When designing any electrical circuits, a power calculation is performed. On its basis, the selection of the main elements is made and the permissible load is calculated. If the calculation for a DC circuit is not difficult (in accordance with Ohm's law, it is necessary to multiply the current by the voltage - P = U * I), then calculating the AC power is not so simple. For an explanation, you will need to turn to the basics of electrical engineering, without going into details, we will give a summary of the main theses.

Full power and its components

In AC circuits, the power is calculated taking into account the laws of sinusoidal changes in voltage and current. In this regard, the concept of total power (S) has been introduced, which includes two components: reactive (Q) and active (P). A graphic description of these quantities can be done through the power triangle (see Fig. 1).

The active component (P) means the power of the payload (irreversible conversion of electricity into heat, light, etc.). This value is measured in watts (W), at the household level it is customary to calculate in kilowatts (kW), in the industrial sector - in megawatts (MW).

The reactive component (Q) describes the capacitive and inductive electrical load in the alternating current circuit, the unit of this value is Var.

Rice. 1. Triangle of powers (A) and voltages (V)

In accordance with the graphical representation, the ratios in the triangle of powers can be described using elementary trigonometric identities, which makes it possible to use the following formulas:

• S = √P 2 + Q 2, - for full power;
• and Q = U * I * cos⁡ φ, and P = U * I * sin φ - for reactive and active components.

These calculations are applicable for a single-phase network (for example, a household 220 V), to calculate the power of a three-phase network (380 V), you need to add a multiplier to the formulas - √3 (with a symmetrical load) or add up the powers of all phases (if the load is unbalanced).

For a better understanding of the process of influence of the components of the total power, let us consider the "pure" manifestation of the load in active, inductive and capacitive form.

Active load

Consider a hypothetical circuit that uses a "pure" resistor and an appropriate AC voltage source. A graphical description of the operation of such a circuit is shown in Figure 2, which displays the main parameters for a certain time range (t).

Figure 2. Power of an ideal active load

We can see that the voltage and current are synchronized in both phase and frequency, while the power is at twice the frequency. Note that the direction of this value is positive and it is constantly increasing.

Capacitive load

As can be seen in Figure 3, the graph of the characteristics of the capacitive load is slightly different from the active one.

Figure 3. Graph of ideal capacitive load

The oscillation frequency of the capacitive power is twice the frequency of the sinusoid of the voltage change. With regard to the total value of this parameter, during one harmonic period, it is equal to zero. In this case, an increase in energy (∆W) is also not observed. This result indicates that it moves in both directions of the chain. That is, when the voltage increases, there is an accumulation of charge in the container. With the onset of a negative half-cycle, the accumulated charge is discharged into the circuit circuit.

In the process of accumulating energy in the load capacity and the subsequent discharge, no useful work is performed.

Inductive load

The graph below shows the nature of a "clean" inductive load. As you can see, only the direction of power has changed, as for the increase, it is equal to zero.

Negative impact of reactive load

In the above examples, options were considered where there is a "clean" reactive load. The active resistance factor was not taken into account. In such conditions, the reactive effect is zero, which means that you can ignore it. As you can imagine, this is impossible in real life. Even if hypothetically such a load would exist, one cannot exclude the resistance of the copper or aluminum conductors of the cable required to connect it to the power source.

The reactive component can manifest itself in the form of heating of active circuit components, for example, a motor, a transformer, connecting wires, a supply cable, etc. A certain amount of energy is spent on this, which leads to a decrease in the main characteristics.

Reactive power acts on the circuit as follows:

• does not perform any useful work;
• causes serious losses and abnormal loads on electrical appliances;
• can cause a serious accident.

That is why, making the appropriate calculations for the electrical circuit, it is impossible to exclude the factor of influence of inductive and capacitive load and, if necessary, provide for the use of technical systems for its compensation.

Power consumption calculation

In everyday life, you often have to deal with the calculation of power consumption, for example, to check the permissible load on the wiring before connecting a resource-intensive electrical consumer (air conditioner, boiler, electric stove, etc.). Also, in such a calculation there is a need when choosing protective circuit breakers for the switchboard through which the apartment is connected to the power supply.

In such cases, it is not necessary to calculate the power by current and voltage; it is enough to sum up the consumed energy of all devices that can be turned on at the same time. Without getting involved in calculations, you can find out this value for each device in three ways:

When calculating, it should be borne in mind that the starting power of some electrical appliances may differ significantly from the nominal. For household devices, this parameter is almost never indicated in the technical documentation, therefore, it is necessary to refer to the corresponding table, which contains the average values ​​of the starting power parameters for various devices (it is advisable to choose the maximum value).

