Electric current is an ordered movement of an uncompensated electric charge. If this movement occurs in the conductor, then the electric current is called conduction current. Electric current can cause Coulomb forces. The field of these forces is called Coulomb and is characterized by the intensity E cool.
The movement of charges can also arise under the influence of non-electric forces, called external (magnetic, chemical). E st is the field strength of these forces.
An ordered movement of electric charges can also arise without the action of external forces (diffusion, chemical reactions in a current source). For the generality of the reasoning, in this case we will also introduce an effective external field E st.
Full work on moving the charge in the circuit section:
Let us divide both parts of the last equation by the value of the charge moving through this section.
.
Potential difference in the circuit section.
Voltage in a section of a circuit is a value equal to the ratio of the total work done when moving a charge in this section to the magnitude of the charge. Those. VOLTAGE IN THE SECTION OF THE CIRCUIT IS THE TOTAL WORK OF MOVING A SINGLE POSITIVE CHARGE IN THE SECTION.
EMF in this area is called a value equal to the ratio of the work done by non-electric energy sources when moving a charge to the value of this charge. EMF IS THE WORK OF OUTSIDE FORCES TO MOVEMENT A SINGLE POSITIVE CHARGE IN A PART OF THE CHAIN.
Third-party forces in an electric circuit work, as a rule, in current sources. If there is a current source in a section of the circuit, then such a section is called non-uniform.
The voltage at an inhomogeneous section of the circuit is equal to the sum of the potential difference at the ends of this section and the EMF of the sources in it. In this case, the EMF is considered positive if the direction of the current coincides with the direction of action of external forces, i.e. from source minus to plus.
If there are no current sources in the area of interest to us, then in this and only in this case the voltage is equal to the potential difference.
In a closed circuit, for each of the sections that form a closed circuit, you can write:
Because the potentials of the initial and final points are equal, then .
Therefore, (2),
those. the sum of the voltage drops in a closed circuit of any electrical circuit is equal to the sum of the emf.
Let us divide both parts of equation (1) by the length of the section.
Where is the strength of the total field, is the strength of the external field, is the strength of the Coulomb field.
For a homogeneous section of the chain.
Current density means - Ohm's law in differential form. THE CURRENT DENSITY IN A HOMOGENEOUS SECTION OF THE CIRCUIT IS DIRECTLY PROPORTIONAL TO THE STRENGTH OF THE ELECTROSTATIC FIELD IN THE CONDUCTOR.
If a Coulomb and external field acts on a given section of the circuit (an inhomogeneous section of the circuit), then the current density will be proportional to the total field strength:
. Means, .
Ohm's law for an inhomogeneous chain section: THE CURRENT STRENGTH IN A NON-UNIFORM SECTION OF THE CIRCUIT IS DIRECTLY PROPORTIONATE TO THE VOLTAGE IN THIS SECTION AND IS INVERSELY PROPORTIONATE TO ITS RESISTANCE.
If the direction E c t and E cool coincide, then the EMF and the potential difference have the same sign.
In a closed circuit, V=O, because the Coulomb field is conservative.
From here:
where R is the resistance of the external part of the circuit, r is the resistance of the internal part of the circuit (ie current sources).
Ohm's law for a closed circuit: THE CURRENT IN A CLOSED CIRCUIT IS DIRECTLY PROPORTIONATE TO THE EMF OF SOURCES AND IS INVERSE PROPORTIONATELY TO THE FULL RESISTANCE OF THE CIRCUIT.
KIRCHHOFF'S RULES.
For the calculation of branched electrical circuits, Kirchhoff's rules are used.
The point in a circuit where three or more wires intersect is called a node. According to the law of conservation of charge, the sum of currents entering and leaving the node is equal to zero. . (Kirchhoff's first rule). THE ALGEBRAIC SUM OF THE CURRENTS PASSING THROUGH THE NODE IS ZERO.
The current entering the node is considered positive, leaving the node - negative. The directions of the currents in the sections of the circuit can be chosen arbitrarily.
