Ohm's law for dummies: concept, formula, explanation. Ohm's law for a circuit section states: current is directly proportional to voltage and inversely proportional to resistance
The concept of tension.
Voltage is a physical quantity that characterizes the electric field that creates current.
Electrical voltage between points A And B electrical circuit or electric field- a physical quantity, the value of which is equal to the ratio of the work of the effective electric field (including external fields) performed when transferring a test electric charge from a point A to the point B, to the value of the test charge.
Voltage characterizes the electric field created by current.
Voltage (U) is equal to the ratio of the work of the electric field to move the charge
to the amount of charge moved in a section of the circuit.
SI unit of voltage:
Concept of resistance.
Electrical resistance- a physical quantity that characterizes the properties of a conductor to prevent the passage of electric current and is equal to the ratio of the voltage at the ends of the conductor to the strength of the current flowing through it.
Resistance for circuits AC and for alternating electromagnetic fields is described in terms of impedance and wave resistance. Resistance (resistor) is also called a radio component designed to introduce active resistance into electrical circuits.
Resistance (often symbolized by the letter R or r) is considered, within certain limits, a constant value for a given conductor; it can be calculated as
R- resistance, Ohm;
U- electrical potential difference (voltage) at the ends of the conductor, V;
I- the strength of the current flowing between the ends of the conductor under the influence of a potential difference, A.
Any body through which electric current flows exhibits a certain resistance to it.
The greater the resistance of a conductor, the worse it conducts electric current, and, conversely, the lower the resistance of the conductor, the easier it is for electric current to pass through this conductor. Consequently, to characterize a conductor (from the point of view of the passage of electric current through it), one can consider not only its resistance, but also the reciprocal of the resistance and called conductivity. Electrical conductivity is the ability of a material to pass electric current through itself. Since conductivity is the reciprocal of resistance, it is expressed as 1/R, denoted conductivity Latin letter g.
5. Elements of electrical circuits. Active elements are the sources electrical energy. They are divided into voltage sources – symbol in the picture. Passive elements– elements that are not sources of electrical energy. They are divided into dissipative and reactive . Dissipative elements– elements that dissipate electrical energy. Elements with such properties convert electrical energy into thermal energy. These elements are resistors. They are characterized by electrical resistance, which is measured in ohms (Ohms). Reactive elements- elements capable of accumulating electrical energy and releasing it either to the source from which this energy was received, or transmitting it to another element. In any case, this element does not convert electrical energy into thermal energy. Such elements are an inductor and a capacitor. An electrical circuit is a connection of electrical elements in which, under the influence of a source of electrical energy, an electric current flows in the elements. Knot– a point of connection of three or more elements. Branch– a section of a chain containing at least one element and located between two nearest nodes. Circuit– a closed part of an electrical circuit. Jumper is an electrical conductor with zero resistance, connected at its ends to two different points in the circuit. The classification of an electrical circuit is carried out according to the following criteria: – the presence or absence of a source of electrical energy in the circuit; – presence or absence of dissipative elements in the chain; – depending on the nature of the current-voltage characteristics of electrical elements; – depending on the number of terminals of the electrical circuit. Passive circuit called a circuit that does not contain a source of electrical energy. In such a chain only dissipative and reactive elements are present. Active circuit A circuit containing at least one source of electrical energy is called. Active circuits include circuits containing amplifying elements - transistors and vacuum tubes.
6. Ohm's law.
The basic law of electrical engineering, with which you can study and calculate electrical circuits, is Ohm's law, which establishes the relationship between current, voltage and resistance. German physicist Georg Ohm(1787 -1854) experimentally established 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:
I = U/R
where R is the electrical resistance of the conductor.
The equation expresses Ohm's law for a circuit section(not containing a current source): The current in a conductor is directly proportional to the applied voltage and inversely proportional to the resistance of the conductor.
The section of the circuit in which emfs do not act. (external forces) are called a homogeneous section of the chain, therefore this formulation of Ohm’s law is valid for a homogeneous section of the chain.
Ohm's law for a circuit section states: current is directly proportional to voltage and inversely proportional to resistance.
Ohm's law . I= , where = R+ R i
7. Kirchhoff's first law. Kirchhoff's second law.
1 Kirchhoff's law (applies to nodal points)
The algebraic sum of the currents of the branches forming the node is equal to 0: ∑i=0
Moreover, the “+” sign is assigned to the current entering the node, and the “-” sign to the current leaving the node.
