What formula is used to calculate the power of an electric current? Electrical power: formula, units of measurement

Electrical energy is the most common type of energy and can rightfully be considered the basis of modern civilization. It has found wide application in everyday life and in all sectors of the national economy. It is difficult to list all the names of electrical household appliances: refrigerators, washing machines, air conditioners, fans, televisions, tape recorders, lighting devices, etc. It is impossible to imagine industry without electrical energy. In agriculture, the use of electricity is continuously expanding: feeding and watering animals, caring for them, heating and ventilation, incubators, air heaters, dryers, etc.

Electric current and its power

Modern science cannot yet fully explain the nature of electricity. For us, however, the idea that electric current is the directed movement of electrons in a conductor is quite sufficient. And that this same current can do work, for example, rotate an electric motor, heat an electric stove, or provide light. This work is a consequence of the fact that under the influence of an electric field, electrons are transferred and moved in a conductor, which also means that some work is done.

As you remember, electric current is characterized by two main parameters: voltage and current.

Voltage is the potential difference between the two poles of the current source in a closed electrical circuit.

Current strength is the amount of electricity passing through a cross-section of a circuit in one second.

It is easy to notice that both terms “voltage” and “current” are not primary; they are defined through other concepts, in this case “potential” and “amount of electricity”. But again we will not delve into physical theories, limiting ourselves to the given definitions, taking them as primary. In the end, it is only important for us to learn how to apply these concepts in practice.

You, of course, know from school that voltage is usually denoted by the letter U and the unit of measurement for voltage is the volt (V). Current strength is measured in amperes (A) and is designated by the Latin letter I.

As already mentioned in the previous article, the ability to produce work is characterized by a quantity called energy. And the ratio of the work performed over a certain period of time to this period of time is called power. Since current can also do work, the concept of power is applicable in this case.

Power permanent electric current is denoted by the letter P and is calculated by the formula P=U*I, that is, it is the product of voltage and current. That is, the greater the voltage and current, the more work is done per unit of time, that is, the greater the power of the electric current. We will not bother to find out why this is exactly so, we will take this statement on faith (it is justified in physics and you can find this justification if you wish).

The unit of electrical power is the watt (W).

One watt is the power developed by an electric current of one ampere at a voltage of one volt.

Larger units of power are:

1 kilowatt (kW) = 1000 W.
1 mega watt (MW) = 1000 kW.

Smaller units:

1 milliwatt (mW) = 10 -3 W;
1 microwatt (µW) = 10 -6 W.

We will encounter power when evaluating solar panels, wind generators and other devices capable of producing electric current.

Electrical circuit

Electrical circuit- a set of devices, elements designed for the flow of electric current, electromagnetic processes in which can be described using the concepts of current strength and voltage.

Electrical circuits are divided into linear and nonlinear. Linear circuits are those that consist only of linear elements - conductors, resistances, capacitors, inductors without ferromagnetic cores. For linear elements, the electrical resistance is constant and the current is directly proportional to the voltage, which is expressed by the well-known Ohm’s law:

The current strength in a section of a circuit is directly proportional to the voltage and inversely proportional to the electrical resistance of a given section of the circuit,

This relationship expresses Ohm's law for a homogeneous section of the circuit: the current strength in the conductor is directly proportional to the applied voltage and inversely proportional to the resistance of the conductor. The value R is usually called electrical resistance. The SI unit of electrical resistance of conductors is the ohm (Ω). A resistance of 1 ohm has a section of the circuit in which, at a voltage of 1 V, a current of 1 A appears. Conductors that obey Ohm’s law are called linear.

It should be noted that there are many materials and devices that do not obey Ohm's law, for example, a semiconductor diode or a gas-discharge lamp. Even for metal conductors, at sufficiently high currents, a deviation from Ohm’s linear law is observed, since the electrical resistance of metal conductors increases with increasing temperature. That is, most real electrical circuits are nonlinear.

Nonlinear circuits contain elements whose electrical resistance depends significantly on current or voltage, as a result of which the current is not directly proportional to the voltage. The dependence of current on voltage in nonlinear circuits is expressed by the so-called current-voltage characteristic, obtained experimentally and depicted by some graph in the current-voltage coordinate system.

Nonlinear elements (amplifiers, generators, etc.) give electrical circuits properties that are unattainable in linear circuits (voltage or current stabilization, DC amplification, etc.).

