10, and using R3, the bridge is balanced. In bridges with a rechord, balancing is achieved by a smooth change in the ratio R3 / R2 at fixed values \u200b\u200bof R1.
In double bridges, the resistances of the connecting wires are not taken into account during measurements, which makes it possible to measure resistances up to 10-6 Ohms. In practice, single-double bridges of the type P329, P3009, MOD-61 and others are used with a measurement range from 10-8 Ohms to 104 MΩ with a measurement error of 0.01 - 2%.
In these bridges, equilibrium is achieved by changing the resistances R1, R2, R3 and R4. In this case, the equalities R1 \u003d R3 and R2 \u003d R4 are achieved. The equilibrium condition of the bridge is determined by the expression Rx \u003d RN (R1 / R2). Here, the resistance RN is the model resistance, part of the bridge. Four wires are connected to the measured resistance Rx: wire 2 - continuation of the bridge power circuit, its resistance does not affect the accuracy of measurements; wires 3 and 4 are connected in series with resistances R1 and R2 greater than 10 ohms, so that their influence is limited; wire 1 is an integral part of the bridge and should be chosen as short and thick as possible.
When measuring resistance in circuits with high inductance, in order to avoid errors and to prevent damage to the galvanometer, it is necessary to carry out measurements at a steady current, and disconnecting before breaking the current circuit.
Regardless of the measurement method, DC resistance measurement is carried out under steady-state thermal conditions, in which the ambient temperature differs from the temperature of the measured object by no more than ± 3 ° C. To transfer the measured resistance to another temperature (for example, for comparison, to 15 ° C), conversion formulas are used.
Resistance measurement
In the manufacture, installation and operation of electrical and radio devices and installations, it is necessary to measure the electrical resistance.
In practice, various methods are used to measure resistances, depending on the nature of the objects and the measurement conditions (for example, solid and liquid conductors, grounding conductors, electrical insulation); from the requirements for accuracy and speed of measurement; from the value of the measured resistances.
Methods for measuring low resistances are significantly different from methods for measuring high resistances, since in the first case, measures must be taken to exclude the influence on the measurement results of the resistance of the connecting wires, transition contacts.
Measuring mechanisms of ohmmeters. For direct measurement of resistances, single- and two-frame magnetoelectric measuring mechanisms are used.
A single-frame mechanism can be used to measure resistances. For this purpose, an additional resistor with constant resistance is introduced into the device and supplied with a power source (for example, a battery of dry cells). The measured resistance is connected with the meter in series (Fig. 1) or in parallel.
When connected in series, the current in the meter where is the resistance of the meter; - power supply voltage.
Given that where 
- sensitivity of the device by current (constant value), we find that the angle of deviation of the arrow of the device at 
depends only on the value of the measured resistance:
If the scale is calibrated by this expression in units of resistance, the device will be an ohmmeter. The voltage of dry elements decreases with time, therefore, an error is introduced into the measurements, the greater, the more the actual voltage differs from the voltage at which the scale was graduated.
An error from voltage variability of the supply source does not occur if the measuring mechanism has two windings located on a common axis at a certain angle to each other (Fig. 2.).
Fig. 1. Fig. 2.
In the two-frame measuring mechanism, which is called a logometer, there are no opposing springs; the rotating and opposing moments are created by electromagnetic forces. Therefore, in the absence of current in the windings, the well-balanced moving part of the device is in indifferent equilibrium (the arrow stops at any scale division). When there is current in the coils, two electromagnetic moments act in opposite directions on the moving part.
The magnetic circuit of the measuring mechanism is designed so that the magnetic induction along the air gap is distributed unevenly, but with the expectation that when the movable part is turned in any direction, the torque decreases and the opposing moment increases (the role of moments changes depending on the direction of rotation).
The moving part stops when 
or . It follows that the position of the arrow on the scale depends on the ratio of currents in the windings, i.e. 
, but does not depend on the voltage of the supply source.
In the diagram of Fig. 2. it is seen that the measured resistance is included in the circuit of one of the coils of the logometer, therefore the current in it, as well as the deviation of the arrow of the device clearly depends on .
Using this dependence, the scale is graduated in units of resistance and then the device is an ohmmeter. Ohmmeters for measuring insulation resistance provide a power source with a voltage of up to 1000 V, so that the measurement is carried out at a voltage approximately equal to the operating voltage of the installation. Such a source may be a built-in magnetoelectric generator with a manual drive or a transformer with a rectifier, included in the AC network.
Ohmmeters designed to measure large resistances (more than 1 MΩ) are called megaohmmeters.
Indirect methods of measuring resistance. The resistance of a resistor or other element of the electric circuit can be determined by the readings of a voltmeter and ammeter (at constant current), using Ohm's law: 
(diagrams of Fig. 3, a, b).According to the scheme in fig. 4 determine the resistance according to the readings of one voltmeter. In position 1 of the switch P a voltmeter measures the voltage of the network, and in position 2 -
voltage at the terminals of the voltmeter. In the latter case 
. From here
Indirect methods are used to measure average resistances, and large resistances are also measured with one voltmeter. The accuracy of these methods significantly depends on the ratio of the measured resistance and the internal resistance of the ammeter and voltmeter. The measurement results can be considered satisfactory in accuracy if the following conditions are met: 
(see the diagram of Fig. 3, a); 
(see the diagram of Fig. 3, b); (see diagram of Fig. 4).
Fig. 3 Fig. 4
Methods and devices of comparison. To measure small and medium resistances, the method of comparing the measured resistance with the reference .
These two resistances in the diagram of Fig. 5 are connected in series, so the current in them is the same. Its value is regulated using a resistor, so that it does not exceed the permissible current for the resistances
and 
.