For example i 1 +i 2 -i 3 -i 4 =0 (node b)
A node is a point in a circuit where three or more branches converge.
m – number of nodes
m-1- equation to solve
i 1 +i 2 -i 3 -i 4 =0 (node b)
2 Kirchhoff's law (applies to any circuit);
The algebraic sum of the EMF acting in the circuit is equal to the algebraic sum of the voltage drops on the passive elements of this circuit, including the internal resistance of the source:
The “+” sign is assigned to the EMF, which coincides in direction with the bypass of the circuit, the “-” sign is assigned to the voltage drop if the direction of the current does not coincide with the direction of the bypass.
For example, for the abfgdca circuit, choosing the traversal direction clockwise (see figure), we write Kirchhoff’s second law as follows:
E 1 -E 2 =r i i 1 -r 4 i 2 -r 02 i 2 -r 5 i 2 +r 2 i 1 +r 01 i 1 .
8. Bridge circuits.
A bridge circuit, an electric bridge, an electric four-terminal network, to one pair of terminals (poles) of which a power source is connected, and to the other - a load. A classic bridge circuit consists of four resistances connected in series in the form of a quadrilateral (Fig.), with points a, b, c and d being called vertices. The branch containing the power source UП is called the power diagonal, and the branch containing the load resistance ZH is called the load diagonal or index diagonal. Resistances Z1, Z2, Z3 and Z4, connected between two adjacent vertices, are called shoulders. Bridge circuit. Diagonals. Bridge circuit, like bridges, connect two opposite vertices (the load diagonal, for example, was previously called a bridge). The diagram presented in Fig. is known in the literature as a four-arm bridge.
9.Obtaining sinusoidal EMF. Effective values sinusoidal currents and voltages.
Alternating current is a current that periodically changes in magnitude and direction.
Receiving alternating current:
Let a frame of area S rotate uniformly in a uniform magnetic field of a permanent magnet with an angular velocity W. The magnetic flux through the frame is Ф=BScosa, where a is the angle between the normal to the frame.
Because with equal Frame rotation angle. Speed W=a/t, then the angle a will change according to the law a=wt, and the formula will take the form: Ф=BScos(wt).
Because at rotation The frames have been crossed. Her mag. The flow changes all the time, then according to the law of el. Ind. There will be a find in it. EMF ind.:
E=dФ/dt =BSwsin(wt)=E 0 sin(wt)
Where E 0 =BSw is the amplitude of the sinusoidal EMF
Thus, a sinusoidal emf appears in the frame, and if the frame is closed to a load, then a sinusoidal current will flow in the circuit.
IfI - current strength,U - voltage, aR - resistance, then
I =
This law isname of Ohm's law , named after the scientist who discovered it.
It is often necessary to regulate the current in a circuit. For this purpose, special devices called rheostats are used. In a rheostat, a wire made of a material with a large resistivity, wound on a ceramic cylinder. Above the winding there is a metal rod along which the contact can move. The contact is pressed against the winding; when it moves, the length of the winding through which the current passes changes, and accordingly the resistance of the rheostat. The rheostat and its symbol in the diagrams are shown in Figure 17.
Ohm's law for a complete circuit
Let it take timet an electric charge will pass through the cross section of the conductorq. Then the work of external forces when moving a charge can be written as follows:
Ast = q.
According to the definition of current
q = It.
That's why
Ast = It .
When performing this work on the internal and external sections of the circuit, the resistance of whichR Andr , some heat is releasedQ . According to the Joule-Lenz law, it is equal to:
Q = I Rt + I r.
According to the law of conservation of energy
A = Q.
Hence,
= IR + I r.
The product of the current and the resistance of a section of a circuit is often called the voltage drop across that section. Thus, the EMF is equal to the sum of the voltage drops in the internal and external sections of the closed circuit. Typically this expression is written like this:
I = /( R + r ).
This dependence was experimentally obtained by G. Ohm, and it is called Ohm’s law for complete chain and reads like this:
The current strength in a complete circuit is directly proportional to the emf of the current source and inversely proportional to the total resistance of the circuit.