AC power

Ohm's law in the form in which it was formulated by you (I=U/R) is valid only for DC circuits. Consequently, the current power formula P=I*U also applies only to DC circuits. In practice, the greatest importance is the calculation of power in circuits of alternating sinusoidal voltage and current.

Power in an alternating current circuit is expressed by a complex number of the form P+i*Q. In this case, its real part is called active power, and its imaginary part is called reactive power.

Active power characterizes the rate of irreversible conversion of electrical energy into other types of energy (thermal and electromagnetic). Reactive power is a quantity characterizing the loads created in electrical devices by fluctuations in the energy of the electromagnetic field in a sinusoidal alternating current circuit

The unit of active power is still the watt, and the unit of reactive power is the reactive volt-ampere (VAr, VAR, var).

But the total power has practical significance, as a value that describes the loads actually imposed by the consumer on the elements of the supply network (wires, cables, distribution boards, transformers, power lines), since these loads depend on the current consumed, and not on the energy actually used by the consumer .

Total power is a value equal to the product of the effective values of the periodic electric current I in the circuit and the voltage U at its terminals: S=U*I; is related to active and reactive power by the relation: S = sqrt, where P is active power, Q is reactive power, sqrt is the square root symbol.

The unit of total electrical power is volt-ampere (V·A, VA).

When designing electrical wiring in a room, you need to start by calculating the current strength in the circuits. An error in this calculation can be costly later. An electrical outlet can melt if exposed to too much current. If the current in the cable is greater than the calculated current for a given material and core cross-section, the wiring will overheat, which can lead to melting of the wire, a break or short circuit in the network with unpleasant consequences, among which the need to completely replace the electrical wiring is not the worst thing.

It is also necessary to know the current strength in the circuit to select circuit breakers, which should provide adequate protection against network overload. If the machine is set with a large margin at its nominal value, by the time it is triggered, the equipment may already be out of order. But if the rated current of the circuit breaker is less than the current that appears in the network during peak loads, the circuit breaker will drive you crazy, constantly cutting off power to the room when you turn on the iron or kettle.

Formula for calculating the power of electric current

According to Ohm's law, current (I) is proportional to voltage (U) and inversely proportional to resistance (R), and power (P) is calculated as the product of voltage and current. Based on this, the current in the network section is calculated: I = P/U.

In real conditions, one more component is added to the formula and the formula for a single-phase network takes the form:

and for a three-phase network: I = P/(1.73*U*cos φ),

where U for a three-phase network is assumed to be 380 V, cos φ is the power factor, reflecting the ratio of the active and reactive components of the load resistance.

For modern power supplies, the reactive component is insignificant; the value of cos φ can be taken equal to 0.95. The exception is powerful transformers (for example, welding machines) and electric motors; they have high inductive reactance. In networks where it is planned to connect such devices, the maximum current should be calculated using a cos φ coefficient of 0.8, or the current should be calculated using the standard method, and then a multiplying factor of 0.95/0.8 = 1.19 should be applied.

Substituting the effective voltage values of 220 V/380 V and a power factor of 0.95, we obtain I = P/209 for a single-phase network and I = P/624 for a three-phase network, that is, in a three-phase network with the same load, the current is three times less. There is no paradox here, since three-phase wiring provides three phase wires, and with a uniform load on each phase it is divided into three. Since the voltage between each phase and working neutral wires is 220 V, the formula can be rewritten in another form, so it is more clear: I = P/(3*220*cos φ).

Selecting the rating of the circuit breaker

Applying the formula I = P/209, we find that with a load with a power of 1 kW, the current in a single-phase network will be 4.78 A. The voltage in our networks is not always exactly 220 V, so it would not be a big mistake to calculate the current strength with a small margin like 5 A for every kilowatt of load. It is immediately clear that it is not recommended to connect an iron with a power of 1.5 kW to an extension cord marked “5 A”, since the current will be one and a half times higher than the rated value. You can also immediately “graduate” the standard ratings of the machines and determine what load they are designed for:

6 A – 1.2 kW;
8 A – 1.6 kW;
10 A – 2 kW;
16 A – 3.2 kW;
20 A – 4 kW;
25 A – 5 kW;
32 A – 6.4 kW;
40 A – 8 kW;
50 A – 10 kW;
63 A – 12.6 kW;
80 A – 16 kW;
100 A – 20 kW.

