Methods of measurements in electrical circuits

Measurement of constant and alternating voltage

Measurement of both permanent and alternating voltage can be made directly by the voltmeters calculated for the operation of the corresponding voltage type. In cases where it is necessary to measure the voltage of more than which the voltmeter is calculated, it is necessary to include an additional resistor to include with it. Then part of the measured voltage will fall on the addition resistor, and the part is on the device. Selecting the amount of resistance of an additional resistor, one can widely expand the possibilities of measuring large stresses. The resistance of the Voltmeter R PP is known and the expansion factor is selected:



where u x is the maximum voltage at the input of the circuit to be measured; U PP - maximum measurement limits directly voltmeter.


The value of the resistance of an additional resistor can be found according to the following formula:


R ext \u003d R PR (N-1)


Usually for the convenience of sample production, the P coefficient P is selected to a multiple 2, 5 or 10.


To measure high voltage variable values, the so-called voltage transformers can be used.


They are lowering transformers, i.e., those in which the number of turns of the secondary winding W 2, to which the voltmeter is connected, less than the number of turns W 1 of the primary winding. The expansion coefficient of measurement limits n \u003d W 1 / W 2. Schemes for connecting voltmeters to measure the voltage are shown in Fig. one.



Fig. one.

Measurement of electromotive power (EMF)

Measurement E has its own characteristics. When the voltmeter is connected to the EDC source to measure it through it, the current will always pass, and since any source of EDC has an internal resistance of R HV, then the voltage at such a source and the voltmeter will measure the value smaller than EDC E.


U \u003d E - IR VN


If there are no requirements for high accuracy of EMF measurement, then to reduce the current, you can use a voltmeter with a large internal resistance, such as electronic. In this case, we can assume that the measured voltage U ~ E. More accurate methods of measurement of EDC are associated with the use of compensation schemes (Fig. 2).





Fig. 2.


In them, the voltage measured by the Voltmeter PV, removed from the variable resistor R, is compared with the voltage at the source of the EMF.


By changing the voltage at the output of an alternating resistor (potentiometer), one can achieve such a condition when the measuring device P shows the lack of current through the source of the EDC. In this case, the testimony of the voltmeter will accurately correspond to the value of the emf of the source, i.e. u \u003d E.

Measurement of current

You can measure the current directly by the ammeter included in the gap of the measured chain (Fig. 3, a).





Fig. 3.


If it is necessary to expand the limits of the ammeter measurement, it is necessary to turn on the resistor in parallel to the ammeter (Fig. 3, b), which is most often called shuntom. . Then through an ammeter will pass only part of the current, and the rest - through the shunt. Since the resistance of ammeters is usually small, then for a substantial expansion of the measurement limits, the spun resistance must be very small. There are formulas for calculating the resistance of the shunt, but usually in practice it is necessary to manually adjust its resistance, controlling the current by the reference ammeter.


For measuring large variable currents, measuring transformers of currents are often used (Fig. 3, B). They have a primary winding included in the gap of the measured chain, has the number of turns of W 1 less than the number of turns of W 2 of the secondary winding, i.e. the transformer is an increase in voltage, but under the current it is lower. The ammeter is connected to the output of the secondary winding of the current transformer. Often, the laboratory current transformers do not have a pre-primary winding in advance, and there is a wide through hole in their housing, through which the experimenter itself wins the required number of turns (Fig. 3, d). Knowing the number of turns of the secondary winding (it is usually indicated on the current transformer housing), you can select the transformation coefficient N \u003d W 1 / W 2 and determine the measured current I x according to the immeter readings of the I PR as follows:


I x \u003d i pr / n


A completely different measurement of currents in electronic circuits, which are usually soldered, manufactured on printed circuit boards; It is almost impossible to make any gap. To measure currents, in these cases, voltmeters are used (usually electronic with large internal resistance to eliminate the effect of the instrument to work the electronic circuit), connecting them to the resistors of the circuit, the values \u200b\u200bof which are either known or can be pre-measured. Taking advantage of the Ohm's law, current strength can be determined:

Measuring resistance

Often when working with electrical installations or when using electronic circuits, it is necessary to measure different resistance. The simplest way to measure resistance is to use two measuring instruments: an ammeter and a voltmeter. With their help, the voltage and current in the resistance of R, connected to the power supply, and according to the law of Ohm, find the amount of the desired resistance:



However, this method of measuring the resistance does not allow to obtain the measurement results with high accuracy, since the effects of the measurement are influenced by its own internal resistances of the ammeter and voltmeter. So, on the picture shown in Fig. 4, and the ammeter scheme measures not only the current passing through the resistance, but also the current passing through the voltmeter than the methodical measurement error is made.





Fig. four. Scheme for measuring the resistance by the Ampmeter and Voltmeter (A) method and the omeme scheme (b)

This method is usually carried out in cases where there are no special instruments - ohmmers. One of the possible omemera schemes (Fig. 4, b) is consistent. It consists of an autonomous power source E, a variable resistor R and a milliammermeter of the magnetoelectric type RA. As a power source, dry elements or batteries are usually used by 1.4 ... 4.5 V.. If the R X resistance is connected to the device outputs, the value of which must be determined, then the circuit will go, the value of which will depend on the resistance value. Since the milliammeter measures this current, then its scale can be directly separated into Omah. The scale of such an ohmmeter is reverse, i.e. zero is in the right part of the scale, since when the input resistance is zero (short circuit mode), the maximum current will flow through the ammeter. If the outer chain is broken, which corresponds to infinitely large resistance at the inlet, the arrow of the milliammeter will be located in the leftmost part of the scale, where the sign is worth it. The scale of such an ohmeter is sharply nonlinear, which to some extent it makes it difficult to read the results. The almeter variable resistor serves to install the device to zero before working with it. To do this, the conclusions of the ohmmeter of the spice and, rotating the handle of the variable resistor, achieve zero instrument readings. Since the emf of the battery is reduced by discharge, such a zero setting must be controlled periodically. With the help of such ohmmeters, you can measure resistance from several ohms to hundreds of kilometers.