From here 
. Unknown voltage drops and measure with a voltmeter or potentiometer. The measurement results are more accurate if the resistances are of the same order, and the resistance of the voltmeter is large enough so that its connection does not affect the main circuit mode.
When measuring low resistances by this method, the voltmeter is connected using potential clamps, which allow excluding the resistance of the main circuit contacts from the measurement results.
Medium and large resistances can be measured by the substitution method (Fig. 6). Ammeter A measure current by setting a switch P in position 1
, and then 2.
The voltage at the input terminals of the circuit is the same, therefore 
.
From here 
.
When measuring large resistances, the ammeter is replaced with a galvanometer with a shunt, which significantly increases the accuracy of the measurement.
To the voltmeter
Fig 5. Fig 6.
The most accurate results when measuring resistance are given by bridge circuits, which in practice are used in various versions, depending on the values \u200b\u200bof the measured resistances and the required measurement accuracy.
More often than others, you can find a device built according to the scheme of Fig. 7, which in practice is called a “single bridge”. In this case, the bridge circuit includes resistances; ; ; which form a closed loop A B C D of four branches (they are called “the shoulders of the bridge”).
A direct current source is included in one diagonal of the circuit, and a galvanometer with a two-sided scale (zero in the middle of the scale) is included in the other.
Suppose that for some resistance, the other resistances are selected so that the current in the measuring diagonal, i.e., the potentials are the same when the circuit breakers are closed and .
In this case ; /; 
;. 
.
Using these equalities, it is easy to obtain an expression for the measured resistance 
. If resistance
and identical in magnitude then. In an industrial-made device, this is a set of resistors (resistance store), compiled according to the ten-day principle. Switches are located on the top cover, with the help of which you can dial any resistance value within certain limits with an accuracy that is determined by the smallest degree of resistance change.
To expand the limits of measurement, the values \u200b\u200bof and are selected so that their ratio can also be changed using the decimal system (for example, 
;
10; 1; 0,1; 0,01;
0,001; 0,0001).
Single bridges are used mainly for measuring average resistances. When measuring low resistances, the measured element is switched on according to a special scheme or special bridges designed for this purpose are used.
Abstract on the topic
Resistance Measurement
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METHODS OF EXPERIMENTAL DETERMINATION OF RESISTANCE
Purpose of work:to study three methods of measuring resistance: the method of ammeter and voltmeter, using an ohmmeter, a compensation method.
Accessories: measured resistors, current source, voltmeter, ammeter, switch, rheostat, resistance shops, reochord, galvanometer, ohmmeter, DC bridge.
Questions Required for Admission
To do the work
1. What is resistance?
2. What is the name of the circuit element that implements the counter current?
3. What determines the resistance R?
4. What methods of measuring resistance do you know?
5. What does an ammeter measure? What are the requirements for ammeters. What are the rules for including them in a chain?
6. What does a voltmeter measure? What are the requirements for voltmeters? What are the rules for including them in a chain?
7. Method of ammeter and voltmeter.
8. How to use an ohmmeter?
9. Explain how the Wheatstone Bridge works.
10. Tell us the order of the work.
Introduction
Resistance ( R) is called a physical quantity characterizing the counteraction to the flow of current in an electrical circuit. Very often, resistance is also called an element of the chain that carries out this opposition. The term resistor is used for this element. The resistance value of the resistor or the entire circuit must be known (measured) in order to correctly calculate, for example, the current in the circuit. The resistance of the resistor depends on the material of the conductor and its size R= r l/ S .
Various external factors also influence the resistance value of a resistor: temperature, illumination, magnetic field, pressure, applied voltage, etc. Special devices that have a very pronounced dependence of resistance on the above factors are called, respectively, thermistors (or in short - thermistors), photoresistors , magnetoresistors, strain gauges, varistors, etc. Thus, by changing the resistance of the resistor, it is possible to judge such purely non-electric quantities as temperature, pressure, etc.
There are several ways to measure resistances.
1. Method of ammeter and voltmeter.
This is the simplest in terms of instruments used and therefore widely used in practice.
2. The method of direct measurement using ohmmeters.
This method does not provide high accuracy of measurements, but also does not require the assembly of a measurement circuit.
3. Bridge methods providing very high measurement accuracy (Wheatstone, Kohlrausch, Thomson bridges, etc.).
The above methods are widely used to measure resistances in the range from 1 ohm to about 10 9 ohms. When measuring resistance less than 1 Ohm, it is necessary to exclude the transition resistance of the contacts and the resistance of the connecting wires. This is done in the compensation method and in the double bridge method. When measuring very large resistances (up to 10 15 Ohms), the capacitor discharge method is used through the measured resistance.
Part 1. Ammeter and Voltmeter Method
The application of this method is based on the use of Ohm's law:
R= U/ I (1)
To calculate the unknown resistance of the resistor R x is necessary at the same time measure current Ithrough this resistor and voltage U at its ends. But since all electrical measuring devices also have resistance, their inclusion in the electric circuit will lead to a change in current and a voltage drop on the remaining elements of the circuit, including the studied resistor. Moreover, depending on how the ammeter and voltmeter are connected, either one or the other device will produce distorted data.
When using the circuit shown in Fig. 1, note that the ammeter measures no current I xflowing through a resistor R x, and the sum of the currents flowing through the resistance and voltmeter: I= I x+ I V . If the resistance of the voltmeter R v>>R x then current through the voltmeter I V we can neglect and assume that a current flows through a resistor with an unknown resistance I. Then
R X \u003d U X/I. (2)
If the ratio between R vand R x it is unknown, then you should first determine the resistance of the voltmeter. The resistance of the voltmeter is often indicated on the scale or on the housing of the device. It can be calculated from the used measuring range and the rated current. , which is usually indicated on the scale of multi-limit devices.