What formula expresses the work of electric current. Electric current work definition

Electrical energy is easily converted into other types of energy - mechanical, chemical, light, internal energy of matter, which is widely used in industry and in everyday life.

A measure of energy change electric current is the work of a current source that creates and maintains an electric field in a circuit.

A stationary electric field that moves charges along a conductor does work. This work is called current work. The work of electric current on a section of the circuit, as follows from the definition of voltage,

\(~A = qU ,\)

Where q - electric charge, passing along a section of the chain, and U- voltage on the site.

Considering that q = It, Where I is the current strength in the conductor, and t- the time of passage of the electric current, for the work of the current we obtain

\(~A = IUt .\)

If R- the resistance of a homogeneous section of the circuit, then, using Ohm’s law for the section of the circuit, you can obtain a formula for calculating the work of the current:

\(~A = I^2Rt = \frac(U^2)(R) t .\)

If a section of the circuit is not homogeneous, then work is performed not only by a stationary electric field, but also by external forces, and full time job determined by the formula

\(~A = I(\varphi_1 - \varphi_2 \pm \varepsilon) t .\)

If there is an electric motor in the circuit, then the energy of the electric current is, firstly, spent on performing mechanical work - useful work A meh, secondly, it is spent on heating the electric motor windings and connecting wires - lost energy. In this case, the efficiency can be calculated as

\(~A_0 = A_(meh) + Q ;\) \(~\eta = \frac(A_(meh))(A_0) = \frac(A_(meh))(A_(meh) + Q) .\ )

Speaking about the efficiency of the current source, under useful work imply work done in an external circuit direct current:

\(~A_p = IUt = I^2Rt .\)

The expended work of the current source is equal to the work of external forces:

\(~A_z = q \varepsilon = I \varepsilon t ,\)

where \(~\varepsilon = I (R + r)\).

Then \(~A_z = I^2 (R + r) t\) .

Source efficiency\(~\eta = \frac(A_p)(A_z) = \frac(IUt)(I \varepsilon t) = \frac(U)(\varepsilon) = \frac(R)(R + r)\), Where U- voltage in the external circuit (voltage at the poles of the current source). Graphical dependency η = f(R) at r= const is shown in Fig. 1.

The SI unit of work done by electric current is the joule (J). 1 J represents current work equivalent to 1 J of mechanical work.

1 J = Cl·B = А·В·s.

The work of electric current is measured by meters.

The speed of current work in a given section of the circuit characterizes the current power. The current power is determined by the formula \(~P = \frac At\) or P = IU.

Using Ohm's law for a section of a circuit, we can write a different formula for current power\[~P = I^2R = \frac(U^2)(R)\]. In this case we're talking about about thermal power.

The unit of current power is watt: 1 W = J/s. Hence J = W s.

In addition, non-system units are used: kilowatt-hour or hectowatt-hour: 1 kWh = 3.6 10 6 J = 3.6 MJ; 1 gWh = 3.6 10 5 J = 360 kJ.

To measure current power, there are special devices - wattmeters.

Literature

Aksenovich L. A. Physics in secondary school: Theory. Tasks. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyakhavanne, 2004. - P. 267-270.

Every body is capable of producing work, this is called body energy. The simplest example is a body raised to a certain height. It has potential energy; if the body is released, it will begin to release energy, converting it into kinetic energy, at which point the body will do work.

Accordingly, the higher the height of the body, the greater its energy will be. Energy never disappears without a trace, it is only transformed into another form - this is one of the main laws of physics.

The same is true with electrical energy, it can be converted into another type of energy - thermal, kinetic, mechanical, chemical, etc.

Therefore, electricity has become so widely used. This type of energy, unlike any other, can be transferred to long distances and store it practically without loss, and it can be obtained quite simply.

Work of electric current

When current flows through a certain section of the electrical circuit, the electric field does a certain amount of work. This is called the work of electric current. To transfer a charge of energy along this circuit, you need to expend a certain amount of energy. It is communicated to the receiver, and part of the energy is spent on overcoming the resistance of wires and sources in the electrical circuit.