Using the “5 amperes per kilowatt” technique, you can estimate the current strength that appears in the network when connecting household devices. You are interested in peak loads on the network, so for the calculation you should use the maximum power consumption, not the average. This information is contained in the product documentation. It is hardly worth calculating this indicator yourself by summing up the rated powers of the compressors, electric motors and heating elements included in the device, since there is also such an indicator as the efficiency factor, which will have to be assessed speculatively with the risk of making a big mistake.

When designing electrical wiring in an apartment or country house, the composition and passport data of the electrical equipment that will be connected are not always known for certain, but you can use the approximate data of electrical appliances common in our everyday life:

electric sauna (12 kW) - 60 A;
electric stove (10 kW) - 50 A;
hob (8 kW) - 40 A;
instantaneous electric water heater (6 kW) - 30 A;
dishwasher (2.5 kW) - 12.5 A;
washing machine (2.5 kW) - 12.5 A;
Jacuzzi (2.5 kW) - 12.5 A;
air conditioner (2.4 kW) - 12 A;
Microwave oven (2.2 kW) - 11 A;
storage electric water heater (2 kW) - 10 A;
electric kettle (1.8 kW) - 9 A;
iron (1.6 kW) - 8 A;
solarium (1.5 kW) - 7.5 A;
vacuum cleaner (1.4 kW) - 7 A;
meat grinder (1.1 kW) - 5.5 A;
toaster (1 kW) - 5 A;
coffee maker (1 kW) - 5 A;
hair dryer (1 kW) - 5 A;
desktop computer (0.5 kW) - 2.5 A;
refrigerator (0.4 kW) - 2 A.

The power consumption of lighting devices and consumer electronics is small; in general, the total power of lighting devices can be estimated at 1.5 kW and a 10 A circuit breaker is sufficient for a lighting group. Consumer electronics are connected to the same outlets as irons; it is not practical to reserve additional power for them.

If you sum up all these currents, the figure turns out to be impressive. In practice, the possibility of connecting the load is limited by the amount of allocated electrical power; for apartments with an electric stove in modern houses it is 10 -12 kW and at the apartment input there is a machine with a nominal value of 50 A. And these 12 kW must be distributed, taking into account the fact that the most powerful consumers concentrated in the kitchen and bathroom. Wiring will cause less cause for concern if it is divided into a sufficient number of groups, each with its own machine. For the electric stove (hob), a separate input with a 40 A automatic circuit breaker is made and a power outlet with a rated current of 40 A is installed; nothing else needs to be connected there. A separate group is made for the washing machine and other bathroom equipment, with a machine of the appropriate rating. This group is usually protected by an RCD with a rated current 15% greater than the rating of the circuit breaker. Separate groups are allocated for lighting and for wall sockets in each room.

You will have to spend some time calculating powers and currents, but you can be sure that the work will not be in vain. Well-designed and high-quality electrical wiring is the key to the comfort and safety of your home.

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Electric current power concept

Electric current power

Before talking about electrical power, we should define the concept of power in a general sense. Typically, when people talk about power, they mean some kind of force that an object has (a powerful electric motor) or an action (a powerful explosion).

But, as we know from school physics, force and power are different concepts, although they have a relationship.

Initially, power (N) is a characteristic related to a certain event (action), and if it is tied to a certain object, then the concept of power is also conditionally correlated with it. Any physical action involves the use of force. The force (F), with the help of which a certain path (S) was traveled, will be equal to the work done (A). And the work done in a certain time (t) will be equated to power.

Power is a physical quantity that is equal to the ratio of the work performed over a certain period of time to the same period of time. Since work is a measure of energy change, we can also say this: power is the rate of energy conversion of the system.

Having understood the concept of mechanical power, we can move on to considering electrical power (electric power). As you should know, U is the work done when moving 1 C, and the current I is the number of coulombs passing in 1 sec. Therefore, the product of current and voltage shows the total work done in 1 second, that is, electrical power, or the power of electric current.

Analyzing the above formula, we can draw a very simple conclusion: since the electrical power P equally depends on the current I and on the voltage U, then, therefore, the same electrical power can be obtained either with a high current and low voltage, or, vice versa , at high voltage and low current (this is used when transmitting electricity over long distances from power plants to places of consumption by transformer conversion at step-up and step-down power substations).

Active electrical power (this is power that is irrevocably converted into other types of energy - thermal, light, mechanical, etc.) has its own unit of measurement - W (Watt). It is equal to the product of 1 V times 1 A. In everyday life and in production, it is more convenient to measure power in kW (kilowatts, 1 kW = 1000 W). Power plants already use larger units - mW (megawatts, 1 mW = 1000 kW = 1,000,000 W).