When the circuit is open, the emf is equal to the voltage at the source terminals and, therefore, can be measured with a voltmeter.
f214. Nuclear forces
The nucleus contains protons, which experience mutual Coulomb repulsion, and neutrons. The stability of nuclei that do not fly apart under the influence of Coulomb repulsive forces indicates that specific attractive forces, called nuclear forces, operate in the nuclei. Nuclear forces cannot be ordinary Coulomb interaction forces. The Coulomb interaction between a proton and a proton is reduced to repulsion, but between a neutron and a proton, or a neutron and a neutron, it is absent. Electrical forces depend on the charge and are small compared to nuclear ones. Gravitational forces also cannot hold the particles in the core because they are too small. For example, the gravitational interaction of two protons is 1036 times less than their Coulomb interaction. The forces of magnetic interaction cannot act as nuclear forces. Calculations “show that the energy” of magnetic interaction, for example, a proton and a neutron in the nucleus of a deuterium atom |H, is about 0.1 MeV, which is much less than the binding energy of nucleons in the nucleus (2.2 MeV).
All this suggests that nuclear forces cannot be reduced to electric, magnetic, or gravitational forces, but represent a specific type of force.
The interaction between nucleons in a nucleus is an example of strong interactions - interactions through nuclear forces.
We are starting to publish materials in the new section “” and in today’s article we will talk about fundamental concepts, without which no discussion can take place electronic device or diagrams. As you may have guessed, I mean current, voltage and resistance😉 In addition, we will not ignore the law that determines the relationship of these quantities, but I won’t get ahead of ourselves, let’s move gradually.
So let's start with the concept voltage.
Voltage.
By definition voltage is the energy (or work) that is expended to move a unit positive charge from a point with a low potential to a point with a high potential (i.e., the first point has a more negative potential compared to the second). We remember from the physics course that the potential of an electrostatic field is a scalar quantity equal to the ratio of the potential energy of a charge in the field to this charge. Let's look at a small example:
There is a constant electric field in space, the intensity of which is equal to E. Consider two points located at a distance d from each other. So the voltage between two points is nothing more than the potential difference at these points:
At the same time, do not forget about the connection between the electrostatic field strength and the potential difference between two points:
And as a result, we get a formula connecting stress and tension:
In electronics, when considering various schemes, voltage is still considered to be the potential difference between points. Accordingly, it becomes clear that voltage in a circuit is a concept associated with two points in the circuit. That is, to say, for example, “voltage in a resistor” is not entirely correct. And if they talk about voltage at some point, then they mean the potential difference between this point and "earth". This is how we smoothly arrived at another most important concept in the study of electronics, namely the concept "Earth":) So here it is "earth" in electrical circuits, it is most often accepted to consider the point of zero potential (that is, the potential of this point is equal to 0).
Let's say a few more words about the units that help characterize the quantity voltage. The unit of measurement is Volt (V). Looking at the definition of the concept of voltage, we can easily understand that to move a charge of magnitude 1 pendant between points having a potential difference 1 Volt, it is necessary to do work equal to 1 Joule. With this, everything seems to be clear and we can move on 😉
And next in line we have one more concept, namely current.
Current, current strength in a circuit.
What is it electric current?
Let's think about what will happen if charged particles, for example, electrons, come under the influence of an electric field... Consider a conductor to which a certain voltage:
From the direction of the electric field strength ( E) we can conclude that title="Rendered by QuickLaTeX.com" height="16" width="60" style="vertical-align: -4px;"> (вектор напряженности всегда направлен в сторону уменьшения потенциала). На каждый электрон начинает действовать сила:!}
Where e is the charge of the electron.
And since the electron is a negatively charged particle, the force vector will be directed in the direction opposite to the direction of the field strength vector. Thus, under the influence of force, particles, along with chaotic motion, also acquire directional motion (velocity vector V in the figure). As a result, there arises electric current 🙂
Current is the ordered movement of charged particles under the influence of an electric field.
The important point is that current is assumed to flow from a point with a more positive potential to a point with a more negative potential, even though the electron is moving in the opposite direction.
Not only electrons can act as charge carriers. For example, in electrolytes and ionized gases, the flow of current is primarily associated with the movement of ions, which are positively charged particles. Accordingly, the direction of the force vector acting on them (and at the same time the velocity vector) will coincide with the direction of the vector E. And in this case, no contradiction will arise, because the current will flow exactly in the direction in which the particles are moving :)
In order to estimate the current in a circuit, they came up with such a quantity as current strength. So, current strength (I) is a quantity that characterizes the speed of movement of an electric charge at a point. The unit of current is Ampere. The current strength in the conductor is equal to 1 Ampere, if for 1 second charge passes through the cross section of the conductor 1 pendant.