Fig. five. Megometer schemes (a) and electric bridge (b)


Measurement of large resistance up to 100 MΩ is usually produced using megometers (Fig. 5, a). In its classic form, it is a combination of an autonomous power supply and a measuring instrument - a logometer. The logometer is a type of a magnetoelectric device, which, instead of one frame, there are two, connected rigidly among themselves under some dof. Also, as in the usual magnetoelectric device, the arrow of the device is connected with them and they are in a magnetic field of a permanent magnet. When passing the current through the windings of the frames, they create torque opposite signs, with the result that the position of the arrow will depend on the relationship of currents within. The chain of one of the frames includes a resistor R, and in the chain is another - resistance R x, the value of which must be determined. The use of the logometer is explained by the fact that its testimony is determined only by the ratio of currents within and does not depend on the change in the supply voltage U PIT. An inductor driven by the operator's hand is used as a stress source for a megometer, or a battery with an electronic voltage converter. Such a power system is determined by the fact that the device requires large stresses - about 500 V, since at smaller voltages currents in the windings of the device would be too small for its normal operation. The use of an autonomous power supply is dictated by the fact that the megometer is often measured by the insulation resistance of cables; At the same time, naturally, the voltage in them is disabled. In addition, it is often measured outdoors where there is no electrical network.


Measurement of low resistance (less than 1 ohms), as well as measuring other resistance in a wide range of values \u200b\u200bwith high accuracy can be carried out using electrical bridges.


The electric bridge (Fig. 5, b) is four resistances (one of them - R x is subject to measurement) included on the ring circuit. Each of the resistance forms a bridge shoulder. In one diagonal of the bridge, a constant supply voltage U PIT is supplied, and a measuring device is connected - a galvanometer R. It is a highly sensitive magnetoelectric device with zero in the middle of the scale. Its purpose is to fix the moment when the current will be absent. The devices of this type are often called zero indicators. One or two resistance in the shoulders of the bridge is made variables, and it is that the instrument's zero readings. The bridge is considered balanced. As the theory of electrical bridges shows, the balance condition is achieved with the equality of the resistance of opposite shoulders, i.e., under the condition R 1 R x \u003d R 2 R 3. Therefore, after balancing the bridge, you can, know the values \u200b\u200bof all resistances, determine the value of unknown resistance




where N \u003d R 2 / R 1 is a multiplier.


Measurement accuracy with DC bridges can be very large. The resulting resistance values \u200b\u200bcan have more than five significant digits. At the same time, the bridge does not allow you to quickly perform measurements, since the balancing process requires a certain time and operator skill.

Measurement of tanks

Determination of the capacitance of the capacitor or other capacitive devices can also be carried out in various ways. The simplest of them is a voltmeter ammeter method (Fig. 6, a).





Fig. 6.


It is largely similar to the same measurement method of resistance, with the difference only that the circuit is powered by variable sinusoidal voltage from the low or high frequency generator (or from the network). Capacitive resistance of the capacitor is determined by the following formula:




where F is the frequency of alternating voltage.


Capacitive resistance is under the law of OBA according to the instrument testimony




Measurement of small capacity of containers is more convenient to produce resonance method (Fig. 6, b). The measured capacitor with x is connected to the known inductance L, forming an oscillating circuit. A sinusoidal voltage from the generator is supplied to the circuit. Using an electronic voltmeter, the voltage on the circuit is measured. With resonance it reaches a maximum.


It is known that the resonant frequency of the contour can be expressed by the following formula:




Therefore, with the known value of inductance in the circuit and determined by maximum testimony of the voltmeter frequency of the resonance, you can find the desired value of the container with x.


The measurement of large containers (for example, electrolytic capacitors) is easiest to produce by discharge of a capacitor to a known resistance R. It is known that in a time equal to the time constant of the circuit of the capacitor discharge, its voltage decreases to it once, where e \u003d 2.71 ... - The basis of the natural logarithm. Condenser discharge chain time constant on a resistor is determined by the ratio



The measurement circuit of the container by this method (Fig. 6, B) consists of a source of constant supply voltage, known by the resistance of the resistor R, the electronic voltmeter PV, switch S, and terminals for connecting the condenser. Using the switch S, the capacitor with x is charged to the power source voltage, and after switching the capacitor to a discharge using the stopwatch, the time T is measured, after which the capacitor is discharged to the voltage U PIT / E. The capacitance of the capacitor is determined by the formula



Capacitance capacitors can also be measured using AC bridges.

Measuring inductors

The measurement of inductors is somewhat more complicated. This is due to the fact that any coil (transformer winding, etc.) has continued resistance except inductance. Therefore, in many cases, the pre-imperative resistance of the inductor inductor is measured:




It can be determined by an ammeter and voltmeter by measuring the voltage and current of the measuring instrument diagrams on alternating voltage (Fig. 7, a) z \u003d u / i. When the constant voltage is applied to the diagram (Fig. 7, b), as already considered above, you can determine the resistivity of the coil R.





Fig. 7.