This suggests that not all of the energy expended is distributed efficiently and not all of it is useful. Consequently, the work done is also not completely effective. IN in this case the formula will look like this: A = UQ.

U is the voltage at the receiver terminals, and Q- This is the charge transferred along a section of the circuit. In this case, you need to take into account Ohm's law for a circuit section , then the formula will look like this: R I2 Δt = U I Δt = ΔA.

Using this formula, you can trace the effect of the law of conservation of energy, which applies to a homogeneous section of the chain.

In 1850, the English physicist Joule Prescott, who made a significant contribution to the study of electricity, discovered a new law. Its essence was to determine the ways in which the work of electric current is converted into thermal energy. At the same time, another physicist, Lenz, was able to make a similar discovery and prove the law, so it was called the “Joule-Lenz law”, in honor of both outstanding physicists of that time.

Electric current power

Power is another characteristic used to determine the operation of electric current. This is a certain physical quantity that characterizes the transformation and speed of energy transfer.

When determining the power of an electric current, it is necessary to take into account such an indicator as instantaneous power. It represents the ratio of instantaneous values ​​of such indicators as current and voltage in the form of a product. This ratio applies to a specific section of the circuit.

Indicators such as work and electric current power are taken into account when creating any electrical circuits. Along with other laws, they are fundamental; failure to comply with them will lead to serious violations.

In order to receive the greatest electric power, you need to take into account the characteristics of the generator, i.e. the resistance in the external circuit should be no more and no less internal resistance generator

Only in this case will the operating efficiency be maximum, because otherwise all the energy of the generator will be spent on overcoming the resistance, and all the work will be uneconomical. Naturally, such an operating scheme can negatively affect the efficiency of the entire electrical circuit.

How to calculate the work done by electric current? We already know that the voltage at the ends of a section of the circuit is numerically equal to the work that is done when an electric charge of 1 C passes through this section. When an electric charge passing through the same area is not 1 C, but, for example, 5 C, the work done will be 5 times greater. Thus, in order to determine the work of electric current on any section of the circuit, it is necessary to multiply the voltage at the ends of this section of the circuit by the electric charge (amount of electricity) passing through it:

where A is work, U is voltage, q is electric charge. The electric charge passing through a section of the circuit can be determined by measuring the strength of the current and the time it passes:

Using this relationship, we obtain a formula for the work of electric current, which is convenient to use in calculations:

The work of an electric current on a section of a circuit is equal to the product of the voltage at the ends of this section by the current strength and the time during which the work was performed.

Work is measured in joules, voltage in volts, current in amperes and time in seconds, so we can write:

1 joule = 1 volt x 1 ampere x 1 second,

1 J = 1 VA s.

It turns out that to measure the work of electric current, three instruments are needed: a voltmeter, an ammeter and a clock. In practice, the work of electric current is measured with special instruments - counters. The design of the meter seems to combine the three devices mentioned above. Electricity meters can now be seen in almost every apartment.

Example. How much work does the electric motor do in 1 hour if the current in the electric motor circuit is 5 A and the voltage at its terminals is 220 V? Engine efficiency 80%.

Let's write down the conditions of the problem and solve it.

Questions

1. What is equal to electrical voltage on the chain section?
2. How can we express the work of electric current in this section through voltage and electric charge passing through a section of a circuit?
3. How to express the work of current in terms of voltage, current and time?
4. What instruments measure the work of electric current?

Exercise 34

1. How much work is done by the electric current in the electric motor in 30 minutes if the current in the circuit is 0.5 A and the voltage at the motor terminals is 12 V?
2. The voltage on the spiral of a light bulb from a flashlight is 3.5 V, the resistance of the spiral is 14 Ohms. How much work does the current do in the light bulb in 5 minutes?
3. Two conductors, each with a resistance of 5 ohms, are connected first in series and then in parallel, and in both cases they are connected to a voltage of 4.5 V. In which case will the work done by the current be greater for the same time and by how many times?