We have already covered the concepts current and voltage, now let's figure out how these quantities are related. And for this we have to study what it is conductor resistance.
Conductor/circuit resistance.
The term “ resistance” already speaks for itself 😉
So, resistance– physical quantity characterizing the properties of a conductor to hinder ( resist) the passage of electric current.
Consider a copper conductor of length l with a cross-sectional area equal to S:
Conductor resistance depends on several factors:
Specific resistance is a tabular value.
The formula with which you can calculate the resistance of a conductor is as follows:
For our case it will be equal 0.0175 (Ohm * sq. mm/m)– resistivity of copper. Let the length of the conductor be 0.5 m, and the cross-sectional area is equal to 0.2 sq. mm. Then:
As you already understood from the example, the unit of measurement resistance is Ohm 😉
WITH conductor resistance everything is clear, it's time to study the relationship voltage, current and circuit resistance.
And here the fundamental law of all electronics comes to our aid - Ohm's law:
The current in a circuit is directly proportional to the voltage and inversely proportional to the resistance of the section of the circuit in question.
Let's consider the simplest electrical circuit:
As follows from Ohm's law, voltage and current in a circuit are related as follows:
Let the voltage be 10 V and the circuit resistance be 200 ohms. Then the current in the circuit is calculated as follows:
As you can see, everything is not difficult :)
Perhaps this is where we will finish today’s article, thank you for your attention and see you soon! 🙂
The current strength in a section of a circuit is directly proportional to the voltage, and inversely proportional to the electrical resistance of a given section of the circuit.
Ohm's law is written as:
Where: I - current (A), U - voltage (V), R - resistance (Ohm).
It should be kept in mind that Ohm's law is fundamental(basic) 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, and heat flows.
Ohm's law defines the relationship between three fundamental quantities: current, voltage and resistance. He states that current is directly proportional to voltage and inversely proportional to resistance.
Current flows from a point with an excess of electrons to a point with a deficiency of electrons. The path followed by the current is called an electrical circuit. All electrical circuits consist of current source, loads And conductors. The current source provides the potential difference, which allows current to flow. The power source can be a battery, generator, or other device. The load resists the flow of current. This resistance can be high or low, depending on the purpose of the circuit. Current in a circuit flows through conductors from source to load. The conductor must give up electrons easily. Most conductors use copper.
The path of electric current to a load can pass through three types of circuits: series circuit, parallel circuit, or series-parallel circuit. The electron current in an electrical circuit flows from the negative terminal of the current source, through the load to the positive terminal of the current source.
As long as this path is not broken, the circuit is closed and current flows.
However, if the path is interrupted, the circuit will become open and current will not be able to flow through it.
The current in an electrical circuit can be changed by changing either the applied voltage or the resistance of the circuit. Current changes in the same proportions as voltage or resistance. If the voltage increases, then the current also increases. If the voltage decreases, the current also decreases. On the other hand, if the resistance increases, then the current decreases. If the resistance decreases, the current increases. This relationship between voltage, current and resistance is called Ohm's law.
Ohm's law states that current in a circuit (series, parallel or series-parallel) is directly proportional to voltage and inversely proportional to resistance
When determining unknown quantities in a circuit, follow these rules:
- Draw a circuit diagram and label all known quantities.
- Carry out calculations for equivalent circuits and redraw the circuit.
- Calculate the unknown quantities.
Remember: Ohm's law is valid for any part of the circuit and can be applied at any time. The same current flows through a series circuit, and to any branch parallel circuit the same voltage is applied.
History of Ohm's Law
Georg Ohm, conducting experiments with a conductor, found that the current strength in a conductor is proportional to the voltage applied to its ends. The proportionality coefficient is called electrical conductivity, and the value is usually called the electrical resistance of the conductor. Ohm's law was discovered in 1826.
Below are animations of circuits illustrating Ohm's law. Note that (in the first picture) the Ammeter (A) is ideal and has zero resistance.
This animation shows how the current in a circuit changes when the applied voltage changes.