Equation (2) implies that WHEN BYPASSING ANY CLOSED LOOP, THE ALGEBRAIC SUM OF VOLTAGE DROPS IS EQUAL TO THE ALGEBRAIC SUM OF EMF IN THIS CIRCUIT , - (Kirchhoff's second rule).
The direction of the contour bypass is chosen arbitrarily. The voltage in a section of the circuit is considered positive if the direction of the current in this section coincides with the direction of bypassing the circuit. EMF is considered to be positive if, during the bypass along the circuit, the source passes from the negative pole to the positive one.
If the chain contains m nodes, then m-1 equation can be made according to the first rule. Each new equation must include at least one new element. The total number of equations compiled according to the Kirchhoff rules must match the number of segments between the nodes, i.e. with the number of currents.
8.3. Ohm's law
8.3.2. Ohm's law for heterogeneous section and for a complete chain
The electromotive force (EMF) of the source is numerically equal to the work done by external forces to move a single positive charge, and is determined by the ratio:
ℰ \u003d A st q,
where A st is the work of external forces (forces of non-Coulomb origin) to move the charge q.
In the International System of Units, electromotive force (EMF) is measured in volts (1 V).
A section of the circuit is called inhomogeneous (Fig. 8.8) if it includes the EMF of the source, i.e. external forces act on it.
Rice. 8.8
Ohm's law for an inhomogeneous section of a chain has the following form:
I \u003d φ 2 - φ 1 + ℰ R + r,
where I is the current strength; ϕ 1 - potential of point A ; ϕ 2 - potential of point B ; ℰ - EMF of the current source; R - section resistance; r is the internal resistance of the current source.
A complete (closed) circuit is shown in fig. 8.9.
Rice. 8.9
Points A and B indicate the terminals of the EMF source. A closed circuit can be divided into two sections:
- internal - a section containing an EMF source;
- external - a section that does not contain an EMF source.
Direction of electric current:
- in the internal circuit - from "minus" to "plus";
- in the external circuit - from "plus" to "minus".
The current strength in a complete ( closed) circuit (see Fig. 8.9) is determined by Ohm's law (the current strength in a closed circuit containing a current source is directly proportional to the electromotive force of this source and inversely proportional to the sum of external and internal resistances):
I = ℰ R + r,
where I is the current strength; ℰ - electromotive force (EMF) of the source, ℰ = A st / q; A st - the work of external forces (forces of non-Coulomb origin) to move a positive charge q; R is the external resistance of the circuit (load); r is the internal resistance of the current source.
Rice. 8.9
The electromotive force (EMF) of a current source in a closed circuit is the sum
ℰ = IR + Ir,
where IR is the voltage drop (potential difference) in the external section of the circuit; Ir - voltage drop in the source; I - current strength; R is the external resistance of the circuit (load); r is the internal resistance of the current source.
The above equation, written in the form
ℰ − Ir = IR,
shows equality potential difference at the terminals of the current source U r = ℰ − Ir and potential difference on the outer section of the circuit U R = IR, i.e.
U r = U R .
Short circuit in the complete circuit takes place if there is no load in the external circuit, i.e. external resistance is zero: R = 0.
Short circuit current i is determined by the formula
Example 8. The EMF of the current source is 18 V. A resistor is connected to the source, the resistance of which is 2 times greater than the internal resistance of the source. Determine the potential difference at the terminals of the current source.
Solution . The potential difference at the source terminals is determined by the formula
U = ℰ − Ir,
where ℰ is the EMF of the current source; I - current strength in the circuit; r is the internal resistance of the current source.
The current strength is determined by Ohm's law for a complete circuit:
I = ℰ R + r,
We substitute this expression into the formula for calculating the potential difference at the source terminals:
U = ℰ − ℰ r R + r = ℰ (1 − r R + r) = ℰ R R + r .
Taking into account the ratio between the resistances of the resistor and the source (R = 2r), we get
U \u003d 2 ℰ 3.
