Power- a physical quantity equal to the ratio of work done to a certain period of time.

There is a concept of average power over a certain period of time Δt. Average power is calculated using this formula: N = ΔA / Δt, instantaneous power according to the following formula: N=dA/dt. These formulas have a rather generalized form, since the concept of power is present in several branches of physics - mechanics and electrophysics. Although the basic principles for calculating power remain approximately the same as in the general formula.

Power is measured in watts. Watt is a unit of power equal to joule divided by second. In addition to the watt, there are other units for measuring power: horsepower, erg per second, mass-force-meter per second.

• • One metric horsepower equal to 735 watts, English - 745 watts.
  • Erg- a very small unit of measurement, one erg is equal to ten to the minus seventh power of watts.
  • One mass-force-meter per second equal to 9.81 watts.

Measuring instruments

Measuring instruments for measuring power are mainly used in electrophysics, since in mechanics, knowing a certain set of parameters (speed and force), you can independently calculate the power. But in the same way, in electrophysics you can calculate power using parameters, but in fact, in everyday life we ​​simply do not use measuring instruments to record mechanical power. Since most often these parameters for certain mechanisms are designated as such. As for electronics, the main device is a wattmeter, used in everyday life in a conventional electric meter.

Wattmeters can be divided into several types according to frequencies:

• • Low frequency
  • Radio frequency
  • Optical

Wattmeters can be either analog or digital. Low-frequency (LF) ones contain two inductance coils, are both digital and analogue, and are used in industry and everyday life as part of conventional electricity meters. Radio frequency wattmeters are divided into two groups: absorbed power and transmitted power. The difference lies in the way the wattmeter is connected to the network; those passing through are connected in parallel to the network, which is absorbed at the end of the network as an additional load. Optical wattmeters are used to determine the power of light fluxes and laser beams. They are mainly used in various industries and laboratories.

Mechanical power

Power in mechanics directly depends on the force and the work that this force performs. Work is a quantity that characterizes the force applied to a body, under the influence of which the body travels a certain distance. Power is calculated by the scalar product of the velocity vector and the force vector: P = F * v = F * v * cos a (force multiplied by the velocity vector and the angle between the force and velocity vector (cosine alpha)).

You can also calculate the power of the rotational movement of the body. P=M* w= π * M * n / 30. Power is equal to (M) torque multiplied by (w) angular velocity or pi (n) multiplied by torque (M) and (n) rotational speed divided by 30.

Power in electrophysics

In electrophysics, power characterizes the rate of transmission or conversion of electricity. There are the following types of power:

• • Instantaneous electrical power. Since power is the work done in certain time, and the charge moves along a certain section of the conductor, we have the formula: P(a-b) = A / Δt. A-B characterizes the area through which the charge passes. A is the work of the charge or charges, Δt is the time it takes the charge or charges to travel through the section (A-B). Using the same formula, other power values ​​are calculated for different situations when you need to measure instantaneous power on a section of conductor.

• • You can also calculate the power of a constant flow: P = I * U = I^2 * R = U^2 / R.

• • AC power cannot be calculated using the formula direct current. There are three types of power in alternating current:
    • Active power(P), which is equal to P = U * I * cos f . Where U and I are the current current parameters, and f (phi) is the shift angle between the phases. This formula is given as an example for single-phase sinusoidal current.
    • Reactive power (Q) characterizes the loads created in devices by oscillations of electrical single-phase sinusoidal alternating current. Q = U * I * sin f . The unit of measurement is reactive volt-ampere (var).
    • Apparent power (S) is equal to the root of the squares of active and reactive power. It is measured in volt-amperes.
    • Inactive power is a characteristic of passive power present in circuits with alternating sinusoidal current. Equal to the square root of the sum of the squares of reactive power and harmonic power. In the absence of higher harmonic power, it is equal to the reactive power module.

What is strength and power? How this indicator is measured, what instruments are used, and how these are used in practice, we will consider later in the article.