In turn, inductive resistance




With a known frequency / voltage value of the supply easy to find the value of the desired inductance



With small inductance values \u200b\u200b(for example, contour coils of radio-electronic devices), you can use the resonant circuit, similar to the container determination scheme with a resonant method.


To measure inductance, alternating current bridges can also be used, special measuring instruments - koons that allow to determine not only the value of inductance, but also such a characteristic as the quality of the coil characterizing the quality of the coil in electronic circuits.

Measuring power

In electrical circuits, the power measurement is more convenient to be considered separately for the circuits of DC and AC.


At constant current, the main formulas for determining the power are as follows:




In accordance with the above formulas, the power in some resistance of the load R can be measured by three ways: using a voltmeter and ammeter (Fig. 8, a), only a voltmeter (Fig. 8, b) and only ammeter (Fig. 8, B) . In all cases, after removal of testimony from devices, mathematical calculations must be carried out to determine the power itself.





Fig. eight.


This can be avoided if you use a special device to measure the power (Fig. 8, d). As a rule, the wattmeters manufactured by the industry are manufactured on the basis of a ferrodynamic device (see Fig. 2.105). Wattmeters have two windings and, accordingly, four outputs. One of the windings is a current, through it there is a current to the load, the power consumed in which is subject to measurement, and the second - voltage winding. It connects directly to the power source.


A variable power measurement has its own characteristics. First, there are three different power:


full power, in * a,



active power, W,



reactive power, var,



In these formulas (φ is the phase shift angle between the current and voltage.


Most often interested in complete and active capacities. Knowledge of full power is necessary to calculate currents in the load, selection of the cross section of wires and fuses. The active power is important because it is precisely it characterizes the power that is transformed into warmth, light, sound, etc.


Measurement of complete power is usually produced by measuring voltage and current to a voltmeter and an ammeter and multiplying the obtained values. The active power is most often measured using ferrodynamic wattmeters, which, in addition to voltage and current, take into account the so-called coefficient of Cosφ.


When the wattmeter windings are connected to the load, as well as at a constant voltage, the wattmeter will directly perform a measurement of active power.


A variable current often has to solve the task of measuring active power in three-phase circuits. Three-phase chains can be of two types: three-wire and four-wire. In three-wire circuits, three wires are suitable for the loads, indicated by letters A, B, C. To measure the active power in such a chain, with any embodiment of the load elements to the wires, it is enough to connect only two wattmeters as shown in Fig. nine.





Fig. 9.: a - three-wire system; B - four-wire system


At the same time, it is necessary to comply with certain rules for connecting wattmeters. The conclusions of the wattmeter windings, marked on its housing as an asterisk, should be addressed towards the source of energy. Therefore, these conclusions were called generator (connected to wires that go from the generator). The total active power of such a three-phase system is like an algebraic amount of two wattmeters. In this case, an option is possible when the readings of one of the wattmeters may be negative, that is, its arrow will go left. To remove the testimony from such a wattmeter, it is necessary to change the wires of the wire suitable for any of the windings, read the measurement result, but to substitute the formula with a negative sign.


Measuring active power in four-wire circuits requires the use of three wattmeters. One of the findings of each wattmeter here connects to the fourth wire, usually called zero. The readings of all wattmeters can only be positive and the total active power consumed by a three-phase chain will be equal to the amount of capacity measured by each of the wattmeters:


РЕ \u003d p 1 + p 2 + p 3.


One of the simplest methods for measuring the amount of electricity is the measurement method using the so-called ballistic galvanometer. It is a device of a magnetoelectric system (see Fig. 2.103) with a deliberately weighted rolling part (with a large moment of inertia). If there is a short-term voltage pulse on the input of such a ballistic galvanometer, then the moving part of the device, having received a pulse torque, will start moving, and after the end of the input pulse, this movement will still continue the arrow of the device, moving along inertia, will rejects to some The values \u200b\u200bof the scale and then return to the original zero position. As a reference on such a device, it is necessary to note that the maximum deflection of the α M arrow from the zero value, which was observed during its movement on the "ballistic trajectory". The theory of such a ballistic galvanometer shows that this countdown on the maximum deflection of the arrow turns out to be a proportional number of electricity passed through the framework of such an instrument, i.e.


α Mach \u003d Q / s 6,


where with ballistical constant, depending on the design features of the galvanometer.


Measuring the amount of electricity q On the plates of a pre-charged condenser can be carried out by discharging it through a ballistic galvanometer, and at the maximum deviation of its arrows to find the desired value of the amount of electricity:


Q \u003d C 6 α Mah


When developing new alloys intended for use in electrical circuits, there is a need to determine their resistivity. Under the resistivity understand the resistance of the conductor with a cross section of 1 mm 2


and 1M length. Accordingly, such a specific resistance p is measured in the units of OM - (mm 2 / m). For its measurement, the segment of the conductor is chosen, preferably a small cross section, and measure its resistance to any of the methods discussed above. After that, the value of this resistance to the cross section of 1 mm2 and length of 1 m, which does not represent any difficulties, are obtained, and the resistance value is obtained. For greater measurement accuracy, it is desirable to take the length of the conductor as greater.


For many insulating materials, it is a certain value to determine their dielectric constant ε. One of the simplest ways to measure it is the method of indirect measurement, followed by the calculation of the magnitude of the dielectric constant. It is known that the capacitance of the simplest capacitor consisting of two identical plates of an area of \u200b\u200bS, located at a distance of δ from each other, with a dielectric filling the entire space between the plates, is determined by the formula




where ε is the dielectric constant of the material between the plates.