The calculation gives the value:
U = 2 ⋅ 18 3 = 12 V.
The potential difference at the source terminals is 12 V.
Example 9: The internal resistance of a battery is 1.5 ohms. When shorted to a resistor with a resistance of 6.0 ohms, the battery of cells gives a current of 1.0 A. Find the strength of the short circuit current.
Solution . The strength of the short circuit current is determined by the formula
where ℰ is the EMF of the current source; r is the internal resistance of the current source.
According to Ohm's law for a complete circuit,
I = ℰ R + r,
where R is the resistance of the resistor.
We express from the written formula the EMF of the source and substitute it into the expression for the strength of the short circuit current:
i = I (R + r) r .
Let's do the calculation:
i \u003d 1.0 ⋅ (6.0 + 1.5) 1.5 \u003d 5.0 A.
The short circuit current for a source with the specified values of EMF and internal resistance is 5.0 A.
Example 10. Six identical resistors of 20 ohms each are connected in a circuit as shown in the figure. A source with an EMF equal to 230 V and an internal resistance of 2.5 ohms is connected to the ends of the section. Find the reading of ammeter A2.
Solution . On fig. a shows a circuit diagram, which indicates the currents flowing in its individual sections.
In the section of resistance R 1 current I 1 flows. Further, the current I 1 branches into two parts:
- in the area with resistors connected in series with resistances R 2, R 3 and R 4, current I 2 flows;
- current I 3 flows in the area of resistance R 5 .
In this way,
I 1 \u003d I 2 + I 3.
These sections are interconnected in parallel, so the voltage drops across them are the same:
I 2 R total 2 \u003d I 3 R 5,
where R total 2 is the resistance of the section with series-connected resistors R 2, R 3 and R 4, R total 2 = R 2 + R 3 + R 4 = 3R, R 2 = R 3 = R 4 = R, R 5 = R.
The written equations form a system:
I 1 \u003d I 2 + I 3, I 2 R total 2 \u003d I 3 R 5. )
Taking into account the expressions for R gen2 and R 5, the system takes the form:
I 1 \u003d I 2 + I 3, 3 I 2 \u003d I 3. )
The solution of the system regarding the strength of the current I 2 gives
I 2 \u003d I 1 4 \u003d 0.25 I 1.
This expression determines the desired value - the current strength in the ammeter A2.
The current strength I 1 is determined by Ohm's law for a complete circuit:
I 1 \u003d ℰ R total + r,
where R total is the total resistance of the external circuit (resistors R 1, R 2, R 3, R 4, R 5 and R 6).
Calculate the total resistance of the external circuit.
To do this, we transform the circuit as shown in Fig. b.
Plots R common2 and R 5 are connected in parallel, their total resistance
R total 1 \u003d R total 2 R 4 R total 2 + R 4 \u003d 3 R 4 \u003d 0.75 R,
where R total2 = 3R; R4=R.
Once again, we transform the circuit as shown in Fig. in .
Sections with resistances R 1 , R common 1 and R 6 are connected in series, their total resistance
R total \u003d R 1 + R total 1 + R 6 \u003d R + 0.75 R + R \u003d 2.75 R,
where R total 1 = 0.75R and R 1 = R 6 = R.
The desired current strength is determined by the formula
I 2 \u003d 0.25 I 1 \u003d 0.25 ℰ 2.75 R + r.
Let's do the calculation:
I 2 \u003d 0.25 ⋅ 230 2.75 ⋅ 20 + 2.5 \u003d 1.0 A.
Ammeter A2 will show a current of 1.0 A.
Example 11. Six identical resistors of 20 ohms each and two capacitors with electric capacitances of 15 and 25 microfarads are connected in a circuit as shown in the figure. A source with an EMF equal to 0.23 kV and an internal resistance of 3.5 ohms is connected to the ends of the section. Find the potential difference between the plates of the second capacitor.
Solution . No current flows between points A and B, since capacitors are included in the circuit between these points. To determine the potential difference between the indicated points, we simplify the circuit by excluding the AB section from consideration.