Force

In the world, all bodies of physical nature begin to move due to force. When exposed to it, with the same or opposite direction of movement of the body, work is done. Thus, some force acts on the body.

Thus, a bicycle moves off thanks to the strength of a person’s legs, and the train is affected by the traction force of an electric locomotive. A similar impact occurs with any movement. The work of a force is the quantity in which the modulus of the force, the modulus of displacement of the point of its application, and the cosine of the angle between the vectors of these indicators are multiplied. The formula in this case looks like this:

A = F s cos (F, s)

If the angle between these vectors is not zero, then work is always done. Moreover, it can have both positive and negative meaning. There will be no force acting on the body at an angle of 90°.

Consider, for example, a cart pulled by the muscular power of a horse. In other words, the work is done by the traction force in the direction of movement of the cart. But when directed downwards or perpendicularly, it does no work (by the way, horsepower is what engine power is measured in).

The work done by a force is a scalar quantity and is measured in joules. She may be:

• resultant (under the influence of several forces);
• non-constant (then the calculation is performed with an integral).

Power

How is this quantity measured? First, let's look at what it is. It is clear that the body begins to move due to the force exerted. However, in practice, in addition to this, it is necessary to know exactly how it is accomplished.

The work may be completed within different time frames. For example, the same action can be performed by a small motor or a large electric motor. The only question is how long it will take to produce it. The quantity responsible for this task is power. How it is measured becomes clear from the definition - this is the ratio of work for a specific time to its value:

By logical steps we arrive at the following formula:

that is, the product of force vectors and speed of movement is power. How is it measured? According to the international SI system, the unit of measurement for this quantity is 1 Watt.

Watt and other power units

Watt means power, where one joule of work is done in one second. The last unit was named after the Englishman J. Watt, who invented and built the first steam engine. But he used another quantity - horsepower, which is still used today. approximately equal to 735.5 watts.

Thus, in addition to Watts, power is measured in metric horsepower. And for a very small value, Erg is also used, equal to ten to the minus seventh power of Watt. It is also possible to measure in one unit of mass/force/meters per second, which is equal to 9.81 Watts.

Engine power

This value is one of the most important in any motor, which comes in a wide range of power. For example, an electric razor has hundredths of a kilowatt, and a spaceship rocket has millions.

Different loads require different power to maintain a certain speed. For example, a car will become heavier if more cargo is placed in it. Then the road will increase. Therefore, to maintain the same speed as in an unloaded state, more power will be required. Accordingly, the engine will consume more fuel. All drivers know this fact.

But at high speeds, the inertia of the machine is also important, which is directly proportional to its mass. Experienced drivers who are aware of this fact find the best combination of fuel and speed when driving so that less gasoline is consumed.

Current power

How is current power measured? In the same SI unit. It can be measured by direct or indirect methods.

The first method is implemented using a wattmeter, which consumes significant energy and heavily loads the current source. It can be used to measure ten watts or more. The indirect method is used when it is necessary to measure small values. The instruments for this are an ammeter and a voltmeter connected to the consumer. The formula in this case will look like this:

With a known load resistance, we measure the current flowing through it and find the power as follows:

P = I 2 ∙ R n.

Using the formula P = I 2 /R n, the current power can also be calculated.

How it is measured in a three-phase current network is also no secret. For this, an already familiar device is used - a wattmeter. Moreover, it is possible to solve the problem of what is measured using one, two or even three instruments. For example, a four-wire installation would require three devices. And for a three-wire with an asymmetric load - two.

The concept of power (M) is associated with the productivity of a particular mechanism, machine or engine. M can be defined as the amount of work done per unit of time. That is, M is equal to the ratio of work to the time spent on its completion. In the generally accepted international system of units (SI), the common unit of measurement M is the watt. Along with this, horsepower (hp) still remains an alternative indicator for M. In many countries around the world, it is customary to measure the M of internal combustion engines in hp, and the M of electric motors in watts.