Electricity has long been used by man to satisfy his needs, but it is invisible, not perceived by the senses, therefore it is difficult to understand. In order to simplify the explanation of electrical processes, they are often compared with the hydraulic characteristics of a moving fluid.

For example, it comes to our apartment through wires from far-away generators and water through a pipe from a pump that creates pressure. However, a disconnected switch prevents the lights from glowing, and a closed water tap prevents water from flowing from the tap. To do the work, you need to turn on the switch and open the tap.

A directed flow of free electrons through the wires will rush to the filament of the light bulb (electric current will go) that will emit light. The water flowing out of the faucet will drain into the sink.

This analogy also makes it possible to understand quantitative characteristics, associate current strength with the speed of fluid movement, and evaluate other parameters.

The mains voltage is compared to the energy potential of the fluid source. For example, an increase in hydraulic pressure by a pump in a pipe will create a high speed of fluid movement, and an increase in voltage (or the difference between the potentials of the phase - the incoming wire and the working zero - the outgoing one) will increase the incandescence of the light bulb, the power of its radiation.

The resistance of the electrical circuit is compared with the braking force of the hydraulic flow. The flow rate is influenced by:

fluid viscosity;

clogging and change in the cross-section of the channels. (In the case of a water tap, the position of the control valve.)

Several factors affect the value of electrical resistance:

the structure of a substance, which determines the presence of free electrons in a conductor and affects;

cross-sectional area and length of the current lead;

temperature.

Electrical power is also compared with the energy flow capabilities in hydraulics and evaluated by the work performed per unit of time. The power of an electrical appliance is expressed in terms of the consumed current and the applied voltage (for AC and DC circuits).

All these characteristics of electricity have been investigated by renowned scientists who have given definitions of current, voltage, power, resistance and described by mathematical methods the mutual connections between them.

The following table shows general relationships for AC and DC circuits that can be used to analyze the performance of specific circuits.

Let's look at a few examples of their use.

Let's say you want to select a current-limiting resistor for the power supply of the lighting circuit. We know the supply voltage of the on-board network "U", equal to 24 volts and the current consumption "I" of 0.5 amperes, which must not be exceeded. According to the expression (9) of Ohm's law, we calculate the resistance "R". R = 24 / 0.5 = 48 ohms.

At first glance, the resistor value is determined. However, this is not enough. For the reliable operation of the sema, it is required to calculate the power by the current consumption.

According to the action of the Joule-Lenz law, the active power "P" is directly proportional to the current "I" passing through the conductor and the applied voltage "U". This relationship is described by formula (11) in the table below.

We calculate: P = 24x0.5 = 12 W.

We get the same value if we use formulas (10) or (12).

The calculation of the power of the resistor by its current consumption shows that in the selected circuit it is necessary to use a resistance of 48 ohms and 12 watts. A resistor of lower power will not withstand the applied loads, it will heat up and burn out over time.

This example shows the dependence of how the load current and the voltage in the network affect the consumer's power.

For a group of outlets designed to power household electrical appliances in the kitchen, you must select a protective circuit breaker. The power of the devices according to the passport data is 2.0, 1.5 and 0.6 kW.

Solution: The apartment uses a 220 volt single-phase alternating network. The total power of all devices connected to work at the same time will be 2.0 + 1.5 + 0.6 = 4.1 kW = 4100 W.

According to the formula (2), we determine the total current of the consumer group: 4100/220 = 18.64 A.

The closest rated circuit breaker has a trip rate of 20 amps. We choose it. The machine with a lower value of 16 A will constantly disconnect from the overload.

Differences in the parameters of electrical circuits on alternating current

Single-phase networks

When analyzing the parameters of electrical appliances, one should take into account the peculiarities of their operation in alternating current circuits, when, due to the influence of industrial frequency, capacitive loads appear in capacitors (they shift the current vector by 90 degrees forward from the voltage vector), and in the coil windings - inductive (the current is 90 degrees behind from voltage). In electrical engineering, they are called. Together, they create reactive power losses "Q", which do not perform useful work.

On active loads, there is no phase shift between current and voltage.

Thus, a reactive component is added to the active value of the power of an electrical appliance in AC circuits, due to which the total power increases, which is usually called full and denoted by the index "S".

Electric current and power frequency voltage vary with time in a sinusoidal manner. Accordingly, there is a change in power. Determining their parameters at different instantaneous moments of time does not make much sense. Therefore, the total (integrating) values ​​are chosen for a certain time period, as a rule, the period of fluctuation T.