On fig. a diagram of a simplified circuit is shown.
Current flows through resistors R 1 , R 2 , R 3 , R 4 and R 6 connected in series. The total resistance of such a circuit is:
R total \u003d R 1 + R 2 + R 3 + R 4 + R 6 \u003d 5R,
where R 1 = R 2 = R 3 = R 4 = R 6 = R.
The current strength I is determined by Ohm's law for a complete circuit:
I = ℰ R total + r = ℰ 5 R + r,
where ℰ is the EMF of the current source, ℰ = 0.23 kV; r is the internal resistance of the current source, r = 3.5 Ohm; Rtot is the total resistance of the circuit, Rtot = 5R.
Calculate the voltage drop between points A and B.
Between points A and B there are resistors with resistances R 2, R 3 and R 4, connected in series, as shown in fig. b.
Their total resistance
R total 1 \u003d R 2 + R 3 + R 4 \u003d 3R.
The voltage drop across the specified resistors is determined by the formula
U AB \u003d IR total1,
or explicitly,
U AB \u003d 3 ℰ R 5 R + r.
Between points A and B, a battery of capacitors C 1 and C 2 is connected, connected in series, as shown in fig. in .
Their total electrical capacity
C total \u003d C 1 C 2 C 1 + C 2,
where C 1 is the capacitance of the first capacitor, C 1 = 15 uF; C 2 - electric capacitance of the second capacitor, C 2 = 25 uF.
Potential difference on the battery plates:
U total = q C total,
where q is the charge on the plates of each of the capacitors (coincides with the battery charge when the capacitors are connected in series), q = = C 1 U 1 = C 2 U 2; U 1 - potential difference between the plates of the first capacitor; U 2 - potential difference between the plates of the second capacitor (desired value).
In explicit form, the potential difference between the capacitor plates is determined by the formula
U total = C 2 U 2 C total = (C 1 + C 2) U 2 C 1.
The voltage drop across the resistors between points A and B coincides with the potential difference across the capacitor bank connected to the indicated points:
U AB \u003d U total.
This equality, written explicitly
3 ℰ R 5 R + r \u003d (C 1 + C 2) U 2 C 1,
allows you to get an expression for the desired value:
U 2 \u003d 3 ℰ R C 1 (5 R + r) (C 1 + C 2) .
Let's do the calculation:
U 2 = 3 ⋅ 0.23 ⋅ 10 3 ⋅ 20 ⋅ 15 ⋅ 10 - 6 (5 ⋅ 20 + 3.5) (15 + 25) ⋅ 10 - 6 = 50 V.
Between the plates of the second capacitor, the potential difference is 50 V.
.Conductors that obey Ohm's law are called linear.
Graphical dependence of current strength on voltage (such graphs are called volt-ampere characteristics, abbreviated VAC) is depicted by a straight line passing through the origin. It should be noted that there are many materials and devices that do not obey Ohm's law, such as 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.
1.5. Series and parallel connection of conductors
Conductors in DC electrical circuits can be connected in series and in parallel.
When the conductors are connected in series, the end of the first conductor is connected to the beginning of the second, etc. In this case, the current strength is the same in all conductors , but the voltage at the ends of the entire circuit is equal to the sum of the voltages across all the wires connected in series. For example, for three conductors connected in series 1, 2, 3 (Fig. 4) with electrical resistances , and we get:
 Rice. 4. |
.
According to Ohm's law for a chain section:
U 1 = IR 1, U 2 = IR 2, U 3 = IR 3 and U=IR(1)
where is the total resistance of a section of a circuit of series-connected conductors. From the expression and (1) we will have 
. In this way,
R \u003d R 1 + R 2 + R 3 . (2)
When the conductors are connected in series, their total electrical resistance is equal to the sum of the electrical resistances of all conductors.
From relations (1) it follows that the voltages on the series-connected conductors are directly proportional to their resistances:
 Rice. five. |
When conductors 1, 2, 3 are connected in parallel (Fig. 5), their beginnings and ends have common points of connection to the current source.
In this case, the voltage on all conductors is the same, and the current strength in an unbranched circuit is equal to the sum of the current strengths in all parallel-connected conductors 
.
For three conductors connected in parallel with resistances , and based on Ohm's law for a section of the circuit, we write
Denoting the total resistance of a section of an electrical circuit of three parallel-connected conductors through , for the current strength in an unbranched circuit, we obtain
, (5)
then from expressions (3), (4) and (5) it follows that:
. (6)
When conductors are connected in parallel, the reciprocal of the total resistance of the circuit is equal to the sum of the reciprocals of the resistances of all parallel-connected conductors.
The parallel switching method is widely used to connect electric lighting lamps and household appliances to the electrical network.
1.6. Resistance measurement
What are the features of measuring resistance?
When measuring low resistances, the measurement result is affected by the resistance of the connecting wires, contacts and contact thermo-emf. When measuring high resistances, it is necessary to take into account volume and surface resistances and take into account or eliminate the influence of temperature, humidity and other causes. Measurement of the resistance of liquid conductors or conductors with high humidity (ground resistance) is carried out on alternating current, since the use of direct current is associated with errors caused by the phenomenon of electrolysis.
Measurement of the resistance of solid conductors is carried out at direct current. Since, on the one hand, errors associated with the influence of the capacitance and inductance of the measurement object and the measuring circuit are excluded, on the other hand, it becomes possible to use magnetoelectric system devices with high sensitivity and accuracy. Therefore, megohmmeters are produced at direct current.
1.7. Kirchhoff rules
Kirchhoff rules– relationships that are performed between currents and voltages in sections of any electrical circuit.
Kirchhoff's rules do not express any new properties of a stationary electric field in conductors with current compared to Ohm's law. The first of them is a consequence of the law of conservation of electric charges, the second is a consequence of Ohm's law for an inhomogeneous section of the circuit. However, their use greatly simplifies the calculation of currents in branched circuits.
Kirchhoff's first rule
In branched chains, nodal points can be distinguished ( nodes ), in which at least three conductors converge (Fig. 6). The currents flowing into the node are considered to be positive; arising from the node - negative.
In the nodes of the DC circuit, no accumulation of charges can occur. This implies Kirchhoff's first rule:the algebraic sum of the strengths of the currents converging in the node is equal to zero:
Or in general terms:
In other words, how much current flows into the node, so much flows out of it. This rule follows from the fundamental law of conservation of charge.
Kirchhoff's second rule
In a branched chain, you can always select a certain number of closed paths, consisting of homogeneous and heterogeneous sections. Such closed paths are called loops. . Different currents can flow in different parts of the selected circuit. On fig. 7 shows a simple example of a branched chain. The circuit contains two nodes a and d, in which the same currents converge; so only one of the nodes is independent (a or d).
The circuit contains one independent node (a or d) and two independent circuits (for example, abcd and adef)
Three contours can be distinguished in the circuit abcd, adef and abcdef. Of these, only two are independent (for example, abcd and adef), since the third does not contain any new sections.
Kirchhoff's second rule is a consequence of the generalized Ohm's law.
Let us write the generalized Ohm's law for the segments that make up one of the contours of the circuit shown in fig. 8, for example, abcd. To do this, for each section, you need to set positive current direction And positive direction of contour traversal. When writing the generalized Ohm's law for each of the sections, it is necessary to observe certain "rules of signs", which are explained in Fig. 8.
For sections of the contour abcd, the generalized Ohm's law is written as:
for plotbc: 
for plot da: 
Adding the left and right sides of these equalities and taking into account that 
, we get:
Similarly, for the contour adef one can write:
According to Kirchhoff's second rule:
in any simple closed circuit, arbitrarily chosen in a branched electrical circuit, the algebraic sum of the products of the current strengths and the resistances of the corresponding sections is equal to the algebraic sum of the EMF present in the circuit:
,
where is the number of sources in the circuit, is the number of resistances in it.
When drawing up the stress equation for the loop, you need to choose the positive direction of bypassing the loop.
If the directions of the currents coincide with the selected direction of bypassing the circuit, then the current strengths are considered positive. EMF are considered positive if they create currents co-directional with the direction of bypassing the circuit.
A special case of the second rule for a circuit consisting of one circuit is Ohm's law for this circuit.
The procedure for calculating branched DC circuits
The calculation of a branched DC electrical circuit is performed in the following order:
arbitrarily choose the direction of currents in all sections of the circuit;
write down independent equations, according to the first Kirchhoff rule, where is the number of nodes in the chain;
arbitrarily closed contours are chosen so that each new contour contains at least one section of the circuit that is not included in the previously selected contours. They write down the second rule of Kirchhoff for them.
In a branched chain containing nodes and sections of the chain between neighboring nodes, the number of independent equations corresponding to the contour rule is .
Based on the Kirchhoff rules, a system of equations is compiled, the solution of which allows you to find the current strengths in the branches of the circuit.
Example 1:
Kirchhoff's first and second rules written for all independent nodes and circuits of a branched circuit, together give the necessary and sufficient number of algebraic equations for calculating the values of voltages and currents in an electrical circuit. For the circuit shown in Fig. 7, the system of equations for determining three unknown currents , and has the form:
,
,
.
Thus, the Kirchhoff rules reduce the calculation of a branched electrical circuit to the solution of a system of linear algebraic equations. This solution does not cause fundamental difficulties, however, it can be very cumbersome even in the case of fairly simple circuits. If, as a result of the solution, the current strength in some section turns out to be negative, then this means that the current in this section goes in the direction opposite to the chosen positive direction.
Conditions for the existence of direct electric current.
Conditions for the existence of direct current. Electromotive force. Ohm's law for a closed circuit and for the active section of the circuit.
Electricity- ordered movement of charged particles under the action of electric field forces or external forces. The direction of motion of positively charged particles is chosen as the current direction.
Electric current is called constant if the strength of the current and its direction do not change over time.
For the existence of a direct electric current, the presence of free charged particles and the presence of a current source are necessary. in which the conversion of any type of energy into the energy of an electric field is carried out.
The electromotive force of the current source is the ratio of the work of external forces to the value of the positive charge transferred from the negative pole of the current source to the positive.
The current strength in a homogeneous section of the circuit is directly proportional to the voltage at a constant section resistance and inversely proportional to the section resistance at a constant voltage.
Where U is the voltage in the section, R is the resistance of the section.
Ohm's law for an arbitrary section of the circuit containing a direct current source.
where φ1 - φ2 + ε \u003d U is the voltage at a given section of the circuit, R is the electrical resistance of a given section of the circuit.
Ohm's law for a complete circuit.
The current strength in a complete circuit is equal to the ratio of the electromotive force of the source to the sum of the resistances of the external and internal sections of the circuit.
where R is the electrical resistance of the outer section of the circuit, r is the electrical resistance of the inner section of the circuit.
The law of conservation of charge and Kirchhoff's rule (conclusion).
The law of conservation of electric charge states that the algebraic sum of the charges of an electrically closed system is conserved.
Kirchhoff's first law follows from the law of conservation of charge. It consists in the fact that the algebraic sum of the currents converging at any node is zero.
Kirchhoff's second rule obtained from the generalized Ohm's law for branched circuits.
In any closed circuit, arbitrarily chosen in a branched electrical circuit, the algebraic sum of the products of the current strengths II on resistance Ri the corresponding sections of this circuit is equal to the algebraic sum of the emf. Ek encountered in this circuit.
Actually, we use pure mathematics. Take, for example, the circuit shown in Fig. 1. The contour consists of three sections. For each section, you can write your own formula based on Ohm's law, but one important point must be taken into account.
Firstly, it is required to write these formulas not as independent ones, but as a system of equations, since the sections of the circuit are the constituent parts of the contour.
Secondly, in order to determine the signs, it is necessary to take into account the direction of the currents and the EMF of the sources. To do this, you need to select the direction of the contour bypass. All currents that coincide in direction with the direction of bypassing the circuit are considered positive, and those that do not coincide with the direction of bypass are considered negative. Current sources are considered positive if they produce current directed towards the bypass of the loop.
Thirdly, the direction of bypassing the contour is chosen arbitrarily. We will take the direction clockwise.
Based on the foregoing, we write down the system of equations. We start with section AB, then BC and CA.
Now it remains to add these equations term by term:
Let's see what we got. On the left in our equation is the sum of the products of currents and the resistance of the corresponding sections, on the right is the sum of all EMF in the circuit. If we take any circuit with any number of sections and sources, then we will still end up with an equation, where on the left there will be the sum of the products of currents and the resistance of the corresponding sections, and on the right - the sum of all EMF in the circuit. Thus, we can write our reasoning in the following form: ------à
The last equation expresses Kirchhoff's second rule.
Electromotive force.
If an electric field is created in the conductor and no measures are taken to maintain it, then the movement of current carriers will very quickly lead to the fact that the field inside the conductor will disappear and the current will stop. In order to maintain the current for a long time, it is necessary to continuously remove the positive charges brought here by the current from the end of the conductor with a lower potential j 2 and transfer them to the end with a higher potential (Fig. 56.1).
The electric field created in the conductor cannot carry out such a transfer of charges. In order for a direct current to exist, the action of some other forces (not Coulomb) is necessary, moving charges against electric forces and maintaining the constancy of electric fields. These can be magnetic forces, it is possible to separate charges due to chemical reactions, diffusion of charge carriers in an inhomogeneous medium, etc. To emphasize the difference between these forces and the forces of the Coulomb interaction, it is customary to denote them by the term outside forces. Devices in which free charges move under the action of external forces are called current sources. These include electromagnetic generators, thermoelectric generators, solar panels. A separate group consists of chemical current sources: galvanic cells, batteries and fuel cells.
The action of external forces can be characterized by introducing the concept of the field strength of external forces: .
The work of external forces to move the charge q on the site dl can be expressed as follows:
throughout the length of the section l:
. (56.1)
The value equal to the ratio of the work of external forces to move the charge to this charge is called electromotive force(EMF):
. (56.2)
In a conductor through which current flows, the electric field strength is the sum of the field strengths of the Coulomb forces and external forces:
Then for the current density we can write
Let us replace the vectors with their projections onto the direction of the closed contour and multiply both sides of the equation by dl:
By substituting , , we reduce the resulting equation to the form
We integrate the resulting expression over the length of the electric circuit:
The integral on the left side of the equation is the resistance R plots 1-2. On the right side of the equation, the value of the first integral is numerically equal to the work of the Coulomb forces to move a unit charge from point 1 to point 2 - this is the potential difference. The value of the second integral is numerically equal to the work of external forces to move a unit charge from point 2 to point 1 - this is electromotive force. In accordance with this, equation (56.3) is reduced to the form
Value IR, equal to the product of the current strength and the resistance of the circuit section, is called voltage drop on the chain section. Voltage drop numerically equal to the work done when moving a unit charge by external forces and the forces of the electric field (Coulomb).
The section of the circuit containing the EMF is called an inhomogeneous section. We find the current strength in such a section from the formula (56.4):
Considering that the current source can be included in the circuit section in two ways, we will replace the sign in front of the EMF with "±":
Expression (56.5) is Ohm's law for an inhomogeneous section of a circuit. The signs "+" or "-" take into account how external forces affect the flow of current in the indicated direction: they contribute or hinder (Fig. 56.2).
If the circuit section does not contain EMF, i.e., is homogeneous, then from formula (56.5) it follows that
From formula (56.5) it follows
where IR- voltage drop on the outer section of the circuit, Ir- voltage drop in the internal section of the circuit.
Consequently, The EMF of the current source is equal to the sum of the voltage drops in the external and internal sections of the circuit.