Varieties of EIM

As the scientific and technological progress A large number of different units of power measurement (PMU) appeared. Among them, the ones in demand today are W, kgsm/s, erg/s and hp. In order to avoid confusion when moving from one measurement system to another, the following EIM table was compiled, in which real power is measured.

Tables of relationships between EIM

EIM	W	kgsm/s	erg/s	hp
1 W	1	0,102	10^7	1.36 x 10^-3
1 kiloW	10^3	102	10^10	1,36
1 megaW	10^6	102 x 10^3	10^13	1.36 x 10^3
1 kgcm per second	9,81	1	9.81 x 10^7	1.36 x 10^-2
1 erg per second	10^-7	1.02 x 10^-8	1	1.36 x 10^-10
1 hp	735,5	75	7.355 x 10^9	1

Measurement of M in mechanics

All bodies in the real world are set in motion by a force applied to them. The effect on the body of one or more vectors is called mechanical work(R). For example, the traction force of a car sets it in motion. This thereby accomplishes mechanical R.

From a scientific point of view, P is a physical quantity “A”, determined by the product of the magnitude of the force “F”, the distance of movement of the body “S” and the cosine of the angle between the vectors of these two quantities.

The work formula looks like this:

A = F x S x cos (F, S).

M "N" in this case will be determined by the ratio of the amount of work to the time period "t" during which the forces acted on the body. Therefore, the formula defining M will be:

Mechanical M engine

The physical quantity M in mechanics characterizes the capabilities of various engines. In cars, the M of the engine is determined by the volume of the liquid fuel combustion chambers. M of a motor is work (the amount of energy generated) per unit of time. During its operation, the engine converts one type of energy into another potential. In this case, the motor converts thermal energy from fuel combustion into kinetic energy of rotational motion.

It is important to know! The main indicator of the M engine is the maximum torque.

It is the torque that creates the traction force of the motor. The higher this indicator, the greater the M of the unit.

In our country, M power units are calculated in horsepower. All over the world there is a trend of calculating M in W. Now it's already power characteristic indicated in the documentation in two dimensions at once in hp. and kilowatts. In what unit to measure M is determined by the manufacturer of power electrical and mechanical installations.

M electricity

Electrical M is characterized by the rate of conversion of electrical energy into mechanical, thermal or light energy. According to the International SI System, a watt is an EIM in which the total power of electricity is measured.

General information. Power measurement is very common in the practice of electrical and electronic measurements on direct and alternating current throughout the entire mastered frequency range - down to millimeter waves and shorter waves.

Of particular importance is the measurement of power in the microwave range, since power is the only characteristic of the electrical mode of the corresponding path, when measuring current and voltage in the microwave is practically impossible due to the large error.

Power is measured by wattmeters ranging from fractions of microwatts to units - tens of gigawatts.

Depending on the measured powers, devices are divided into low wattmeters (<10 мВт), средней (10 мВт... 10 Вт) и большой (>10 W) power.

The basic unit of power is the watt (W). Multiples and submultiples are also used:

Gigawatt (1 GW = W);

Megawatt (1 MW = W);

Kilowatt (1 kW = W);

Milliwatt (1 mW = W);

Microwatt (1 µW = W).

International designations of power units are given in Appendix 1.

Power can be measured not only in absolute, but also in relative units - decibels:

To measure power, indirect and direct methods are used. In the catalog classification, electronic wattmeters are designated as follows: Ml - exemplary, M2 - transmitted power, M3 - absorbed power, M4 - bridges for power meters, M5 - converters (heads) of wattmeters.

Electromechanical wattmeters are classified according to the power units indicated on their scales and front panels: W - wattmeters: kW - kilowattmeters; mW - milliwatt meters; W - microwattmeters.

