Electrical circuits. Electromotive force. Formulas, laws, rules, examples on TOE What is the electromotive force of a current source

- EMF.
EMF is not a force in the Newtonian sense (an unfortunate name for a quantity, retained as a tribute to tradition).
ε i occurs when it changes magnetic flux F penetrating the contour.

Additionally see the presentation "Electromagnetic induction", as well as the videos "Electromagnetic induction", "Faraday's experiment", cartoons "Electromagnetic induction", "Rotation of the frame in a magnetic field (generator)"

- EMF of induction during the movement of one of the conductors of the circuit (so that F changes). In this case, the conductor length l, moving at a speed v becomes a power source.

- EMF of induction in a circuit rotating in a magnetic field with a speed ω.

Other formulas where EMF occurs:

- Ohm's law for a complete circuit. In a closed circuit, the EMF generates an electric current I.

The direction of the induction current is determined according to the rules:
- rule Lenz- induction current arising in a closed circuit counter acts to change the magnetic flux that caused this current;
- for a conductor moving in a magnetic field, it is sometimes easier to use the rule right hand- if you place the open right hand palm so that into it included magnetic field lines IN, A thumb set aside pointed direction of speed v, That four fingers hands will point direction of induction current I.

- EMF of self-induction when the current in the conductor changes.

If the poles of a charged capacitor are closed to each other, then under the influence of the accumulated between its plates, in the external circuit of the capacitor in the direction from the positive pole to the negative, the movement of charge carriers - electrons begins.

However, during the discharge process, the field acting on moving charged particles rapidly weakens until it disappears completely. Therefore, the flow of electric current that has arisen in the discharge circuit has a short-term character and the process quickly decays.

To maintain current in a conducting circuit for a long time, devices are used that are inaccurately called in everyday life (in a strictly physical sense, this is not the case). Most often, these sources are chemical batteries.

Due to the electrochemical processes occurring in them, opposite forces accumulate at their terminals. Forces of a non-electrostatic nature, under the influence of which such a distribution of charges is carried out, are called external forces.

The following example will help to understand the nature of the concept of EMF of a current source.

Imagine a conductor in an electric field, as shown in the figure below, that is, in such a way that an electric field also exists inside it.

It is known that under the influence of this field, an electric current begins to flow in the conductor. The question now arises as to what happens to charge carriers when they reach the end of a conductor, and whether this current will remain the same over time.

We can easily conclude that in an open circuit, as a result of the influence of the electric field, charges will accumulate at the ends of the conductor. In this regard, it will not remain constant and the movement of electrons in the conductor will be very short-lived, as shown in the figure below.

Thus, in order to maintain a constant current flow in a conducting circuit, this circuit must be closed, i.e. be in the shape of a loop. However, even this condition is not sufficient to maintain the current, since the charge always moves towards a lower potential, and the electric field always does positive work on the charge.

Now, after traveling through a closed circuit, when the charge returns to the starting point where it started its journey, the potential at this point should be the same as it was at the beginning of the movement. However, the flow of current is always associated with a loss of potential energy.

Therefore, we need some external source in the circuit, on the terminals of which a potential difference is maintained, which increases the energy of the movement of electric charges.

Such a source allows the charge to travel from a lower potential to a higher one in the direction opposite to the movement of electrons under the action of an electrostatic force trying to push the charge from a higher potential to a lower one.

This force, which causes the charge to move from a lower to a higher potential, is commonly called a current source - this is a physical parameter that characterizes the work expended on moving charges inside the source by external forces.

As devices that provide the EMF of the current source, as already mentioned, batteries are used, as well as generators, thermoelements, etc.

We now know that, due to its internal emf, it provides a potential difference between the outputs of the source, contributing to the continuous movement of electrons in the opposite direction to the electrostatic force.

The EMF of the current source, the formula of which is given below, as well as the potential difference, is expressed in volts:

E \u003d A st / Δq,

where A st is the work of external forces, Δq is the charge moved inside the source.