Fig. 10. Scheme for measuring dielectric constant insulation materials


The measurement of the dielectric constant of the material is made using a condenser (Fig. 10), between the plates of which the subject material is placed, as well as measuring the capacity of such an elementary capacitor by any of the methods described above. The numerical value of dielectric constant is determined by the formula




The development of radio electronics and installations for high-frequency effects on the materials of mechanical engineering led to the fact that almost all space is filled with electromagnetic waves.


Millions of transmitting radio stations work in the world, many of which emit significant capacities (for example, long-distance radar stations, broadcast radio stations, etc.). To evaluate electromagnetic waves, it is often necessary to determine their level. Usually, the level of electromagnetic waves is judged by the electric field strength, the magnitude of which is analytically recalculated in the power of the electromagnetic field. The electric field strength is most often measured using a frame antenna (Fig. 11), which is a flat coil wound on the frame of any dielectric. (In fig. 11 For simplicity, only one turn is depicted.)





Fig. eleven.


The orientation diagram of such an antenna shows that the maximum of the received radiation occurs from the side lying in the coil's turn plane. This allows not only to measure the electric field strength, but also determine the direction to the source of high-frequency emissions at the maximum voltage value at the outlet of the frame during its turns relative to the vertical axis. The electric field strength is determined by the magnitude of the voltage at the output of the frame according to the following formula, V / m:




where u is the voltage at the outlet of the frame, in; F - frequency of the received signal, Hz; n is the number of turns in the frame; S- frame area, m 2.


Usually, the geometric dimensions of the frame, depending on the frequency of the signal, the field strength of which is determined by certain limitations. In particular, at frequencies of more than 30 MHz, more accurate results are obtained, if instead of the frame antenna, use a half-wave dipole, which is a conductor in half the wavelength, cut in the middle. The dipole voltage is removed from the central cut part. The value of the electric field strength can be determined by the following formula:




where F-frequency, Hz; U- Voltage at the outlet of the dipole, V.


The dipole, as well as the frame, allows you to determine the direction from which the signal comes, as it has a certain orientation, which can be seen from the orientation diagram. The maximum of the received signals is determined by the perpendicular to the dipole plane. That is how television antennas are oriented towards the television tower.


The voltage at the outlet of the frame or dipole can be measured using an electronic voltmeter directly at strong signals or applying electronic amplifiers. In this case, using selective properties of amplifiers, you can determine the level of strength of the electrical field of a certain frequency. It should be noted that the signal level at the outlet of the frame and partially dipole is made up of a large number of electromagnetic fields that exist in space in the area of \u200b\u200bthe location of the receiving device from various sources (transmitters).


If you need to determine the frequency of the high-frequency signal, if it is strong, using the direct inclusion of the electronic frequency meter to exit the frame or dipole. With weak signals and the use of amplifiers, it is possible to determine the frequencies of signals that are invisible in a frame or dipole, that is, as usual along the radio receiver, you can determine the wavelength or frequency of the received station.

Current measurement.To measure the current in the Ampmeter 2 chain (Fig. 332, a) or milliammer meter in the electrical circuit, with a receiver 3 of electrical energy.

In order for the inclusion of an ammeter, there is no effect on the operation of electrical installations and it did not create large losses of energy, ammeters are performed with small internal resistance. Therefore, almost resistance can be considered equal to zero and neglect the voltage caused by it. The ammeter can be turned on in the chain only sequentially with the load. If the ammeter is connected directly to the source 1, then through the coil of the device will go very high current (the ammeter resistance is not enough) and it burns.

To expand the limits of measurement of ammeters intended for operation in the DC circuits, they are included in the chain parallel to the shunt 4 (Fig. 332, b). In this case, only part I and the measured current I are passed through the device, inversely proportional to its resistance R A. B aboutthe extended part I w shutters through the shunt. The device measures the voltage drop on the shunt, depending on the current passing through the shunt, i.e. it is used as a malelololtmeter. The scale of the device is graded in amperes. Knowing the resistance of the device R a and the shunt R w can be in the current I A A fixed by the device, to determine the measured current:

I \u003d i a (r a + r w) / r sh \u003d i and n (105)

where n \u003d i / i a \u003d (r a + r sh) / r w is the coefficient of shunting. It is usually chosen equal to or multiple 10. The spun resistance required for measuring the current I, in N times greater than the current of the device I,

R Ш \u003d R \u200b\u200ba / (n-1) (106)

Constructively shunts are either mounted in the instrument housing (shunts per currents up to 50 A), or installed outside it and connected to the device with wires. If the device is designed for permanent operation with a shunt, then its scale is graded immediately in the values \u200b\u200bof the current current, taking into account the shunt coefficient and no calculations for determining the current is not required. In the case of applying external (individual devices), the shunts indicate the rated current to which they are calculated, and the rated voltage on the clips (calibrated shunts). According to the standards, this voltage can be 45, 75, 100 and 150 mV. Shunts are selected to the instruments so that at rated voltages on the shunt clips, the arrow of the device deviated to the entire scale. Consequently, the nominal stresses of the device and the shunt should be the same. There are also individual shunts designed to work with a specific device. Shunts are divided into five accuracy classes (0.02; 0.05; 0.1; 0.2; 0.5). Class designation meets percentage permissible error.

In order to increase the cowage temperature during current passage, there was no effect on the testimony of the instrument, the shunts are made of materials with high resistivity and a small temperature coefficient (Konstanta, Manganin, Nickelin, etc.). To reduce the effect of temperature on the ammeter readings, in sequentially with the coil of the device, in some cases, an additional resistor from constant-tana or other similar material is included.

Voltage measurement. To measure the voltage U, acting between any two points of the electrical circuit, Voltmeter 2 (Fig. 332, B) attach to these points, i.e., parallel to the source 1 of electrical energy or receiver 3.