Power measurement in DC and AC circuits low frequencies. To measure power in DC and AC circuits of industrial frequencies, electromechanical wattmeters of electrodynamic and ferrodynamic systems are most often used.

In laboratory practice, wattmeters of the electrodynamic system of the 3rd, 4th and 5th accuracy classes (0.1; 0.2; 0.5) are mainly used. In industry, for technical measurements, wattmeters of the ferrodynamic system of the 6th, 7th and 8th accuracy classes (1.0, 1.5 and 2.5) are used.

Single-limit wattmeter scales are graduated in the values ​​of the measured quantity (watts, kilowatts, etc.). Multi-range wattmeters have a non-graduated scale. Before using such wattmeters, with the known rated current value and nominal voltage value of the selected limit, as well as the number of scale divisions of the wattmeter used, it is necessary to determine its division value With(device constant) at according to the formula

Knowing the division value for a given wattmeter in the selected limit, it is easy to calculate the value of the measured power. The measured power value will be

Where P - counting the number of divisions on the instrument scale.

Electrodynamic system wattmeters are used to measure power in DC and AC circuits with a frequency of up to several kilohertz.

Ferrodynamic system wattmeters are used to measure power in DC and AC circuits of industrial frequencies.

On direct and alternating current of low, medium and high frequencies, indirect methods of measuring power are used, i.e. voltages, currents and phase shifts are determined by subsequent power calculations. The active power of two-phase alternating current in a circuit with a complex load is determined by the formula

Where U, I- RMS voltage and current;

Phase shift between current and voltage.

In a chain with pure active load , when=0,=1, AC power is

, (3.33)

power pulse current:

In practice, the average power over the pulse repetition period is usually measured:

(3-35)

Where q- duty cycle: q =;

Pulse duration;

Pulse shape factor 1;

Pulse repetition period.

High frequency power measurement methods. There are two typical methods for measuring power (depending on its type: absorbed or transmitted).

Absorbed power is the power consumed by the load. In this case, the load is replaced by its equivalent, and the measured power is completely dissipated on this load equivalent, and then the power of the thermal process is measured. The load of the wattmeter completely absorbs the power, therefore such devices are called absorbed power wattmeters (Fig. 3.16, A). Since the load must completely absorb the measured power, the device can only be used when the consumer is disconnected. The measurement error will be smaller, the more fully the matching of the input impedance of the wattmeter with the output impedance of the source under study or the characteristic impedance of the transmission line is ensured.

Rice. 3.16. Methods for measuring absorbed (about) and transmitted power with wattmeters (b)

Passing power- this is the power transmitted by the generator to the real load. The devices that measure it are called transmitted power wattmeters. Such wattmeters consume a small fraction of the source power, and the main part of it is allocated in the actual payload (Fig. 3.16, b).

Transmitted power wattmeters include devices using Hall transducers, with an absorbing wall, and other devices.

In the high and ultra-high frequency range, indirect power measurement methods are not used, since the current strength and voltage drop are different in different sections of the transmission line; In addition, connecting a measuring device changes the operating mode of the measuring circuit. Therefore, other methods are used in microwaves: 1 for example, converting electromagnetic energy into thermal energy (calorimetric method), changing the resistance of a resistor (thermistor method).

Calorimetric method Power measurements are characterized by high accuracy. This method is used throughout the radio frequency range when measuring relatively high powers where heat loss occurs. The calorimetric method is based on the conversion of electrical energy into thermal energy when some liquid is heated in a wattmeter calorimeter (Fig. 3.17). Next, the power is estimated by determining, from a known temperature difference and a known volume of liquid flowing through the calorimeter:

, (3.36)

where is the coefficient of the liquid used;

- volume of heated liquid.

Rice. 3.17. Calorimetric wattmeter device

The error of the calorimetric method is 1...7%.

Thermistor (bolometric) method power measurement is based on the use of the property of thermistors to change their resistance under the influence of the power of electromagnetic oscillations they absorb. Thermistors and bolometers are used as thermistors.