The body's ability to produce work is called body energy. Thus, the measure of the amount of energy is work. The energy of a body is greater, the more work this body can produce during its movement. Energy does not disappear, but passes from one form to another. For example, in a generator, mechanical energy is converted into electrical energy, and in an engine, electrical energy is converted into mechanical energy. However, not all energy is useful, i.e. part of it is spent on overcoming the internal resistance of the source and wires.

Work of electric current is numerically equal to the product of voltage, current in the circuit and the time it passes. The unit of measurement is Joule.

An electrical measuring instrument is used to measure the work or energy of an electric current − electric energy meter.

Electrical energy, in addition to joules, is measured in watt hours or kilowatt hours:

1 Wh = 3,600 J, 1 kWh = 1,000 Wh.

Electric current power – is the work produced (or consumed) per unit of time. The unit of measurement is Watt.

To measure the power of electric current, an electrical measuring device is used − wattmeter.

The multiple units of power are kilowatt or megawatt:

1 kW = 1,000 W, 1 MW = 1,000,000 W.

In table 1 shows the power of a number of devices.

Table 1

The relationships between power, current, voltage and resistance are shown in Fig. 1.

P U

I R

R·I

Rice. 1

The rate at which mechanical or other energy is converted into electrical energy at a source is called source power:

Where W And– electrical energy of the source.

The rate at which electrical energy is converted in the receiver into other types of energy, in particular thermal energy, is called receiver power:

Power that determines involuntary energy consumption, for example, for heat losses in a source or in conductors, is called power loss:

According to the law of conservation of energy, the power of the source is equal to the sum of the power of consumers and losses:

This expression represents power balance.

The efficiency of energy transfer from source to receiver is characterized by the coefficient of performance (COP) of the source:

Where R 1 or R ist – power supplied by the energy source to the external circuit;

R 2 – power received from outside or power consumed;

∆P or R 0 (R vn ) – power spent to overcome losses in the source or receiver of energy.

Electric current is the directed movement of electrically charged particles. When moving particles collide with molecules and ions of a substance, the kinetic energy of the moving particles is transferred to the ions and molecules, resulting in heating of the conductor. Thus, electrical energy is converted into thermal energy.

In 1844, Russian academician E.H. Lenz and English scientists Joulem simultaneously and independently of each other, a law was discovered that describes the thermal effect of current.

Joule-Lenz law : When an electric current passes through a conductor, the amount of heat generated by the conductor is directly proportional to the square of the current, the resistance of the conductor and the time during which the electric current flows through the conductor:

WhereQ– amount of heat, J,I– current strength, A;R– conductor resistance, Ohm;t– time during which the electric current flowed through the conductor, s.

The Joule-Lenz law is used in calculating the thermal conditions of electricity sources, power lines, consumers and other elements of the electrical circuit. The conversion of electricity into heat is of very great practical importance. At the same time, the thermal effect in many cases turns out to be harmful (Fig. 2).

Work of electric current

Attached to the circuit shown in Figure 1 is constant pressure U.

U = φ A – φ B

During t amount of electricity flows through the circuit Q. The forces of the electric field acting along the conductor transferred the charge during this time Q from point A exactly B. The work of electric field forces or, what is the same, the work of electric current can be calculated using the formula:

A = Q × ( φ A – φ B) = Q × U,

Because Q = I × t, then finally:

A= U × I × t,

Where A– work in joules; I– current in amperes; t– time in seconds; U– voltage in volts.

According to Ohm's law U = I × r. Therefore, the work formula can be written like this:

A = I 2× r × t.

Electric current power

The work done per unit time is called power and is denoted by the letter P.

From this formula we have:

A = P × t.

Power unit:

1 (J/sec) is otherwise called a watt (W). Substituting the expression for the work of electric current into the power formula, we have:

P = U × I(W).