In order for the inclusion of the voltmeter, there was no effect on the operation of electrical installations and it did not create large losses of energy, voltmeters are performed with greater resistance. Therefore, it is practically possible to neglect the current passing on the voltmeter.

To expand the limits of the voltmeter measurement, the addition resistor 4 (R D) is sequentially with the winding of the device (R / Fig. 332, d). At the same time, only a part of the U V of the measured voltage U is accounting for the device, proportional to the resistance of the R V instrument.

Knowing the resistance of the added resistor and the voltmeter, by the value of the voltage U V fixed by the voltmeter, determine the voltage acting in the chain:

U \u003d (R V.+ R. D.) / R. V. * U. V. \u003d Nu. V. (107)

The value of N \u003d U / U V \u003d (R V + R D) / R V shows how many times the measured voltage U is more voltage U v, which occurs on the device, i.e., how many times the limit of the voltage measurement limit is increasing when an additional resistor.

The resistance of the added resistor necessary to measure the voltage U, in the variety of the larger voltage of the UV instrument, is determined by the formula R d \u003d (n - 1) R v.

The added resistor can be integrated into the instrument and simultaneously used to reduce the effect of the ambient temperature on the instrument reading. For this purpose, the resistor is made of a material having a small temperature coefficient, and its resistance significantly exceeds the coil resistance, as a result of which the overall resistance of the device becomes almost independent of temperature change. According to accuracy, additional resistors are divided into the same accuracy classes as shunts.

Voltage divisors.To expand voltmeter measurement limits, voltage dividers are also used. They allow you to reduce the voltage to be measured to a value corresponding to the nominal voltage voltmeter (limit voltage on its scale). The ratio of the input voltage of the divider U 1 to the output U 2 (Fig. 333, a) is called fission coefficient. At idling U 1 / U 2 \u003d (R 1 + R 2) / R2 \u003d 1 + R 1 / R 2. In voltage divisors, this ratio can be selected equal to 10, 100, 500, etc., depending on which

the outputs of the divider is connected to the voltmeter (Fig. 333, b). The voltage divider makes a small error in the measurement only if the resistance of the voltmeter R v is sufficiently large (current passing through the divider, small), and the resistance of the source to which the divider is connected, is not enough.

Measuring transformers.To enable electrical measuring devices in the AC circuit, measuring transformers are used to ensure the safety of the service personnel when performing electrical measurements in high voltage circuits. The inclusion of electrical measuring devices into these chains without such transformers is prohibited by safety regulations. In addition, measuring transformers expand the limits of measuring instruments, i.e., it allows you to measure large currents and voltages using simple devices calculated to measure small currents and stresses.

Measuring transformers are divided into voltage transformers and current transformers. Voltage transformer 1 (Fig. 334, a) is used to connect voltmeters and other devices that should react to voltage. It is performed as the usual two-winding lowering transformer: the primary winding is connected to two points, between which the voltage is required, and the secondary to the voltmeter 2.

In the diagrams, the voltage transformer is depicted as an ordinary transformer (in Fig. 334, and is shown in the circle).

Since the resistance of the voltmeter winding connected to the voltage transformer is large, the transformer works practically in idling mode, and can be considered with a sufficient degree of accuracy that the voltages U 1 and U 2 on the primary and secondary windings will be directly proportional to the number of turns? 1 and? 2 of both transformer windings, i.e.

U 1 / u 2 \u003d? one /? 2 \u003d N. (108)

Thus, pick up the appropriate number of turns? 1 and? 2 transformer windings, high voltages can be measured, submitting small voltages to the electrical measuring device.

The U 1 voltage can be determined by multiplying the measured secondary voltage U 2 to the transformation coefficient of the transformer N.

Voltmeters intended for permanent operation with voltage transformers are graded at the factory based on the transformation coefficient, and the values \u200b\u200bof the measured voltage can be directly counted on the instrument scale.

To prevent the danger of damage to the service personnel by electric shock in case of damage to the transformer isolation, one element of its secondary winding and steel transformer casing must be grounded.

Current transformer 3 (Fig. 334, b) serves to connect ammeters and other devices that should react to the variable current flowing through the chain. It is performed in the form

conventional two-winding increases transformer; The primary winding is turned on in series in the measured current circuit, an ammeter 4 is connected to the secondary winding.

The circuit designation of the measuring transformers of the current is shown in Fig. 334, B in a circle.

Since the resistance of the ammeter winding connected to the current transformer is usually small, the transformer practically operates in a short circuit mode, and with a sufficient degree of accuracy, we can assume that currents I 1 and I 2 passing along its windings will be inversely proportional to the number of turns? 1 and? 2 of these windings, i.e.

I 1 / i 2 \u003d? one /? 2 \u003d N. (109)

Consequently, choose the number of turns appropriately? 1 and? 2 transformer windings, you can measure large currents I 1, passing through an electrical measuring device Small currents I 2. Current I 1 may be determined by multiplying the measured secondary current I 2 by n.

Ampmeters intended for permanent operation together with current transformers are graded at the factory based on the transformation coefficient, and the values \u200b\u200bof the measured current i 1 can be directly counted on the instrument scale.

To prevent the danger of damage to the service personnel in the case of damage to the insulation of the transformer, one of the clips of the secondary winding and the transformer casing grounds.

On er p. p. Using the so-called current pass transformers (Fig. 335). In such a transformer, the magnetic pipe 3 and the secondary winding 2 are mounted on the passage insulator 4, which is serviced to input high voltage in the body, and the role of the primary winding of the transformer performs a copper rod 1 passing inside the insulator.