Reactive electrical power is a quantity that characterizes this type of electrical load that is created in devices (electrical equipment) by energy fluctuations (inductive and capacitive) of the electromagnetic field. For conventional alternating current, it is equal to the product of the operating current I and the voltage drop U by the sine of the phase angle between them: Q = U×I×sin(angle). Reactive power has its own unit of measurement called VAR (volt-ampere reactive). Denoted by the letter Q.

Using an example, active and reactive electrical power can be expressed as follows: given is an electrical device that has heating elements and an electric motor. Heating elements are usually made of high resistance material. When an electric current passes through the heating element's spiral, the electrical energy is completely converted into heat. This example is typical of active electrical power.

The electric motor of this device has a copper winding inside. It represents inductance. And as we know, inductance has the effect of self-induction, and this contributes to the partial return of electricity back to the network.

This energy has some offset in current and voltage values, which causes a negative impact on the electrical grid (further overloading it).

Capacitance (capacitors) also has similar abilities. It is capable of accumulating charge and releasing it back. The difference between capacitance and inductance lies in the opposite displacement of the values of current and voltage relative to each other. This energy of capacitance and inductance (phase-shifted relative to the value of the supply network) will, in fact, be reactive electrical power.

Trouble-free operation of the device depends on compliance of the technical characteristics of the device with the power supply network standards. Knowing the voltage, resistance and current in the circuit, the electrician will understand how to find the power. The formula for calculating an important parameter depends on the properties of the network to which the consumer is connected.

Mechanical devices and electrical devices are designed to perform work. According to Newton's second law, kinetic energy that acts on a material point during a certain period of time produces a useful effect. In electrodynamics, a field created by a potential difference transfers charges along a section of an electrical circuit.

The amount of work produced by the current depends on the intensity of the electricity. In the middle of the 19th century, D. P. Joule and E. H. Lenz solved the same problem. In the experiments, a piece of high-resistance wire was heated when a current was passed through it. Scientists were interested in the question of how to calculate the power of a circuit. To understand the process occurring in the conductor, the following definitions should be introduced:

Power is the work done by current in a conductor over a period of time. The statement is described by the formula: P = A ∕ ∆t.

On a section of the circuit, the potential difference at points a and b does work to move electric charges, which is determined by the equation: A = U ∙ Q. Current is the total charge passed in the conductor per unit time, which is mathematically expressed by the relation: U ∙ I = Q ∕ ∆t. After transformations, the formula for electric current power is obtained: P = A ∕ ∆t = U ∙ Q ∕ ∆t = U ∙ I. It can be argued that work is carried out in the circuit, which depends on the power determined by the current and voltage at the contacts of the connected electrical device.

DC performance

In a linear circuit without capacitors and inductors, Ohm's law is observed. A German scientist discovered the relationship between current and voltage from circuit resistance. The discovery is expressed by the equation: I = U ∕ R. Given the value of the load resistance, the power is calculated in two ways: P = I ² ∙ R or P = U ² ∕ R.

If the current in the circuit flows from plus to minus, then the energy of the network is absorbed by the consumer. This process occurs when the battery is charging. If the current flows in the opposite direction, then power is transferred to the electrical circuit. This happens when the network is powered by a running generator.

AC power

The calculation of variable circuits is different from the calculation of the performance parameter in a direct current line. This is due to the fact that voltage and current vary in time and direction.

In a circuit with a phase shift of current and voltage, the following types of power are considered:

Active.
Reactive.
Full.

Active ingredient

The active part of the useful power takes into account the rate of irreversible conversion of electricity into thermal or magnetic energy. In a current line with one phase, the active component is calculated by the formula: P = U ∙ I ∙ cos ϕ.

In the international system of SI units, productivity is measured in watts. The angle ϕ determines the voltage offset relative to the current. In a three-phase circuit, the active part is the sum of the powers of each individual phase.

Reverse losses

Network power is used to operate capacitors, inductors, and electric motor windings. Due to the physical properties of such devices, energy, which is determined by reactive power, is returned to the circuit. The magnitude of the return is calculated using the equation: V = U ∙ I ∙ sin ϕ.

The unit of measurement is watt. It is possible to use a non-systemic counting measure var, the name of which is made up of the English words volt, amper, reaction. Translation into Russian respectively means “volt”, “ampere”, “reverse action”.