To maintain a given value of electric current in a conductor, some external source of energy is required, which would always provide the required potential difference at the ends of this conductor. Such sources of energy are the so-called sources of electric current, which have some given electromotive force, which is able to create and maintain a potential difference for a long time.

The electromotive force or abbreviated EMF is indicated by the Latin letter E. Unit of measurement is volt. Thus, in order to obtain a continuous movement of electric current in a conductor, an electromotive force is needed, that is, a source of electric current is required.

Historical reference. The first such source of current in electrical engineering was the "voltaic column", which was made of several copper and zinc circles lined with cowhide soaked in a weak acid solution. Thus, the simplest way to obtain an electromotive force is considered to be the chemical interaction of a number of substances and materials, as a result of which chemical energy is converted into electrical energy. Power sources in which the electromotive force of the EMF is generated by a similar method are called chemical current sources.

Today, chemical power sources - batteries and all possible types of batteries - are widely used in electronics and electrical engineering, as well as in the electric power industry.

Various types of generators are also common, which, as the only source, are able to supply industrial enterprises with electrical energy, provide lighting to cities, to operate railway, tram and metro systems.

EMF acts in exactly the same way both on chemical sources and on generators. Its action is to create a potential difference at each of the power supply terminals and maintain it for the entire necessary time. The terminals of the power supply are called poles. At one of the poles, a shortage of electrons is always created, i.e. such a pole has a positive charge and is marked " + ”, and on the other hand, on the contrary, an increased concentration of free electrons is created, i.e. this pole has a negative charge and is marked with the sign " - ».

EMF sources are used to connect various devices and devices that are consumers of electrical energy. With the help of wires, consumers are connected to the poles of current sources, so that a closed electrical circuit is obtained. The potential difference that has arisen in a closed electrical circuit has received a name and is denoted by the Latin letter "U". Voltage unit one volt. For example, the entry U=12 V indicates that the voltage of the EMF source is 12 V.

In order to measure voltage or emf, a special measuring device is used - .

If it is necessary to make correct measurements of EMF or power supply voltage, the voltmeter is connected directly to the poles. With an open electrical circuit, the voltmeter will show the EMF. When the circuit is closed, the voltmeter will display the voltage value at each terminal of the power supply. PS: The current source always develops more EMF than the voltage at the terminals.

Video lesson: EMF

Video lesson: Electromotive force from a physics teacher

The voltage at each of the terminals of the current source is less than the electromotive force by the value of the voltage drop that occurs on the internal resistance of the power source:

For ideal sources, the voltage at the terminals does not depend on the amount of current drawn.

All sources of electromotive force have parameters that characterize them: open circuit voltage U xx, short circuit current I kz and internal resistance (for a DC source R ext). U xx is the voltage when the source current is zero. At an ideal source at any current U xx \u003d 0. I kz is the current at zero voltage. For an ideal voltage source, it is infinite I kz = ∞. Internal resistance is determined from the ratios . Since the voltage at an ideal voltage source is constant at any current ∆U = 0, then its internal resistance also has zero values.

R ext \u003d ΔU / ΔI \u003d 0;

With a positive voltage and current, the source sends its electrical energy to the circuit and operates in the generator mode. With the opposite current flow, the source receives electrical energy from the circuit and operates in the receiver mode.

In the case of an ideal current source, its value does not depend on the magnitude of the voltage at its terminals: i = const.

Since the current from an ideal current source is unchanged ∆I = 0, then it has an internal resistance equal to infinity.

R ext \u003d ΔU / ΔI \u003d ∞

With a positive voltage and current, the source sends energy into the circuit and operates in generator mode. In the opposite direction, it works in receiver mode.

With a real source of electromotive force, the voltage across the terminals decreases as the current increases. Such a CVC corresponds to an equation for determining the voltage at any current value.