Conditions for current transformers are different from ordinary. For example, the opening of the secondary winding of the current transformer when the primary winding is turned on is unacceptable, as this will cause a significant increase in the magnetic flux and, as a result, the temperature of the core and the transformer winding, that is, the output of it. In addition, a large event may be induced in an open secondary winding of the transformer. C, dangerous for the personnel of measurement.

When the instruments are turned on by means of measuring transformers, there are errors of two types: error in the transformation ratio and the angular error (with a change in voltage or current of the ratio 1 / U 2 and I 1 / i 2, the phase shift angle between primary and secondary voltages and currents deviates 180 °). These errors increase with the load of the transformer above the nominal. The angular error affects the results of the measurement

relations of which depend on the phase shift angle between voltage and current (for example, wattmeters, electric energy meters, etc.). Depending on the errors allowed, the measuring transformers are divided into accuracy classes. Accuracy class (0.2; 0.5; 1, etc.) corresponds to the greatest permanent error in the transformation ratio as a percentage of its nominal value.

Creative abilities are an alloy of many qualities. The question of the components of the creative potential of a person remains still open, although at the moment there are several hypotheses relating to this problem.

Creative abilities are divided into three main groups:

1) abilities associated with motivation (interests and inclinations);

2) abilities associated with temperament (emotionality);

3) mental abilities.

R. Sternberg (58) indicates that the process of creativity is possible in the presence of three special intellectual abilities:

Synthetic ability to see problems in a new light and avoid the usual way of thinking;

Analytical ability to estimate whether the ideas of further development cost;

Practically contextual ability to convince others in the values \u200b\u200bof the idea.

If an individual is too developed analytical ability to detriment to two others, he is a brilliant criticism, but not the Creator. The synthetic ability, not supported by analytical practices, generates a lot of new ideas, but not substantiated research and useless. The practical ability without two others can lead to brightly presented, but "poor-quality" ideas. For creativity, the independence of thinking from stereotypes and external influence is necessary.

Creativity, from the point of view of Sternberg, involves the ability to go for reasonable risk, willingness to overcome obstacles, internal motivation, tolerance (tolerance) to uncertainty, willingness to confront the opinion of others.

Famous domestic researcher of the problem of creativity A.N. Onions (25), relying on the biography of outstanding scientists, inventors, artists and musicians allocate the following creative abilities:

1) the ability to see the problem where others do not see it;

2) the ability to minimize mental operations, replacing several concepts with one and using more and more sensitive symbols;

3) the ability to apply the skills acquired when solving one task to solve another;

4) the ability to perceive validity entirely, without frauding it into parts;

5) the ability to easily associate remote concepts;

6) memory ability to issue the necessary information at the right moment;

7) thinking flexibility;

8) the ability to choose one of the alternatives to solve the problem before it is verified;

9) the ability to include newly perceived information in the knowledge systems available;

10) the ability to see things as they are, to highlight the observed from what is brought by interpretation;

11) Ease of generation of ideas;

12) creative imagination;

13) the ability to refine the details, to the improvement of the initial plan.

Candidates of psychological sciences V.T. Kudryavtsev and V. Sinelnikov (20), based on a wide historical and cultural material (the history of philosophy, social sciences, art, individual spheres of practice) was allocated the following universal creative abilities in the process of human history:

1) Imagination realism - a shape of some significant, general trend or patterns of the development of a holistic object, before a person has a clear concept about it and can enter it into a system of strict logical categories;

2) the ability to see the whole before parts;

3) the overall-converter nature of creative solutions. The ability to solve the problem is not easy to choose, but to independently create an alternative;

4) Experimentation - the ability to consciously and purposefully create conditions in which the items most convex detect their hidden in conventional situations, as well as the ability to trace and analyze the features of "behavior" of objects under these conditions.

Teachers-scientists and practices GS Altshulller, V.M. Tsurikov, V.V. Mitrofanov, M.S. Gafitulin, M.S. Rubin, M.N. Suckterman (14; 16; 17; 20; 30; 48; 53; 54) engaged in the development of programs and methods of creative education on the basis of TRIZ (the theory of solutions of inventive tasks) and Ariz (algorithm for the solutions of inventive tasks), believe that one of the components The creative potential of a person makes up the following abilities:

1) the ability to risk;

2) divergent thinking;

3) flexibility in thinking and action;

4) the speed of thinking;

5) the ability to express original ideas and invent new;

6) rich imagination;

7) perception of the ambiguity of things and phenomena;

8) high aesthetic values;

9) Developed intuition.

IN AND. Andreev (3) proposed a structural model that allows you to highlight the following integrated components (blocks) of the creative abilities of the personality:

1. Motivational and creative activity and identity orientation;

2. Intellectual and logical abilities of the individual;

3. Intellectual-heuristic, intuitive personality abilities;

4. The worldview properties of the individual, promoting creative activities;

5. Personality abilities to self-government in educational and creative activities;

6. Communicative and creative personality abilities;

7. The effectiveness of creative activities.

In our opinion, the methods of these scientists are more suitable for children of senior school age. Therefore, we consider what the abilities allocated other scientists.

At ld Stolyarenko (43) The following abilities characterizing creativity are allocated: plasticity (the ability to produce multiple solutions), mobility (a quick transition from one aspect of the problem to another, not limited to one single point of view), originality (generating unexpected, non-bank, nontrivial solutions).

