What does the formula for current work determine? Work of electric current: general characteristics, formula, practical significance

Current work

The work of the electric field on movement free charges in a conductor is called the work of current. When a charge q moves along a conductor, the field does work A = qU (see § 53), where U is the potential difference at the ends of the conductor. Since q = It, the work done by the current can be written as

Joule-Lenz law

Let us consider the practically important case when the main effect of the current is the thermal effect. In this case, according to the law of conservation of energy, the amount of heat released in the conductor is equal to the work done by the current: Q = A. Therefore

1. Prove that the amount of heat Q released in a conductor with current is also expressed by the formulas

Q = I 2 Rt, (2)
Q = (U 2 /R)t. (3)

Clue. Use formula (1) and Ohm's law for the chain section.

We derived formulas (1) – (3) using the law of conservation of energy, but historically the relation Q = I 2 Rt was independently established experimentally by the Russian scientist Emilius Christianovich Lenz and the English scientist J. Joule several years before the discovery of the law of conservation of energy .
Joule-Lenz law: the amount of heat released during time t in a conductor with resistance R, the current strength of which is equal to I, is expressed by the formula

Application of the Joule–Lenz law to series and parallel connected conductors

Let us find out in which cases it is more convenient to use formula (2) to compare the amount of heat released in conductors, and in which cases it is more convenient to use formula (3).

The formula Q = I 2 Rt is convenient to use when the current strength in the conductors is the same, that is, when they are connected in series (Fig. 58.1).

From this formula it is clear that when serial connection conductors, more heat is released in the conductor whose resistance is greater. Wherein

Q 1 /Q 2 = R 1 /R 2.

The formula Q = (U 2 /R)t is convenient to use when the voltage at the ends of the conductors is the same, that is, when they are connected in parallel (Fig. 58.2).

From this formula it is clear that when parallel connection conductors, a greater amount of heat is released in a conductor whose resistance is lower. Wherein

Q 1 /Q 2 = R 2 /R 1.

2. With a series connection, 3 times more heat was released in the first conductor than in the second. In which conductor will the greater amount of heat be released when they are connected in parallel? How many times more?

3. There are two conductors with resistance R 1 = 1 Ohm and R 2 = 2 Ohm. They are connected to a voltage source of 6 V. How much heat will be released in 10 s if:
a) connect only the first conductor?
b) connect only the second conductor?
c) connect both conductors in series?
d) connect both conductors in parallel?
e) what is the ratio of the values ​​of the amount of heat Q1/Q2 if the conductors are connected in series? Parallel?

Let's put experience
We will connect two incandescent lamps with different filament resistances to the network in parallel and in series (Fig. 58.3, a, b). We will see that when connecting lamps in parallel, one lamp shines brighter, and when connected in series, the other lamp shines brighter.

4. Which of the lamps (1 or 2) has more resistance? Explain your answer.

5. Explain why, when connected in series, the filament of each lamp is less incandescent than the filament of the same lamp when connected in parallel.

6. Why, when a lamp is turned on in a lighting network, does the filament become white-hot, but the connecting wires connected in series in it hardly heat up?

2. Current power

The current power P is the ratio of the work done by the current A to the time period t during which this work is performed:

The unit of power is watt (W). The current power is equal to W if the work done by the current in 1 s is equal to 1 J. Derived units are often used, for example kilowatt (kW).

7. Prove that the current power can be expressed by the formulas

P = IU, (5)
P = I 2 R, (6)
P = U 2 /R. (7)

Clue. Use formula (4) and Ohm's law for the section of the chain.

8. Which of the formulas (5) – (7) is more convenient to use when comparing current power:
a) in series-connected conductors?
b) in parallel connected conductors?

9. There are conductors with resistance R 1 and R 2. Explain why when these conductors are connected in series

P 1 / P 2 = R 1 / R 2 ,

and with parallel

P 1 / P 2 = R 2 / R 1 .

10. The resistance of the first resistor is 100 Ohms, and the second is 400 Ohms. In which resistor will the current power be greater and how many times greater if they are connected to a circuit with a given voltage:
a) sequentially?
b) in parallel?
c) What will be the current power in each resistor in a parallel connection if the voltage in the circuit is 200 V?
d) What is the total current power in two resistors at the same circuit voltage if they are connected in series? parallel?

The power of an electrical appliance is the current power in this device. So, the power of an electric kettle is approximately 2 kW.

Usually the power of the device is indicated on the device itself.

Below are approximate power values ​​of some devices.
Flashlight lamp: about 1W
Energy-saving lighting lamps: 9-20 W
Incandescent lighting lamps: 25-150 W
Electric heater: 200-1000 W
Electric kettle: up to 2000 W

All electrical appliances in the apartment are connected in parallel, so the voltage on them is the same.

11. A 2 kW electric kettle is connected to a 220 V network.
a) What is the resistance of the heating element in operating mode (when the kettle is on)?
b) What is the current strength?

12. On the base of the first lamp it is written “40 W”, and on the base of the second – “100 W”. These are the power values ​​of the lamps in operating mode (with a hot filament).
a) What is the resistance of the filament of each lamp in operating mode if the voltage in the circuit is 220 V?
b) Which of the lamps will shine brighter if these lamps are connected in series and connected to the same network? Will this lamp shine as brightly as when connected in parallel?

13. The electric heater has two heating elements with resistance R 1 and R 2, and R 1 > R 2. Using a switch, the heater elements can be connected to the network individually, as well as in series or parallel. The network voltage is U.
a) At what switching on of the elements will the heater power be maximum? What will it be equal to?
b) At what switching on of the elements will the heater power be minimal (but not equal to zero)? What will it be equal to?
c) What is the ratio R 1 /R 2 if the maximum power is 4.5 times greater than the minimum?