U \u003d U xx - R ext × I,

Where , is calculated by the formula

R ext \u003d ΔU / Δ I≠ 0

It can also be calculated via U xx And I kz

R vn \u003d U xx / II kz

When a current source is connected to any closed circuit, the area bounded by this circuit begins to be pierced by external magnetic lines of force. Each line of force, from the outside, crossing the conductor, inducing an EMF of self-induction in it.

>>Physics: Electromotive force

Any current source is characterized by electromotive force, or, for short, EMF. So, on a round battery for a flashlight it is written: 1.5 V. What does this mean?
Connect two metal balls carrying charges of opposite signs with a conductor. Under the influence of the electric field of these charges, an electric current arises in the conductor ( fig.15.7). But this current will be very short-lived. The charges quickly neutralize each other, the potentials of the balls become the same, and the electric field disappears.
Third party forces. In order for the current to be constant, it is necessary to maintain a constant voltage between the balls. This requires a device current source), which would move the charges from one ball to another in the direction opposite to the direction of the forces acting on these charges from the electric field of the balls. In such a device, in addition to electric forces, the charges must be affected by forces of non-electrostatic origin ( fig.15.8). Only one electric field of charged particles ( Coulomb field) is not capable of maintaining a constant current in the circuit.

Any forces acting on electrically charged particles, with the exception of forces of electrostatic origin (i.e., Coulomb), are called outside forces.
The conclusion about the need for external forces to maintain a constant current in the circuit will become even more obvious if we turn to the law of conservation of energy. The electrostatic field is potential. The work of this field when moving charged particles in it along a closed electric circuit is zero. The passage of current through the conductors is accompanied by the release of energy - the conductor heats up. Therefore, there must be some source of energy in the circuit that supplies it to the circuit. In it, in addition to the Coulomb forces, third-party, non-potential forces must necessarily act. The work of these forces along a closed contour must be different from zero. It is in the process of doing work by these forces that charged particles acquire energy inside the current source and then give it to the conductors of the electric circuit.
Third-party forces set in motion charged particles inside all current sources: in generators at power plants, in galvanic cells, batteries, etc.
When the circuit is closed, an electric field is created in all conductors of the circuit. Inside the current source, the charges move under the influence of external forces vs. Coulomb forces(electrons from a positively charged electrode to a negative one), and in the external circuit they are set in motion by an electric field (see Fig. fig.15.8).
The nature of extraneous forces. The nature of outside forces can be varied. In power plant generators, external forces are forces acting from the magnetic field on electrons in a moving conductor.
In a galvanic cell, for example, the Volta cell, chemical forces act. The Volta element consists of zinc and copper electrodes placed in a solution of sulfuric acid. Chemical forces cause the zinc to dissolve in the acid. Positively charged zinc ions pass into the solution, and the zinc electrode itself becomes negatively charged. (Copper dissolves very little in sulfuric acid.) A potential difference appears between the zinc and copper electrodes, which determines the current in a closed electrical circuit.
The action of external forces is characterized by an important physical quantity called electromotive force(abbreviated EMF).
The electromotive force of the current source is equal to the ratio of the work of external forces when moving the charge along a closed circuit to the value of this charge:

Electromotive force, like voltage, is expressed in volts.
We can also talk about the electromotive force in any part of the circuit. This is the specific work of external forces (the work of moving a unit charge) not in the entire circuit, but only in this area. Electromotive force of a galvanic cell is a value numerically equal to the work of external forces when moving a unit positive charge inside the element from one pole to another. The work of external forces cannot be expressed in terms of the potential difference, since external forces are non-potential and their work depends on the shape of the charge trajectory. So, for example, the work of external forces when moving a charge between the terminals of a current source outside the source itself is equal to zero.
Now you know what EMF is. If 1.5 V is written on the battery, then this means that third-party forces (chemical in this case) do 1.5 J of work when moving a charge of 1 C from one pole of the battery to another. Direct current cannot exist in a closed circuit if external forces do not act in it, that is, there is no EMF.