The famous American psychologist D. Gilford (28) allocated 16 such intelligent abilities. Among them: Thought fluency (the number of ideas arising per unit time), the flexibility of thought (the ability to switch from one idea to another), originality (the ability to generate new non-standard ideas), curiosity (sensitivity to problems in the surrounding world), the ability to develop hypothesis , fantasticity (complete convergence of response from reality in the presence of a logical connection between the incentive and reaction), completeness (the ability to improve its "product" or give it a finished look).

Further development, the problem was obtained in the works of P. Trenza (58). Its approach is based on the fact that the abilities caused by creativity include: ease, which is estimated as a speed of completion of the task, the flexibility assessed as the number of switching from one class of objects to another, and originality, assessed as the minimum frequency of the occurrence of this response in a homogeneous group . In this approach, the criterion of creativity is not the quality of the result, but the characteristics and processes that activate creative productivity: fluency, flexibility, originality and care of tasks. According to Torrens, the maximum level of creative achievements is possible with a combination of triad factors: creative abilities, creative skills and creative motivation.

In psychology, it is customary to associate the ability to creative activity, primarily with the peculiarities of thinking. Creative thinking characterize associativity, dialecticity and systemicity.

Associativity is the ability to see the connection and similar features in subjects and phenomena, at first glance not comparable. Formulate contradictions and find a way to resolve them allows dialectyness of thinking. Another quality forming creative thinking is a systematic, i.e. the ability to see an item or phenomenon as a holistic system, perceive any subject, any problem comprehensively, in the entire diversity of connections; The ability to see the unity of relationships in phenomena and the laws of development. The development of these qualities makes thinking flexible, original and productive.

A number of scientists (15; 27; 37; 55; 57; 58) is based on the relationship of creative thinking with associations. S. Mednist notes that thinking is considered the more creative, the more distant are the ideas between which the associations arise, they must in turn meet the requirements of the task and characterize the usefulness. In the ways of creative solutions based on associations, are intuitive, finding similarities between individual elements (ideas), and mediating some ideas of others.

Creativity covers some combination of thought and personal qualities that defines the ability to work. One of the components of creativity is the ability of the personality. Many of the researchers stand out in creative behavior motivation, values, personal features of the individual. Under the influence of motivation, creativity indicators are increasing.

KM Gurevich, E.M. Borisov (1) notes that there are points of view on the motivation of creativity as a striving for risk, to check the limit of their capabilities and how to attempt to best realize themselves, to maximize their capabilities, to fulfill new, unusual activities, apply new ways of activity.

A.M. Matyushkin (30) believes that the achievement motivation is necessary for creativity. According to Ya.A. Ponomarev (36), the basis of creativity is the global irrational motivation of the alienation of a person from the world. Features of the motivation of a creative personality seeing them in satisfaction not so much by the achievement of the result of creativity, but in the process itself, the desire for creative activity.

There is also a special approach that binds the level of intelligence and the level of creative abilities on a completely different basis. According to this approach, presented by MA Vollah and N.A. Kogan (28), the personal features of a schoolchildren depend on various combination of intelligence levels and creativity.

We in our study adhered to opinions that for optimal manifestation of creative abilities, cognitive and motivational spheres of individuals should interact as an organic integer.

It is impossible not to take into account the social environment in which the person is formed. Moreover, it must be actively forming. Therefore, the development of creative abilities depends on what opportunities will provide the environment to implement that potential, which is in varying degrees of each person. The whole environment should contribute to the development of creative abilities. V.N. Druzhinin notes that "creativity formation is possible only in a specially organized medium" (17,231). For example, M. Will and N. Kogan (28) speak out against rigid time limits, the atmosphere of competitiveness and the only criterion for the correctness of the response. In their opinion, for the manifestation of creativity, we need a relaxed, free situation, ordinary life situations, when the subject may have free access to additional information on the subject of the task.

D.B. Epiphany (7.64) allocated a unit of measurement of creative abilities called "Intellectual Initiative". She considers it as synthesis of mental abilities and the motivational structure of the personality, manifested in "the continuation of mental activity outside the required, outside the solution of the problem, which is placed in front of a person."

Analysis of psychological and pedagogical literature on the development of creative abilities showed that the unified approach to the assessment of creative abilities has not yet been developed. Despite the difference in approaches to their definition, the researchers unanimously identify the creative imagination and the quality of creative thinking (the flexibility of thought, originality, curiosity, etc.) as the required components of creative abilities. As a criterion, it is the creation of a new product, as well as a person's realization of his own individuality, while not necessarily the creation of some kind of product, etc. Almost in all approaches emphasizes such an important distinguishing feature of creativity, as the ability to go beyond the specified situation, the ability to formulate Own goal.

Based on the analysis of various approaches to the problem of developing creative abilities, we allocate the main directions in the development of the creative abilities of younger students: the use of methods of organization and motivation of creative activity, the development of imagination and the development of the qualities of thinking.

Creative abilities are an alloy of many qualities. And the question of the components of the creative potential of a person remains still open, although there are currently several hypotheses relating to this problem. Many psychologists associate the ability to creative activities, primarily with the peculiarities of thinking. In particular, the famous American psychologist Gilford, who was engaged in the problems of human intelligence, found that creative personalities are typical of the so-called divergent thinking. People who have such a type of thinking, when solving any problem, do not concentrate all their efforts to find the only correct solution, but begin to look for solutions for all possible areas in order to consider as much options as possible. Such people tend to form new combinations of elements that most people know and use only in a certain way, or form connections between two elements that do not have anything in first glance. The divergent method of thinking underlies creative thinking, which is characterized by the following main features:

  • 1. The speed is the ability to express the maximum number of ideas (in this case it is important not their quality, but their number).
  • 2. Flexibility - the ability to express a wide variety of ideas.
  • 3. Originality - the ability to generate new non-standard ideas (this can manifest itself in responses, solutions that are inconsistent with generally accepted).
  • 4. Finished - the ability to improve your "product" or to give it a finished look.