Thermistor is a semiconductor wafer (or disk) enclosed in a glass container. Thermistors have a negative temperature coefficient, i.e. As the temperature increases, their resistance decreases.

Bolometer It is a thin plate of mica or glass with a layer (film) of platinum deposited on it. Film bolometers have very high sensitivity (up to ... W). Bolometers have a positive temperature coefficient, i.e. As the temperature increases, their resistance increases.

The sensitivity and reliability of thermistors are higher than bolometers, but the parameters of bolometers are more stable, so they are used in standard wattmeters (subgroup M1).

The thermistor method provides high sensitivity, so it is used for measuring low and medium powers. The use of couplers and dividers allows the method to be used for measuring high powers. The error of thermistor wattmeters is 4... 10% and most often depends on the degree of load consistency.

The main metrological characteristics of wattmeters that you need to know when choosing a device include the following:

Type of device (absorbed or transmitted power);

Power measurement range;

Frequency range;

Permissible measurement error;

Coefficient standing wave(SWR) power meter input or reflectance module.

Control questions

1. Give the rule for including an ammeter in the circuit under study.

2. What is the purpose of shunts?

3. How does the resistance of an ammeter change with a shunt connected?

4. How is the shunt connected to the ammeter?

5. Which system of ammeters are most often used when measuring direct current?

6. Which system of ammeters are used to measure the power I of high-frequency alternating current?

7. What rules must be followed when measuring high-frequency current?

8. Give an equivalent circuit of an ammeter for measuring low frequency current.

9. Give an equivalent circuit of an ammeter for measuring high-frequency current.

10. List the main parameters of the ammeter.

11. What is the requirement for internal resistance ammeter?

12. Why can’t you use an electromechanical ammeter of an electrodynamic system when measuring high-frequency alternating current?

13. List the advantages of ammeters of a magnetoelectric system.

14. List the disadvantages of ammeters of the magnetoelectric system.

15. How many shunts does an electromechanical ammeter with five measurement limits contain?

16. What is the fundamental difference between a voltmeter and an ammeter?

17. How is a voltmeter connected to a circuit?

18. What is the purpose of additional resistors?

19. What needs to be done to expand the voltage measurement range of an electromechanical voltmeter?

20. List the advantages and disadvantages of electromechanical voltmeters.

21. By what criteria are electronic analog voltmeters classified?

22. According to what structural diagrams Are electronic analog voltmeters being built?

23. List the advantages and disadvantages of electronic analog voltmeters.

24. Why do voltmeters of type U - D have high sensitivity?

25. Why do D-U type voltmeters have a wide frequency range?

26. What are the advantages of electronic digital voltmeters over electronic analogue ones?

27. Why do electronic analog voltmeters have a scale graduated in decibels?

28. What are the main metrological characteristics of choosing a voltmeter?

29. In what units is voltage measured?

30. What are multimeters?

31. What instruments can measure power in DC circuits?

32. What instruments can be used to measure power in alternating sinusoidal current circuits of industrial frequencies?

33. What method can be used to measure low power in the microwave range?

34. What method can be used to measure high power in the microwave range?

35. What you need to know when determining power pulse signal?

36. Determine the power allocated to the resistor R= 1 kOhm when a constant current of 5 mA flows.

37. Determine the dissipation of the resistor R- 2 kOhm power if a sinusoidal current with an amplitude of 4 mA flows through it.

38. What is the calorimetric method for measuring power?

39. What is the thermistor method of power measurement?

40. What is a bolometer and where is it used?

41.Indicate the advantages of a thermistor compared to a bolometer.

42. Indicate the disadvantages of a thermistor compared to a bolometer.

43. List the advantages and disadvantages of electrodynamic wattmeters.

44. To which group and subgroup do absorbed power wattmeters belong?

45. What part of the energy is consumed by wattmeters of transmitted power?