If the voltage leads the current, then the phase displacement is considered greater than zero. Otherwise, the phase shift is negative. Depending on the value of sin ϕ, the reactive component is positive or negative. The presence of an inductive load in the circuit allows us to talk about the reversible part being greater than zero, and the connected device consumes energy. The use of capacitors makes the reactive performance negative and the device adds energy to the network.

To avoid overloads and changes in the set power factor, compensators are installed in the circuit. Such measures reduce electricity losses, reduce current waveform distortion and allow the use of wires of a smaller cross-section.

In full force

Total electrical power determines the load that a consumer places on the network. The active and reversing components are combined with the total power by the equation: S = √ (P² + V²).

With an inductive load, the indicator is V ˃ 0, and the use of capacitors makes V ˂ 0. The absence of capacitors and inductors makes the reactive part equal to zero, which returns the formula to its usual form: S = √ (P ² + V ²) = √ (P ² + 0) = √ P ² = P = U ∙ I. Total power is measured in the off-system unit “volt-ampere”. Short version - B ∙ A.

Utility criterion

Power factor characterizes the consumer load from the point of view of the presence of the reactive part of the work. In a physical sense, the parameter determines the current shift from the applied voltage and is equal to cos ϕ. In practice, this means the amount of heat generated on the connecting conductors. The heating level can reach significant values.

In the energy industry, power factor is denoted by the Greek letter λ. The range of change is from zero to one or from 0 to 100%. At λ = 1, the energy supplied to the consumer is spent on work; there is no reactive component. Values λ ≤ 0.5 are considered unsatisfactory.

The trouble-free operation of devices in an electrical line is due to the correct calculation of technical parameters. A set of formulas derived from the laws of Joule - Lenz and Ohm helps to find the current power in a circuit. A schematic diagram, correctly designed taking into account the features of the devices used, increases the performance of the electrical network.

Connecting a consumer to a household or industrial electrical network whose power is greater than that for which the cable or wire is designed is fraught with the most unpleasant, and sometimes catastrophic, consequences. If the electrical wiring inside the living space is properly organized, circuit breakers will constantly trip or fuses (plugs) will blow.

If protection is performed incorrectly or is missing altogether, this can lead to:

to burnout of the power wire or cable;
melting of insulation and short circuit between wires;
overheating of copper or aluminum cable conductors and fire.

Therefore, before connecting a consumer to the electrical network, it is advisable to know not only its rated electrical power, but also the current consumed from the network.

Calculation of power consumption

The formula for calculating power by current and voltage is familiar from a school physics course. Calculation of electric current power (in watts) for a single-phase network is carried out according to the expression:

in which U is voltage in volts
I – current in amperes;
Cosφ is the power factor, depending on the nature of the load.

The question may arise - why do we need a formula for calculating current power when it can be found out from the passport of the connected device? Determination of electrical parameters, including power and current consumption, is necessary at the electrical wiring design stage. The cross-section of the wire or cable is determined by the maximum current flowing in the network. To calculate current by power, you can use the converted formula:

The power factor depends on the type of load (active or reactive). For everyday calculations, it is recommended to take its value equal to 0.90...0.95. However, when connecting electric stoves, heaters, incandescent lamps, the load of which is considered active, this coefficient can be considered equal to 1.

The above formulas for calculating power by current and voltage can be used for a single-phase network with a voltage of 220.0 volts. For a three-phase network they have a slightly modified form.

Calculation of power of three-phase consumers

Determining power consumption for a three-phase network has its own specifics. The formula for calculating the electric current power of three-phase household consumers is as follows:

Р=3.00.5 ×U×I×Cosφ or 1.73×U×I×Cosφ,

Calculation features

The above formulas are intended for simplified household calculations. When determining the effective parameters, the actual connection must be taken into account. A typical example is the calculation of power consumption from a battery. Since the current flows in the circuit is constant, the power factor is not taken into account, since the nature of the load does not affect the power consumption. For both active and reactive consumers, its value is taken equal to 1.0.

The second nuance that should be taken into account when carrying out household electrical calculations is the actual voltage value. It is no secret that in rural areas, network voltage can fluctuate within fairly wide limits. Therefore, when using calculation formulas, it is necessary to substitute real parameter values in them.

The task of calculating three-phase consumers is even more difficult. When determining the current flow in the network, it is necessary to additionally take into account the type of connection - “star” or “delta”.