Knowing the differences between the parameters of the circuits for alternating current and direct current allows you to correctly calculate the power through current and voltage in each specific case.

Three-phase networks

In principle, they consist of three identical single-phase circuits, shifted relative to each other on the complex plane by 120 degrees. They differ slightly in loads in each phase, which shift the current from the voltage by an angle phi. Due to this unevenness, a current I0 is created in the neutral wire.

The voltage in this system consists of phase voltages (220 V) and line voltages (380 V).

The power of a three-phase current device connected to the circuit is the sum of the components in each phase. It is measured using special devices: wattmeters (active component) and varmeters (reactive). It is possible to calculate the total power consumption of a three-phase current device based on measurements of the wattmeter and varmeter using the triangle formula.

There is also an indirect measurement method based on the use of a voltmeter and ammeter with subsequent calculations of the obtained values.

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Electric current power concept

Electric current power

Before talking about electrical power, you should define the concept of power in a general sense. Usually, when people talk about power, they mean some kind of power possessed by this or that object (powerful electric motor), or an action (powerful explosion).

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

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 implies the impact of force. The force (F), with the help of which a certain path (S) was traversed, will be equal to the perfect work (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 perfect work that is 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 at which the system's energy is converted.

Having dealt with the concept of mechanical power, you can move on to considering electrical power (power of electric current). 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 second. Therefore, the product of current and voltage shows the total work performed in 1 second, that is, the electrical power, or the power of the electrical current.

Analyzing the above formula, a very simple conclusion can be drawn: since the electric power P is equally dependent on the current I and on the voltage U, then, therefore, the same electric power can be obtained either at high current and low voltage, or, vice versa , at high voltage and low current (this is used when transmitting electricity over remote distances from power plants to places of consumption by means of 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 - heat, light, mechanical, etc.) has its own unit of measurement - W (Watt). It is equal to the product of 1 V by 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 = 1,000 kW = 1,000,000 W).

Reactive electrical power is a quantity that characterizes this type of electrical load, which is created in devices (electrical equipment) by energy fluctuations (inductive and capacitive) of the electromagnetic field. For a 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). It is designated by the letter Q.

For example, active and reactive electrical power can be expressed as follows: given an electrical device that has heating elements and an electric motor. The heating elements are usually made of high resistance material. When electric current passes through the heating element spiral, electric 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 bias in the values ​​of current and voltage, which causes a negative effect on the power grid (additionally overloading it).

Capacitance (capacitors) have similar abilities. She is able to accumulate charge and give it back. The difference in capacitance and inductance is the opposite bias of the current and voltage values ​​relative to each other. Such energy of capacitance and inductance (out of phase with respect to the value of the supply mains) will, in fact, be reactive electrical power.

With the help of this video tutorial, you can independently study the topic "Electric current power". Using this video, you can get an idea of ​​a new concept - the power of an electric current. The teacher will talk about what power is - work per unit of time - and how to correctly use and calculate this value.

Definition

Power is the work done per unit of time.

In the documents for each electrical device, as a rule, two values ​​are indicated: the voltage (usually 220 V) and the power of this device.

To determine the electrical power, you need to divide the work of the electrical current by the time this current flows through the electrical circuit.

P - electrical power (in mechanics N - mechanical power)

What about work

Work is measured in Joules (J);

Time - in seconds (s);

Power (electrical and mechanical) is measured in Watts (W).

Power meter - wattmeter (Fig. 1).

Rice. 1. Wattmeter

Work is defined as the product of current strength and voltage and time of current flowing through an electrical circuit.

In the formula for calculating the work, we will substitute it in the formula for calculating the power, the time t will be reduced. This means that the power does not depend on the time the electric current flows in the circuit, but is defined as the product of voltage and current.

From Ohm's law for a section of a chain

Electric power is a quantity that characterizes the performance of a given device. In everyday life, all devices are designed for the same voltage - 220 V. From the first equation it follows that if the power increases, the voltage is constant, then the current will also increase.

For example, when water is heated in an electric kettle, the wire that connects the kettle to the electrical circuit heats up. This means that the power of the kettle is large enough, the voltage is 220 V, and the current that flows in the circuit of the switched on electric kettle is also large enough.

By paying for electric energy, we pay for the work of electric current. This payment is made on a kilowatt-hour basis.

1 kW = 1000 W;

1 hour = 3600 s;

(work is defined as power multiplied by time);

1 kWh = 3,600,000 J.