???
1. Why is the electric field of charged particles (Coulomb field) unable to maintain a constant electric current in the circuit?
2. What forces are usually called third-party?
3. What is called electromotive force?

G.Ya.Myakishev, B.B.Bukhovtsev, N.N.Sotsky, Physics Grade 10

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EMF. Numerically, the electromotive force is measured by the work done by a source of electrical energy in the transfer of a single positive charge throughout a closed circuit. If the source of energy, doing work A, provides transfer throughout the closed charge circuit q, then its electromotive force ( E) will be equal to

The SI unit for electromotive force is the volt (v). A source of electrical energy has an emf of 1 volt if, when moving through the entire closed circuit of a charge of 1 coulomb, work is done equal to 1 joule. The physical nature of electromotive forces in different sources is very different.

self induction- the occurrence of EMF induction in a closed conducting circuit when the current flowing through the circuit changes. When the current changes I in the circuit, the magnetic flux also changes proportionally B through the surface bounded by this contour. A change in this magnetic flux, due to the law of electromagnetic induction, leads to the excitation of an inductive emf in this circuit E. This phenomenon is called self-induction.

The concept is related to the concept of mutual induction, being its special case.

Power. Power is the work done per unit of time. Power is the work done per unit of time, i.e. to transfer charge to el. the circuit or in a closed circuit expends energy, which is equal to A \u003d U * Q, since the amount of electricity is equal to the product of the current strength, then Q \u003d I * t, it follows that A \u003d U * I * t. P=A/t=U*Q/t=U*I=I*t*R=P=U*I(I)

1W=1000mV, 1kW=1000V, Pr=Pp+Po power balance formula. Pr-generator power(EMF)

Pr=E*I, Pp=I*U useful power, i.e. power that is consumed without loss. Po=I^2*R-lost power. In order for the circuit to function, it is necessary to maintain a balance of power in the electric circuit.

12.Ohm's law for a circuit section.

The current strength in a circuit section is directly proportional to the voltage at the ends of this conductor and inversely proportional to its resistance:
I=U/R;

1)U=I*R, 2)R=U/R

13.Ohm's law for a complete circuit.

The current strength in the circuit is proportional to the EMF acting in the circuit and inversely proportional to the sum of the circuit resistances and the internal resistance of the source.

EMF of the voltage source (V), - current in the circuit (A), - resistance of all external elements of the circuit (Ohm), - internal resistance of the voltage source (Ohm) .1) E \u003d I (R + r)? 2)R+r=E/I

14.Series, parallel connection of resistors, equivalent resistance. Distribution of currents and voltage.

When connected in series several resistors end of the first resistor connected to the beginning of the second, the end of the second - to the beginning of the third, etc. With such a connection passes through all elements of the series circuit
the same current I.

Ue=U1+U2+U3. Therefore, the voltage U at the source terminals is equal to the sum of the voltages across each of the resistors connected in series.

Re=R1+R2+R3, Ie=I1=I2=I3, Ue=U1+U2+U3.

When connected in series, the resistance of the circuit increases.

Parallel connection of resistors. A parallel connection of resistances is such a connection in which the beginnings of the resistances are connected to one terminal of the source, and the ends to the other terminal.

The total resistance of the resistors connected in parallel is determined by the formula

The total resistance of resistors connected in parallel is always less than the smallest resistance included in this connection.

when the resistances are connected in parallel, the voltages across them are equal to each other. Ue=U1=U2=U3 Current I flows into the circuit, and currents I 1, I 2, I 3 flow out of it. Since moving electric charges do not accumulate at a point, it is obvious that the total charge flowing to the branch point is equal to the total charge flowing away from it: Ie=I1+I2+I3 Therefore, the third property of a parallel connection can be formulated as follows: The magnitude of the current in the unbranched part of the circuit is equal to the sum of the currents in the parallel branches. For two parallel resistors: