Ohm's law- a physical law that defines the relationship between electrical quantities - voltage, resistance and current for conductors.
It was first discovered and described in 1826 by the German physicist Georg Ohm, who showed (using a galvanometer) the quantitative relationship between electromotive force, electric current and the properties of the conductor as a proportional relationship.
Subsequently, the properties of a conductor capable of resisting electric current based on this dependence began to be called electrical resistance (Resistance), denoted in calculations and diagrams by the letter R and measured in Ohms in honor of the discoverer.
The source of electrical energy itself also has internal resistance, which is usually denoted by the letter r.
Ohm's law for a circuit section
From the school physics course, everyone is well aware of the classical interpretation of Ohm’s Law:
The current strength in a conductor is directly proportional to the voltage at the ends of the conductor and inversely proportional to its resistance.
This means if there is resistance to the ends of the conductor R= 1 ohm voltage applied U= 1 Volt, then the magnitude of the current I in the conductor will be equal to 1/1 = 1 Ampere.
This leads to two more useful relationships:
If a current of 1 Ampere flows in a conductor with a resistance of 1 Ohm, then at the ends of the conductor there is a voltage of 1 Volt (voltage drop).
If there is a voltage of 1 Volt at the ends of the conductor and a current of 1 Ampere flows through it, then the resistance of the conductor is 1 Ohm.
The above formulas in this form can be applied to alternating current only if the circuit consists only of active resistance R.
In addition, it should be remembered that Ohm's Law is valid only for linear circuit elements.
A simple online calculator is provided for practical calculations.
Ohm's law. Calculation of voltage, resistance, current, power.
After resetting, enter any two known parameters.
Ohm's law for a closed circuit
If you connect an external circuit with a resistance to the power source R, current will flow in the circuit taking into account the internal resistance of the source:
I- Current strength in the circuit.
- Electromotive force (EMF) - the magnitude of the power source voltage independent of the external circuit (without load). Characterized by the potential energy of the source.
r- Internal resistance of the power supply.
For electromotive force, external resistance R and internal r are connected in series, which means the magnitude of the current in the circuit is determined by the value of the emf and the sum of the resistances: I = /(R+r) .
The voltage at the terminals of the external circuit will be determined based on the current and resistance R relationship, which has already been discussed above: U = IR.
Voltage U, when connecting the load R, will always be less than the EMF by the value of the product I*r, which is called the voltage drop across the internal resistance of the power supply.
We encounter this phenomenon quite often when we see partially discharged batteries or accumulators in operation.
As the discharge progresses, their internal resistance increases, therefore, the voltage drop inside the source increases, which means the external voltage decreases U = - I*r.
The lower the current and internal resistance of the source, the closer in value its EMF and voltage at its terminals U.
If the current in the circuit is zero, therefore = U. The circuit is open, the emf of the source is equal to the voltage at its terminals.
In cases where the internal resistance of the source can be neglected ( r≈ 0), the voltage at the source terminals will be equal to the EMF ( ≈ U) regardless of the external circuit resistance R.
This power source is called voltage source.
Ohm's law for alternating current
If there is inductance or capacitance in an AC circuit, its reactance must be taken into account.
In this case, the entry for Ohm's Law will look like:
Here Z- total (complex) resistance of the circuit - impedance. It includes active R and reactive X components.
Reactance depends on the ratings of the reactive elements, on the frequency and shape of the current in the circuit.
You can learn more about complex resistance on the impedance page.
Taking into account the phase shift φ
created by reactive elements, Ohm's Law is usually written for sinusoidal alternating current in a complex form:
Complex current amplitude. = I amp e jφ
- complex voltage amplitude. = U amp e jφ
- complex resistance. Impedance.
φ
- phase shift angle between current and voltage.
e- constant, the base of the natural logarithm.
j- imaginary unit.
I amp, U amp- amplitude values of sinusoidal current and voltage.
Nonlinear elements and circuits
Ohm's law is not a fundamental law of nature and can be applied in limited cases, for example, for most conductors.
It cannot be used to calculate voltage and current in semiconductor or vacuum devices, where this dependence is not proportional and can only be determined using the current-voltage characteristic (volt-ampere characteristic). This category of elements includes all semiconductor devices(diodes, transistors, zener diodes, thyristors, varicaps, etc.) and vacuum tubes.
Such elements and the circuits in which they are used are called nonlinear.
For an electrician and electronics engineer, one of the basic laws is Ohm's Law. Every day, work poses new challenges for a specialist, and often it is necessary to select a replacement for a burnt out resistor or group of elements. An electrician often has to change cables; to choose the right one, you need to “estimate” the current in the load, so you have to use the simplest physical laws and relationships in everyday life. The importance of Ohm's Law in electrical engineering is colossal, by the way, most theses electrical engineering specialties are calculated by 70-90% using one formula.
Historical reference
The year Ohm's Law was discovered was 1826 by the German scientist Georg Ohm. He empirically determined and described the law on the relationship between current, voltage and type of conductor. Later it turned out that the third component is nothing more than resistance. Subsequently, this law was named after the discoverer, but the matter was not limited to the law; a physical quantity was named after his name, as a tribute to his work.
The quantity in which resistance is measured is named after Georg Ohm. For example, resistors have two main characteristics: power in watts and resistance - unit of measurement in Ohms, kilo-ohms, mega-ohms, etc.
Ohm's law for a circuit section
To describe an electrical circuit that does not contain EMF, you can use Ohm's law for a section of the circuit. This is the most simple form records. It looks like this:
Where I is the current, measured in Amperes, U is the voltage in volts, R is the resistance in Ohms.
This formula tells us that current is directly proportional to voltage and inversely proportional to resistance - this is the exact formulation of Ohm's Law. The physical meaning of this formula is to describe the dependence of the current through a section of the circuit with a known resistance and voltage.
Attention! This formula is valid for direct current, for alternating current it has slight differences, we will return to this later.
In addition to the ratio electrical quantities this form tells us that the graph of the current versus voltage in the resistance is linear and the function equation is satisfied:
f(x) = ky or f(u) = IR or f(u)=(1/R)*I
Ohm's law for a section of a circuit is used to calculate the resistance of a resistor in a section of a circuit or to determine the current through it at a known voltage and resistance. For example, we have a resistor R with a resistance of 6 ohms, a voltage of 12 V is applied to its terminals. We need to find out how much current will flow through it. Let's calculate:
I=12 V/6 Ohm=2 A
An ideal conductor has no resistance, but due to the structure of the molecules of the substance of which it is composed, any conducting body has resistance. For example, this was the reason for the transition from aluminum to copper wires in home electrical networks. The resistivity of copper (Ohm per 1 meter length) is less than that of aluminum. Accordingly, copper wires heat up less and withstand higher currents, which means you can use a wire of a smaller cross-section.
Another example is that the spirals of heating devices and resistors have a high resistivity, because are made from various high-resistivity metals, such as nichrome, kanthal, etc. When charge carriers move through a conductor, they collide with particles in the crystal lattice, as a result of which energy is released in the form of heat and the conductor heats up. The greater the current, the more collisions, the greater the heating.
To reduce heating, the conductor must either be shortened or its thickness (cross-sectional area) increased. This information can be written as a formula:
R wire =ρ(L/S)
Where ρ is the resistivity in Ohm*mm 2 /m, L is the length in m, S is the cross-sectional area.
Ohm's law for parallel and series circuits
Depending on the type of connection, different patterns of current flow and voltage distribution are observed. For a section of a circuit connecting elements in series, voltage, current and resistance are found according to the formula:
This means that the same current flows in a circuit of an arbitrary number of elements connected in series. In this case, the voltage applied to all elements (the sum of the voltage drops) is equal to the output voltage of the power source. Each element individually has its own voltage applied and depends on the current strength and resistance of the particular one:
U el =I*R element
The resistance of a circuit section for parallel-connected elements is calculated by the formula:
1/R=1/R1+1/R2
For a mixed connection, you need to reduce the chain to an equivalent form. For example, if one resistor is connected to two parallel-connected resistors, then first calculate the resistance of the parallel-connected ones. You will get the total resistance of two resistors and all you have to do is add it to the third one, which is connected in series with them.
Ohm's law for a complete circuit
A complete circuit requires a power source. An ideal power source is a device that has the only characteristic:
- voltage, if it is a source of EMF;
- current strength, if it is a current source;
Such a power source is capable of delivering any power with unchanged output parameters. In a real power source, there are also such parameters as power and internal resistance. In essence, internal resistance is an imaginary resistor installed in series with the EMF source.
The Ohm's Law formula for a complete circuit looks similar, but the internal resistance of the IP is added. For a complete chain it is written by the formula:
I=ε/(R+r)
Where ε is the EMF in Volts, R is the load resistance, r is the internal resistance of the power source.
In practice, the internal resistance is fractions of an Ohm, and for galvanic sources it increases significantly. You have observed this when two batteries (new and dead) have the same voltage, but one produces the required current and works properly, and the second does not work, because... sags at the slightest load.
Ohm's law in differential and integral form
For a homogeneous section of the circuit, the above formulas are valid; for a non-uniform conductor, it is necessary to divide it into the shortest segments so that changes in its dimensions are minimized within this segment. This is called Ohm's Law in differential form.
In other words: the current density is directly proportional to the voltage and conductivity for an infinitely small section of the conductor.
In integral form:
Ohm's law for alternating current
When calculating AC circuits, instead of the concept of resistance, the concept of “impedance” is introduced. Impedance is denoted by the letter Z, it includes active load resistance R a and reactance X (or R r). This is due to the shape of the sinusoidal current (and currents of any other shapes) and the parameters of the inductive elements, as well as the laws of commutation:
- The current in a circuit with inductance cannot change instantly.
- The voltage in a circuit with a capacitor cannot change instantly.
Thus, the current begins to lag or advance the voltage, and full power divided into active and reactive.
X L and X C are the reactive components of the load.
In this regard, the value cosФ is introduced:
Here – Q – reactive power due to alternating current and inductive-capacitive components, P – active power (distributed on active components), S – apparent power, cosФ – power factor.
You may have noticed that the formula and its representation overlaps with the Pythagorean theorem. This is indeed true, and the angle Ф depends on how large the reactive component of the load is - the greater it is, the greater it is. In practice, this leads to the fact that the current actually flowing in the network is greater than that recorded by the household meter, while enterprises pay for full power.
In this case, resistance is presented in complex form:
Here j is the imaginary unit, which is typical for the complex form of equations. It is less often denoted as i, but in electrical engineering the effective value of alternating current is also denoted, therefore, in order not to be confused, it is better to use j.
The imaginary unit is equal to √-1. It is logical that there is no such number when squared that can result in a negative result of “-1”.
How to remember Ohm's law
To remember Ohm's Law, you can memorize the wording in simple words type:
The higher the voltage, the higher the current; the higher the resistance, the lower the current.
Or use mnemonic pictures and rules. The first is the presentation of Ohm's law in the form of a pyramid - briefly and clearly.
A mnemonic rule is a simplified form of a concept for simple and easy understanding and study. Can be either in verbal form or in graphic form. To correctly find the required formula, cover the desired quantity with your finger and get the answer in the form of a product or quotient. Here's how it works:
The second is a caricature representation. It is shown here: the more Ohm tries, the more difficult it is for Ampere to pass, and the more Volts, the easier it is for Ampere to pass.
Ohm's law is one of the fundamental ones in electrical engineering; without its knowledge, most calculations are impossible. And in everyday work it is often necessary to convert or determine current by resistance. It is not at all necessary to understand its derivation and the origin of all quantities - but the final formulas are required to be mastered. In conclusion, I would like to note that there is an old joke saying among electricians: “If you don’t know Om, stay at home.” And if every joke has a grain of truth, then here this grain of truth is 100%. Explore theoretical basis, if you want to become a professional in practice, and other articles from our site will help you with this.
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The closed circuit (Fig. 2) consists of two parts - internal and external. Inner part of the chain is a current source with internal resistance r; external- various consumers, connecting wires, devices, etc. The total resistance of the external part is indicated by R. Then the total resistance of the circuit is r + R.
According to Ohm's law for the outer section of the circuit 1 → 2 we have:
\(~\varphi_1 - \varphi_2 = IR .\)
Internal chain section 2 → 1 is heterogeneous. According to Ohm's law, \(~\varphi_2 - \varphi_1 + \varepsilon = Ir\). Adding these equalities, we get
\(~\varepsilon = IR + Ir . \qquad (1)\)
\(~I = \frac(\varepsilon)(R + r) . \qquad (2)\)
The last formula is Ohm's law for a closed circuit direct current. The current strength in the circuit is directly proportional to the emf of the source and inversely proportional to the total resistance of the circuit.
Since for a homogeneous section of the circuit the potential difference is voltage, then \(~\varphi_1 - \varphi_2 = IR = U\) and formula (1) can be written:
\(~\varepsilon = U + Ir \Rightarrow U = \varepsilon - Ir .\)
From this formula it is clear that the voltage in the external section decreases with increasing current in the circuit at ε = const.
Let us substitute the current strength (2) into the last formula and obtain
\(~U = \varepsilon \left(1 - \frac(r)(R + r) \right) .\)
Let us analyze this expression for some limiting operating modes of the circuit.
a) With an open circuit ( R → ∞) U = ε , i.e. the voltage at the poles of the current source when the circuit is open is equal to the emf of the current source.
This is the basis for the possibility of approximately measuring the EMF of a current source using a voltmeter, the resistance of which is much greater than the internal resistance of the current source (\(~R_v \gg r\)). To do this, a voltmeter is connected to the terminals of the current source.
b) If a conductor whose resistance is \(~R \ll r\) is connected to the terminals of a current source, then R + r ≈ r, then \(~U = \varepsilon \left(1 - \frac(r)(r) \right) = 0\) , and the current strength \(~I = \frac(\varepsilon)(r)\) - reaches its maximum value.
Connecting a conductor with negligible resistance to the poles of a current source is called short circuit, and the maximum current for a given source is called short circuit current:
\(~I_(kz) = \frac(\varepsilon)(r) .\)
For sources with low values r(for example, lead-acid batteries r= 0.1 - 0.01 Ohm) the short circuit current is very high. A short circuit in lighting networks powered from substations is especially dangerous ( ε > 100 V), I kz can reach thousands of amperes. To avoid fires, fuses are included in such circuits.
Let's write Ohm's law for a complete circuit in the case of series and parallel connection of current sources to a battery. When connecting sources in series, the “-” of one source is connected to the “+” of the second, the “-” of the second to the “+” of the third, etc. (Fig. 3, a). If ε 1 = ε 2 = ε 3 a r 1 = r 2 = r 3 then ε b = 3 ε 1 , r b = 3 r 1 . In this case, Ohm's law for the complete chain has the form\[~I = \frac(\varepsilon_b)(R + r_b) = \frac(3 \varepsilon_1)(R + 3r_1)\], or for n identical sources \(~I = \frac(n \varepsilon_1)(R + nr_1)\).
A series connection is used in the case when the external resistance is \(~R \gg nr_1\), then \(~I = \frac(n \varepsilon_1)(R)\) and the battery can provide a current in n times greater than the current from one source.
At parallel connection current sources, all “+” sources are connected together and “-” sources are also connected together (Fig. 3, b). In this case
\(~\varepsilon_b = \varepsilon_1 ; \r_b = \frac(r_1)(3).\)
Where does \(~I = \frac(\varepsilon_1)(R + \frac(r_1)(3))\) come from.
For n identical sources \(~I = \frac(\varepsilon_1)(R + \frac(r_1)(n))\) .
Parallel connection of current sources is used when it is necessary to obtain a current source with low internal resistance or when current must flow in the circuit for normal operation of the electrical consumer. greater than permissible current one source.
Parallel connection is beneficial when R small compared to r.
Sometimes a mixed combination of sources is used.
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 vyhavanne, 2004. - P. 262-264.
often finds application in working with electricity. Thanks to a pattern discovered by the German physicist Georg Ohm, today we can calculate the amount of current flowing in a wire or the required wire thickness to connect to the network.
History of discovery
The future scientist was interested in . He conducted many tests related to . Due to the imperfection of the measuring instruments of that time, the first research results were erroneous and hindered further development question. Georg published the first scientific work in which he described the possible relationship between voltage and current. His subsequent works confirmed the assumptions, and Om formulated his famous law. All the works were included in the 1826 report, but the scientific community did not notice the works of the young physicist.
Five years later, when the famous French scientist Poulier came to the same conclusion, Georg Ohm was awarded the Copley Medal for making a great contribution to the development of physics as a science.
Today, Ohm's Law is used throughout the world, recognized as a true law of nature. .
Detailed description
Georg's law shows the value of electricity in specific network, which depends on the resistance to the load and internal elements of the power source. Let's look at this in detail.
A conventional device that uses electricity (for example, an audio speaker) when connected to a power source forms a closed circuit (Figure 1). Let's connect the speaker to the battery. The current that flows through the speaker also follows through the power source. The flow of charged particles will meet the resistance of the wire and the internal electronics of the device, as well as the resistance of the battery (the electrolyte inside the can has a certain effect on electricity). Based on this, the resistance value of a closed network is the sum of the resistance:
- Power supply;
- Electrical device.
Connecting a conventional electrical device (speaker) to a power source (car battery)
The first parameter is called internal, the second - external resistance. The resistance of the electrical source is marked with the symbol r.
Let's imagine that a certain current T passes through the power source/electrical device network. To maintain a stable value of electricity in the external network, in accordance with the law, a potential difference must be observed at its ends, which is equal to R*T. A current of the same magnitude passes inside the circuit. As a result, maintaining a constant value of electricity within the network requires a potential difference at the ends of the resistance r. According to the law, it must be equal to T*r. While maintaining a stable current in the network, the value of the electromotive force is equal to:
E=T*r+T*R
From the formula it follows that the EMF is equal to the sum of the voltage drop in the internal and external networks. If we take the value of T out of brackets, we get:
E=T(r+R)
T=E/(r+R)
Examples of problems applying the law to a connected network
1) A rheostat with a resistance of 5 Ohms is connected to an EMF source of 15 V and a resistance of 2 Ohms. The task is to calculate the current and voltage at the terminals.
Calculation
- Let's imagine Ohm's law for a connected network: T=E/(r+R).
- We calculate the voltage reduction using the formula: U= E-Tr=ER/(R+r).
- Let's substitute the available values into the formula: T= (15 V)/((5+2) Ohm) = 2.1 A, U=(15 V* 5 Ohm)/(5+1) Ohm = 12.5 V
Answer: 2.1 A, 12.5 V.
2) When connecting a resistor with a resistance of 30 Ohms to the galvanic elements, the current in the network took on a value of 1.5 A, and when connecting the same element with a resistance of 15 Ohms, the current became 2.5 A. The task is to find out the value of the emf and the internal resistance of the circuit of galvanic elements.
Calculation
- Let's write down Georg Ohm's law for a connected network: T=E/(r+R).
- From it we derive formulas for internal and external resistance: E=T_1 R_1+T_1 r, E= T_2 R_2 + T 2r.
- Let's equate the parts of the formula and calculate the internal resistance: r=(T_1 R_1-T_2 R_2)/(T_2-T_1).
- Let's substitute the obtained values into the law: E=(T_1 T_2 (R_2-R_1))/(T_2-T_1).
- Let's carry out the calculations: r=(1.5 A∙30 Ohm-2.5A∙15 Ohm)/(2.5-1.5)A=7.5 Ohm, E=(1.5 A∙2.5A(30-15)Ohm)/( (2.5-1.5)A)=56 V.
Answer: 7.5 Ohm, 56 V.
Scope of application of Ohm's law for a closed circuit
Ohm's law is an electrician's universal tool. It allows you to correctly calculate the current and voltage in the network. The operating principle of some devices is based on Ohm's law. In particular, fuses.
Short circuit is an accidental short circuit of two sections of the network, not provided for by the design of the equipment and leading to malfunctions. To prevent such phenomena, special devices are used that turn off the power to the network.
If an accidental short circuit occurs with a large overload, the device will automatically stop supplying current.
Ohm's law in this case finds its place in the DC circuit section. There may be many more processes in a complete scheme. Many actions when building an electrical network or repairing it should be carried out taking into account Georg Ohm's law.
To fully study the relationship between current parameters in conductors, the following formulas are presented: 
More complex expression law for practical application: 
Resistance is represented by the ratio of voltage to current in a circuit. If the voltage is increased by n times, the current value will also increase by n times.
The works of Gustav Kirgoff are no less famous in electrical engineering. Its rules are used in calculations of branched networks. These rules are based on.
The scientist's works were used in the invention of many everyday things, such as incandescent lamps and electric stoves. Modern advances in electronics owe much to the discoveries of 1825.
If points 1 and 2 coincide, then the expression for Ohm’s law for the section takes on a simpler form:
where is the total resistance of the closed circuit including the internal resistance of the sources, and is the algebraic sum of the emf. in this chain.
The current that occurs when the external resistance is zero is called short circuit current.
Lecture 10.
Connection of conductors.
Using Ohm's law for a section of a circuit, it can be shown that the resistances of series and parallel connections of conductors are equal, respectively:
Proof:
Note that when connecting conductors in parallel, the total resistance is always less than the smallest resistance in the parallel connection. See for yourself.
Joule-Lenz law.
When current passes through a conductor, resistance generates heat, which is dissipated in environment. Let's find this amount of heat. For this we will use the law of conservation of energy and Ohm's law.
Let's consider homogeneous section of the circuit where a constant potential difference is maintained. The electric field does work:
If there is no transformation into mechanical, chemical or other types of energy other than thermal in the area, then the amount of heat released is equal to the work of the electric field:
.
The thermal power is equal to:
The final amount of heat is found by integration over time:
This formula expresses the Joule–Lenz law. The mechanism of heat release is associated with the conversion of additional kinetic energy, which current carriers acquire in an electric field, into excitation energy of lattice vibrations when carriers collide with atoms at lattice sites.
Let us find an expression for the Joule–Lenz law in local form. For this purpose, we select an elementary volume in the conductor in the form of a cylinder with a generatrix along the vector. Let the cross section of the cylinder be , and its length . Then, according to the Joule–Lenz law, the amount of heat released in this volume over time is:
where is the volume of the cylinder. Dividing the last ratio by we obtain a formula that determines the thermal power released per unit volume of the conductor:
Specific thermal power is measured in .
The resulting relationship expresses the Joule–Lenz law in local form: the specific thermal power of the current is proportional to the square of the current density and the specific resistance of the conductor at a given point.
In this form, the Joule–Lenz law is applicable to inhomogeneous conductors of any shape, and does not depend on the nature of external forces. If only electrical forces act on the carriers, then based on Ohm’s law:
If a section of the circuit contains an emf source, then the current carriers will be acted upon not only by electrical forces, but also by external forces. In this case, the heat that is released in the area is equal to the algebraic sum of the work of electrical and external forces.
Let's multiply Ohm's law in integral form by the current strength:
Here on the left is (thermal power), and on the right is the algebraic sum of the powers of electrical and external forces, which is called current power.
In a closed circuit:
those. The power of heat generation is equal to the power of external forces.
Ohm's differential law
IN 
Let's select a conductor from the array (through which electric current flows I) a small cylinder located along the electric current lines in the conductor Fig. 5.2. Let the length of the cylinder be dl and the cross section dS. Then
ABOUT 
here
AND 
Using the definition for the current density (5.1) and for the conductivity of the conductor (5.4), we finally obtain the expression, which is called Ohm’s differential law
Work and power produced by electric current
When a charge moves between points with a certain potential difference corresponding to the voltage drop U work and power produced:
E 
This law was obtained experimentally and was called the Joule–Lenz law. If, like the previous case, we proceed to the consideration of small volumes, then it is not difficult to obtain the Joule–Lenz law in differential form (5.6-5.8):
Kirchhoff's laws
Kirchhoff's first rule
Let's consider an electrical circuit with branches Fig. 5.3. We will call branching points nodes. In a steady-state process, when the electric current flowing through the circuit is constant, the potentials of all points in the circuit are also unchanged. This can happen if electric charges do not accumulate or disappear at the nodes of the chain.
Thus, in a steady state, the amount of electricity flowing into the node is equal to the amount of electricity leaving the node. It follows from this Kirchhoff's first rule:
The algebraic sum of the forces of electric currents converging at a node is equal to zero (5.9) (currents entering the node are taken with + signs, and currents leaving the node with - sign)
I1+i2+i3-i4-i5=0
ΣI i =0 5.9.
Conductor connections
In practice, it is often necessary to use different connections of conductors
P 
serial connection Fig.5.4.
P 
With such a connection, the electric current in all parts of the circuit and on all its elements is the same I=
I 1
=
I 2
=
I 3
=…
I n. The voltage at the ends of the circuit between points A and B is the sum of the voltages at each of its elements U AB =
U 1
+
U 2
+
U 3
+…
U n. Thus.
Parallel connection Fig.5.5
Ohm's law for a closed circuit containing e.m.f.
R 
Let's consider an unbranched electrical circuit containing E.M.F.( E) with internal resistance r and containing external resistance R Fig.5.6
The total work to move the charge along the entire circuit will be the sum of the work in the external circuit and the work inside the source A=A external +A source .
Moreover, the work in the external circuit related to the amount of charge is, by definition, the potential difference on the external circuit (voltage drop on the external circuit) A external / q= U. And the work throughout the circuit related to the charge is, by definition, E.M.F. A/ q= E. From here E= U+ A source / q. On the other side A source = I2 rt. From here A source / q= Ir. Thus we finally get: E= U+ Ir
Or E= I(R+ r) 5.12
Under E implies the sum of all E.M.F. included in an unbranched circuit, and by r and R we mean the sum of all internal and external resistances in the unbranched circuit.
The current strength is the same for the entire unbranched closed circuit containing E.M.F. is directly proportional to the E.M.F. and is inversely proportional to the circuit impedance.
Kirchhoff's second rule
Consider the branched chain Fig. 5.7. Let's call the section between two neighboring nodes a branch. Since branching takes place only at neighboring nodes, within the branch the current strength is maintained in magnitude and direction. Any circuit can be considered as a set of circuits, and for each circuit the following is true:
In any closed circuit, mentally isolated from an electrical circuit, the algebraic sum of the products of the resistances of the corresponding sections of the circuit, including the internal resistances of the sources, and the current strength in the circuit is equal to the algeboraic sum of all E.M.F. in a chain
Ohm's law for a closed circuit
If an electric field is created in a conductor and measures are not taken to maintain it, then the movement of charges will very quickly lead to the fact that the field inside the conductor will disappear and the current will stop, therefore, to maintain a constant current for a long time, two conditions must be met: the electrical circuit must be closed; in the electrical circuit along with areas in which the positive
Since the charges move in the direction of decreasing potential, there must be sections in which these charges move in the direction of increasing potential, i.e., against the forces of the electrostatic field (see the part of the circuit depicted by the dashed line in Fig. 5).
Only forces of non-electrostatic origin, called external forces, can move positive charges against the forces of an electrostatic field. A quantity equal to the work of external forces to move a unit positive charge is called electromotive force (EMF) e, acting in a circuit or on its section. EMF e measured in volts (V). The EMF source has some internal resistance, depending on its design. This resistance is connected in series with the source in a common electrical circuit. Galvanic cells and direct current generators are used as sources of EMF (Fig. 6).
If an unbranched closed electrical circuit (Fig. 7) contains several series-connected elements with resistance and sources of emf e to, having internal resistance, then it can be replaced by the equivalent circuit shown in Fig. 6. The current strength in an equivalent circuit is determined by Ohm’s law for a closed circuit:
;
EMF, like current strength, is an algebraic quantity. If the EMF promotes the movement of positive charges in the chosen direction, then e> 0, if the emf prevents the movement of positive charges in a given direction, then e < 0. Чтобы определить знак ЭДС, необходимо показать в электрической цепи направление движения положительных зарядов. Positive charges in an electrical circuit they move from the positive pole of the source to the negative pole. If, along this direction, we move inside the source from the negative pole to the positive, then e> 0, if we move inside the source from the positive pole to the negative, then e < 0.
Rice. 6 Fig. 7
From Ohm's law for a closed circuit it follows that the voltage drop U at the source terminals is less than the EMF. Really, e, or e. Since, according to Ohm’s law, for a homogeneous section of the circuit, the voltage at the source terminals is , then
3) using Ohm’s law for a closed circuit, establish the relationship between current strength and EMF.
Tell me Ohm's law
Ohm's law is a physical law that defines the relationship between voltage, current and conductor resistance in an electrical circuit. Named after its discoverer, Georg Ohm.
It so happened that in this section of the page there were two verbal formulations of Ohm’s law:
1. The essence of the law is simple: if, during the passage of current, the voltage and properties of the conductor do not change, then
The current strength in a conductor is directly proportional to the voltage between the ends of the conductor and inversely proportional to the resistance of the conductor.
2. Ohm's law is formulated as follows: The current strength in a homogeneous section of the circuit is directly proportional to the voltage applied to the section, and inversely proportional to the characteristic of the section, which is called the electrical resistance of this section.
It should also be borne in mind that Ohm's law is fundamental and can be applied to any physical system in which there are flows of particles or fields that overcome resistance. It can be used to calculate hydraulic, pneumatic, magnetic, electrical, light, heat flows, etc., just like Kirchhoff’s Rules, however, this application of this law is used extremely rarely within the framework of highly specialized calculations.
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The German physicist G. Ohm experimentally established in 1826 that the current strength I flowing through a homogeneous metal conductor (i.e., a conductor in which no external forces act) is proportional to the voltage U at the ends of the conductor: 
where R = const.
The value R is usually called electrical resistance. A conductor that has electrical resistance is called a resistor. This relationship expresses Ohm's law for a homogeneous section of the circuit: the current strength in the conductor is directly proportional to the applied voltage and inversely proportional to the resistance of the conductor.
The SI unit of electrical resistance of conductors is the ohm (Ω). A resistance of 1 ohm has a section of the circuit in which a current of 1 A occurs at a voltage of 1 V.
Conductors that obey Ohm's law are called linear. The graphical dependence of the current I on the voltage U (such graphs are called current-voltage characteristics, abbreviated as VAC) is depicted by a straight line passing through the origin of coordinates. It should be noted that there are many materials and devices that do not obey Ohm's law, for example, 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.
For a section of a circuit containing an emf, Ohm's law is written in the following form:
IR = U12 = φ1 – φ2 + E = Δφ12 + E.
This relationship is usually called the generalized Ohm's law.
In this fig. shows a closed DC circuit. The chain section (cd) is uniform.
According to Ohm's law,
IR = Δφcd.
Section (ab) contains a current source with an emf equal to E.
According to Ohm's law for a heterogeneous area,
Ir = Δφab + E.
Adding both equalities, we get:
I(R + r) = Δφcd + Δφab + E.
But Δφcd = Δφba = – Δφab.
That's why
This formula expresses Ohm's law for a complete circuit: the current strength in a complete circuit is equal to the electromotive force of the source divided by the sum of the resistances of the homogeneous and inhomogeneous sections of the circuit.
Little prince
In integral form: i=L*U | L-electrical conductivity, 1/R
In differential form: j=A*E | A - electrical conductivity of the medium, j - current density
For a closed loop: i= E/(r+R) | already brought...
For alternating currents: uo=io*sqrt (r^2 + (w*L -1/w*C)^2) |uo io - amplitudes of current and voltage, r - active resistance of the circuit, which is in brackets and squared - reactive component, sqrt = square root....
Olya Semyonova
Ohm's law is an empirical physical law that determines the relationship between the electromotive force of a source (or electrical voltage) with the strength of the current flowing in the conductor and the resistance of the conductor. Installed by Georg Ohm in 1826 and named after him.
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