The formula for electric current power can also be expressed in terms of current consumption and consumer resistance:

In addition to the watt, larger units of measurement of electrical power are used in practice. Electrical power is measured in:

100 W = 1 hectowatt (gW);
1000 W = 1 kilowatt (kW);
1,000,000 W = 1 megawatt (MW).

Electrical power is measured by a special device - a wattmeter. The wattmeter has two windings (coils): series and parallel. The series coil is a current coil and is connected in series with the load in the section of the circuit where measurements are made, and the parallel coil is a voltage coil, and accordingly it is connected in parallel to this load. The operating principle of the wattmeter is based on the interaction of two magnetic fluxes created by current, flowing through the winding of the moving coil (current coil), and the current passing through the fixed coil (voltage coil). When the measured current passes through the windings of the moving and stationary coils, two magnetic fields are formed, during the interaction of which the moving coil tends to position itself so that its direction magnetic field coincided with the direction of the magnetic field of the stationary coil. The torque is counteracted by the torque created by the helical springs, through which the measured current is conducted into the moving coil. The counteracting moment of the springs is directly proportional to the angle of rotation of the coil. An arrow mounted on a moving coil indicates the value of the measured quantity. The wattmeter connection diagram is shown in Figure 2.

If you decide to measure the power consumption of any load you have, and you do not have a wattmeter, you can “make” a wattmeter with your own hands. From the formula P = I × U It can be seen that the power consumed in the network can be determined by multiplying the current by the voltage. Therefore, to determine the power consumed from the network, two instruments should be used, a voltmeter and an ammeter. Having measured the current consumption with an ammeter and the voltage of the supply network with a voltmeter, it is necessary to multiply the ammeter reading by the voltmeter reading.

So, for example, the power consumed by the resistance r, with an ammeter reading of 3 A and a voltmeter of 220 V, it will be:

P = I × U= 3 × 220 = 660 W.

For practical measurements electrical work(energy) joule is too small a unit.

If time t substitute not in seconds, but in hours, we get larger units of electrical energy:

1 J = 1 W × sec;
1 W × h = 3600 watts × seconds = 3600 J;
100 W × h = 1 hectowatt × hour (gW × h);
1000 W × h = 1 kilowatt × hour (kW × h).

Electrical energy is measured by electrical energy meters.

Video 1. Operation and power of electric current

Video 2. A little more about power

Example 1. Determine the power consumed by the electric motor if the current in the circuit is 8 A and the motor is connected to a 220 V network.

P = I × U= 8 × 220 = 1760 W = 17.6 GW = 1.76 kW.

Example 2. What is the power consumed by an electric stove if the stove draws a current of 5 A from the network and the resistance of the stove's coil is 24 ohms?

P = I 2× r= 25 × 24 = 600 W = 6 gW = 0.6 kW.

When converting mechanical power into electrical power and vice versa, it must be remembered that
1 horsepower (hp) = 736 W;
1 kilowatt (kW) = 1.36 l. With.

Example 3. Determine the energy consumed by a 600 W electric stove over 5 hours.

A = P × t= 600 × 5 = 3000 W × h = 30 gW × h = 3 kW × h

Example 4. Determine the cost of burning twelve electric lamps within a month (30 days), if four of them, 60 W each, burn for 6 hours a day, and the remaining eight lamps, 25 W each, burn for 4 hours a day. Energy price (tariff) 2.5 rubles per 1 kW × h.

Power of four lamps 60 W each.

P= 60 × 4 = 240 W.

t= 6 × 30 = 180 hours.

A = P × t= 240 × 180 = 43200 W × h = 43.2 kW × h.

The power of the remaining eight lamps is 25 W each.

P= 25 × 8 = 200 W.

Number of hours of burning of these lamps per month:

t= 4 × 30 = 120 hours.

Energy consumed by these lamps:

A = P × t= 200 × 120 = 24000 W × h = 24 kW × h.

Total amount of energy consumed:

43.2 + 24 = 67.2 kW × h

Cost of all energy consumed:

67.2 × 2.5 = 168 rubles.