Famous domestic researchers of the problem of creativity A.N. Onions, relying on the biography of outstanding scientists, inventors, artists and musicians allocate the following creative abilities.

  • 1. The ability to see the problem where others do not see it.
  • 2. The ability to minimize mental operations, replacing several concepts with one and using more and more sensitive symbols.
  • 3. Ability to apply the skills acquired when solving one task to solve another.
  • 4. The ability to perceive validity entirely, without frauding it into parts.
  • 5. The ability to easily associate remote concepts.
  • 6. Memory ability to issue the desired information at the right moment.
  • 7. Flexibility of thinking.
  • 8. The ability to choose one of the alternatives to solve the problem before it is verified.
  • 9. The ability to include newly perceived information in the already available knowledge systems.
  • 10. The ability to see things as they are, to allocate the observed from what is introduced by interpretation.
  • 11. Ease of generation of ideas.
  • 12. Creative imagination.
  • 13. The ability to refine the details, to the improvement of the initial design.

Candidates of psychological sciences V.T. Kudryavtsev and V. Sinelnikov, based on a broad historical and cultural material (the history of philosophy, social sciences, art, individual practitioners) allocated the following universal creative abilities in the process of human history.

  • 1. The release of imagination is a figurative grasp of some substantial, general trend or patterns of development of the braid object, before a person has a clear concept about it and can enter it into a system of strict logical categories.
  • 2. The ability to see the whole before parts.
  • 3. Supported - the conversion character of creative solutions. The ability to solve the problem is not easy to choose from the alternatives imposed from outside, but to create an alternative.
  • 4. Experimentation - the ability to consciously and purposefully create conditions in which the items most convex detect their hidden in conventional situations, as well as the ability to trace and analyze the characteristics of the "behavior" of objects under these conditions.

Scientists and teachers involved in the development of programs and methods of creative education on the basis of TRIZ (the theory of solutions of inventive tasks) and Ariz (the algorithm for solving inventive tasks) believe that one of the components of the human creative potential is the following abilities.

  • 1. Ability to risk.
  • 2. Divergent thinking.
  • 3. Flexibility in thinking and action.
  • 4. The speed of thinking.
  • 5. The ability to express original ideas and invent new ones.
  • 6. Rich imagination.
  • 7. Perception of the ambiguity of things and phenomena.
  • 8. High aesthetic values.
  • 9. Developed intuition.

Analyzing the above points of view on the issue of components of creative abilities It can be concluded that despite the difference in approaches to their definition, the researchers unanimously identify creative imagination and the quality of creative thinking as a mandatory components of creative abilities.

Speaking about the formation of abilities, it is necessary to dwell on the question of when, from what age the creative abilities of children should be developed. Psychologists call different deadlines from one and a half to five years. There is also a hypothesis that developing creative abilities is necessary from early age. This hypothesis finds confirmation in physiology.

The fact is that the brain of the child is particularly growing and "rushing" in the first years of life. This is a ripening, i.e. The increase in the number of brain cells and the anatomical bonds between them depends on both the diversity and the intensity of the work of already existing structures and on how stimulated by the education environment new ones. This period of "ripening" is the time of the highest sensitivity and plasticity to external conditions, the time of the highest and most widest possible development opportunities. This is the most favorable period to start the development of the whole manifold of human abilities. But the child is beginning to develop only those abilities, for the development of which there are incentives and conditions for the "moment" of this ripening. The more favorable conditions, the closer they are optimal, the more successful development begins. If the maturation and start of operation (development) coincide in time, they are synchronously, and the conditions are favorable, then development is easy - with the highest possible accelerations. Development can achieve the greatest height, and the child can become capable, talented and ingenious.

However, the possibility of developing abilities, reaching a maximum in the "moment" of ripening, do not remain unchanged. If these possibilities are not used, that is, the corresponding abilities do not develop, do not function if the child does not work as necessary activities, then these opportunities begin to be lost, degraded and the faster than weaker functioning. It is a focus of development opportunities - an irreversible process. Boris Pavlovich Nikitin, for many years engaged in the problem of the development of the creative abilities of children called this phenomenon of Nouverts (irreversible extinction of opportunities for the effective development of abilities). Nikitin believes that Nouveras particularly negatively affects the development of creative abilities. The rupture in time between the moment of ripening the structures, the necessary formation of creativity and the beginning of the focused development of these abilities leads to a serious difficulty of their development, slows down its pace and leads to a decrease in the final level of development of creative abilities. According to Nikitin, it was the irreversibility of the process of degradation of development opportunities that caused the opinion of the innateness of creative abilities, as usual no one suspects that the possibilities of the effective development of creative abilities were missed in preschool age. And a small number of people in society with high creative potential is explained by the fact that in childhood only very few were in the conditions conducive to the development of their creative abilities.

From a psychological point of view, preschool childhood is a favorable period for the development of creative abilities because at this age children are extremely inquisitive, they have a lot of desire to know the world around.

And parents encouraging curiosity, informing children knowledge, involving them in various activities, contribute to the expansion of child experience. And the accumulation of experience and knowledge is the necessary prerequisite for future creative activities. In addition, thinking of preschoolers is more free than thinking more adult children. It is not yet crushed by dogma and stereotypes, it is more independent. And this quality is necessary to develop in every way. Pre-school childhood is also a sensitive period for the development of creative imagination.