Received a unit for calculating the work of electric current - 1 kW ∙ h = 3 600 000 J.

Based on the foregoing, we can conclude that it is impossible to plug several devices into the same outlet at once. The voltage is a constant value (220 V), and the current in the circuit changes. The more devices are turned on, the more electric current in the circuit.

Bibliography

1. Gendenshtein L.E., Kaidalov A.B., Kozhevnikov V.B. / Ed. Orlova V.A., Roizen I.I. Physics 8. - M .: Mnemosyne.
2. A.V. Peryshkin Physics 8. - M .: Bustard, 2010.
3. Fadeeva A.A., Zasov A.V., Kiselev D.F. Physics 8. - M .: Education.

1. Electrono.ru ().
2. Electricalschool.info ().
3. Stoom.ru ().

Homework

1. P. 51, 52, questions 1-6, pp. 121, 1-3, p. 122, task 25 (2). A.V. Peryshkin Physics 8. - M .: Bustard, 2010.
2. Find the power of the current in an electric lamp if the current in it is 0.4 A, and the voltage in the circuit is 220 V.
3. What instruments can be used to measure the power of an electric field?

Every modern appliance has electrical power. Its digital value is indicated by the manufacturer on the body of the hair dryer or electric kettle, on the lid of the food processor.

Units

The calculation of electrical power allows you to determine the cost of electrical energy consumed by various devices for a certain period of time. Excessive watts and kilowatts lead to failure of wires, deformation of contacts.

The relationship between electric current and power consumed by devices

Electrical power is work that is done over a period of time. When plugged into an outlet, it does work, measured in watts (W). The body indicates the amount of energy that will be consumed by the device for a certain period of time, that is, the consumed electrical power is given.

Power consumption

It is spent so that electrons move in the conductor. In the case of one electron with a unit charge, it is comparable to the value of the mains voltage. The total energy that is required to move all electrons will be determined as the product of the voltage and the number of electrons in the circuit during the operation of the electrical device. Below is the formula for electrical power:

Considering that the number of electrons flowing through the cross-section of a conductor over a period of time is an electric current, it can be represented in an expression for the desired value. The formula for electrical power will look like:

In reality, you have to calculate not the power itself, but the magnitude of the current, knowing the mains voltage and the rated power. Having determined the current that is consumed by a certain device, you can correlate the rating of the outlet and the circuit breaker.

Calculation examples

For a kettle, the electric power of which is designed for two kilowatts, the current consumption is determined by the formula:

I = P / U = (2 * 1000) / 220 = 9A

To connect such a device to a regular electrical network, a 6-amp connector is clearly not suitable.

The above relationships between power and electric current are relevant only when the voltage and current values ​​are completely in phase. The electrical power formula is suitable for almost all household electrical appliances.

Exceptional situations

In the event that a large capacity or inductance is present in the circuit, the formulas used will be unreliable, they cannot be used to carry out mathematical calculations. For example, the electrical power for an AC motor would be determined as follows:

cosφ is the power factor, which for electric motors is 0.6-0.8 units.

When determining the parameters of the device in a three-phase network with a voltage of 380 V, it is necessary to sum up the power from individual values ​​for each phase.

Calculation example

For example, in the case of a three-phase boiler designed for a power of 3 kW, 1 kW is consumed in each phase. Let's calculate the value of the phase current according to the formula:

I = P / U_ph = (1 * 1000) / 220 = 4.5A.

A modern person is characterized by the constant use of electricity in production and in everyday life. He uses devices that consume electric current, uses devices that produce it. When working with such sources, it is important to consider the maximum capabilities that are assumed in the technical specifications.

Such a physical quantity as electrical power is one of the main indicators of any device that functions when a stream of electrons flows through it. For the transportation or transmission of electrical power in a large volume required in industrial conditions, high-voltage electrical transmission lines are used.

Energy conversion is carried out at powerful transformer substations. Three-phase conversion is typical for industrial and household appliances in various fields of application. For example, thanks to this transformation, incandescent lamps of different denominations function.

In theoretical electrical engineering, there is such a thing as instantaneous electrical power. This value is associated with the flow through a certain surface for a small time interval of a single elementary charge. The work is performed by this charge, which is associated with the concept of instantaneous power.

By performing simple math calculations, you can determine the amount of power. Knowing this value, you can select the voltage for the full functioning of a variety of household and industrial appliances. In this case, you can avoid the risks associated with the burnout of expensive electrical appliances, as well as the need to periodically change the electrical wiring in the apartment or office.