The following animation shows how the current in a circuit changes as the resistance changes.
Ohm's law.
I = U/R
Where U is the voltage at the ends of the section, I is the current strength, R is the resistance of the conductor.
R=U/I
These formulas are valid only when the network experiences only resistance.
Motion condition electric charges in a conductor is the presence of an electric field in it, which is created and maintained by special devices called current sources.
The main quantity characterizing a current source is its electromotive force.
Electromotive force of a source (abbreviated EMF) is a scalar physical quantity that characterizes the work of external forces capable of creating a potential difference at the source terminals (poles).
It is equal to the work of external forces to move a charged particle with a positive unit charge from one pole of the source to the other, i.e.
In SI, EMF is measured in volts (V), i.e. in the same units as voltage.
Outside forces source - these are forces that separate charges in the source and thereby create a potential difference at its poles. These forces can be of a different nature, but not electrical (hence the name) - Mechanical forces, the chemical environment in the battery; luminous flux in photocells.
The direction of the EMF is the direction of the forced movement of positive charges inside the generator from minus to plus under the influence of a nature other than electrical.
Internal resistance generator is the resistance of the structural elements inside it.
If the electrical circuit is divided into two sections - external, with resistance R, and internal, with resistance r, That EMF source current will be equal to the sum of the voltages on the external and internal sections of the circuit:
According to Ohm's law, the voltage in any section of the circuit is determined by the magnitude of the flowing current and its resistance:
Since, therefore
, (3)
those. The voltage at the poles of the source in a closed circuit depends on the ratio of the resistances of the internal and external sections of the circuit. If approximately equal U.
Electrical resistance.
The property of a conductor material to prevent electric current from passing through it is called electrical resistance.
From Ohm's law: R = U / I
The unit of electrical resistance is 1 ohm.
A conductor has a resistance of 1 ohm and carries a current of 1 A at a voltage of 1 V.
The reciprocal of resistance is called electrical conductivity:
The unit of conductivity is siemens:
The reciprocal of specific conductivity is called resistivity p, i.e.
An increase in temperature is accompanied by an increase in the chaotic thermal motion of particles of matter, which leads to an increase in the number of collisions of electrons with them and complicates the ordered movement of electrons.
Resistance is a resistor.
Method of nodal potentials.
Example 2.7.4.
Determine the values and directions of currents in the branches using the method of nodal potentials for the circuit in Fig. 2.7.4 if:
E1=108 V; E2=90 V; Ri1=2 Ohm; Ri2=1 Ohm; R1=28 Ohm; R2=39 Ohm; R3=60 Ohm.
Solution.
We determine the currents in the branches.
Two node method.
One of the common methods for calculating electrical circuits is two node method.This method is used when there are only two nodes in the chain
Loop current method.
The algorithm of actions is as follows:
According to Kirchhoff's second law, regarding loop currents, we compose equations for all independent loops. When writing an equality, assume that the direction of bypassing the circuit for which the equation is being drawn up coincides with the direction of the circuit current of the given circuit. It should also be taken into account that two circuit currents flow in adjacent branches belonging to two circuits. The voltage drop across consumers in such branches must be taken from each current separately.
We arbitrarily set the direction of the real currents of all branches and designate them. Real currents must be marked in such a way as not to be confused with contour currents. To number real currents, you can use single Arabic numerals (I1, I2, I3, etc.).
During algebraic summation without changing the sign, a loop current is taken whose direction coincides with the accepted direction of the real branch current. Otherwise, the loop current is multiplied by minus one.
An example of calculating a complex circuit using the loop current method.
Rice. 1. Electrical circuit diagram for an example of calculation using the loop current method
Solution. To calculate a complex circuit using this method, it is enough to compose two equations, according to the number of independent circuits. We direct the loop currents clockwise and denote them I11 and I22 (see Figure 1).
According to Kirchhoff’s second law regarding loop currents, we compose the equations:
We solve the system and get the loop currents I11 = I22 = 3 A.
It should be noted as a positive fact that in the loop current method, in comparison with the solution according to Kirchhoff’s laws, it is necessary to solve a system of equations of a lower order. However, this method does not allow one to immediately determine the real currents of the branches.
Ohm's law.
According to Ohm's law for a certain section of a circuit, the current strength in a section of the circuit is directly proportional to the voltage at the ends of the section and inversely proportional to the resistance.