Additional questions and tasks

14. Figure 58.4 shows electrical diagram a section of a circuit consisting of four identical resistors. The voltage throughout the entire circuit is constant. Assume that the temperature dependence of the resistor resistance can be neglected.

a) Which resistor has the highest voltage? the smallest?
b) Which resistor has the greatest current? the smallest?
c) In which resistor is the most a large number of warmth? the smallest amount of heat?
d) How will the amount of heat generated in each of resistors 2, 3, 4 change if resistor 1 is short-circuited (that is, replaced with a conductor with very low resistance)?
e) How will the amount of heat generated in each of resistors 2, 3, 4 change if the wire is disconnected from resistor 1 (that is, replaced with a conductor with a very high resistance)?

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, work 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.

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 area 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 = U Q.

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 power of electric current 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.

Electricity meters are installed in each apartment or private house, according to the readings of which the owners pay bills on a monthly basis. Such control devices take into account the number of kilowatt-hours consumed by all electrical appliances and light sources over a certain period of time. Many people wonder what these “kilowatt hours” are. The answer is simple: this is how the work of the current is measured.

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Appearance of an apartment meter, which keeps track of the work performed by the electric current

Current work

Every person uses electricity specific goals. Electric current performs a certain work, passing through an electrical circuit, as a result of which electrical appliances, lighting equipment, etc. function.

The work of an electric current is a quantity numerically equal to the product of the strength of the electric current and the voltage at the ends of the circuit section and the time period during which such work was performed. If any of these derivatives changes in one direction or another, then the work done by the current will decrease or increase.

This current characteristic is denoted by the capital Latin letter “A”, and is measured in joules or kilowatt-hours, abbreviated “J” and “kWh”, respectively.

On a note. The work of the current shows how much electricity has been converted into other types of energy (thermal or light) over a specific period. For electricity, the law of conservation of energy is true.

The formula by which the work done by electric current is measured is as follows:

A = U*I*t, where:

• A is a quantitative indicator of the work performed by the current;
• U – electrical voltage in the circuit;
• I – electric current strength;

and, having only data on the strength of the electric current and resistance in the electrical circuit, this value is calculated by the formula:

In this formula, the following quantities are lettered:

• A – work of electric current;
• U – voltage in the circuit;
• R – resistance on the circuit section;
• I – current strength;
• t is the time during which the electric current was operating.

Interesting to know. Meters usually take into account the work of electric current in kWh. This unit is used in practice more often than the generally accepted unit of electrical work, the joule, named after the famous physicist. The fact is that the Joule is a rather small unit, and 1 kWh = 3,600,000 J.

To measure the work of current, devices such as a voltmeter, ammeter, and watch are needed. In practice, measurements are carried out using a prefabricated device - an electricity meter.

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An electrical circuit in which a voltmeter and an ammeter are connected to measure the work of an electric current

Current power

Also important is the concept of electric current power, which is directly dependent on the work performed.

The power of the electric current is numerically equal to the ratio of the work done to the time during which this work was done. Electrical power is similar in definition to mechanical power, but is denoted by the letter P.

From the definition of power follows the formula:

P = A/t, where:

• P – electric current power;
• A – work performed by current;
• t is the time during which the electric current was operating.

If you replace the numerator in this formula with U*I*t, you get the following equality:

The unit of measurement for electrical power is the Watt (W). 1 W is equal to a current of 1 A with a voltage of 1 V. Watt– a rather small unit, so in practice additional ones are used:

• kW (kilowatt);
• MW (megawatt);
• GW (gigawatt).

The power of the electric current is experimentally determined using an ammeter and a voltmeter or a special device - a wattmeter.

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Each of us has a meter at home, according to which we pay for electricity monthly. We pay for a certain number of kilowatt-hours. What are these kilowatt hours? What exactly are we paying for? Let's figure it out :)

We use electricity for specific purposes. Electric current does some work, and as a result our electrical appliances function. What is the work of electric current? It is known that the work done by the current to move an electric charge on a certain section of the circuit is numerically equal to the voltage on this section. If the charge differs, for example, in big side, then, accordingly, more work will be done.

Work of current on a section of a circuit: formula

So, we come to the conclusion that the work done by the current is equal to the product of the voltage in a section of the electrical circuit and the amount of charge. The charge, as is known, can be found by multiplying the current strength and the time the current passes. So, we get the formula for determining the work of the current:

A=Uq , q=It , we get A=UIt ;

where A is work, U is voltage, I is current, q is charge, t is time.

The current work is measured in joules (1 J). 1 J = 1 V * 1 A * 1 s. That is, to measure the work done by the current, we need three instruments: ammeter, voltmeter and clock. Electricity meters that are installed in apartments seem to combine all of the above-mentioned devices in one. They measure the work done by current. The work of the current in our apartment is the energy that it expended on all devices connected to the apartment’s network. This is what we pay for. However, we pay not by joules, but by kilowatt-hours. Where do these units come from?

Electric current power

To understand this issue, we need to consider one more concept - the power of the electric current. Current power is the work done by current per unit time. That is, power can be found by dividing work by time. And work, as we already know, is the product of current, voltage and time. Thus, the time will be reduced, and we will obtain the product of current and voltage. For current power, the formula will be as follows:

P=A/t , A=UIt , we get P=UIt/t , that is, P=UI ;

where P is the current power. Power is measured in watts (1 W). Multiple quantities are used - kilowatts, megawatts.

The work and power of electric current are closely related. In fact, work is the current power at each moment of time, taken over a certain period of time. That is why meters in apartments measure current work not in joules, but in kilowatt-hours. It's just that 1 watt of power is a very small amount of power, and if we paid for watts-per-second, we would pay for tens and hundreds of thousands of such units. To simplify calculations, the unit “kilowatt-hour” was adopted.