Electrical resistance is a physical quantity that characterizes. "Electrical resistance. Electrical resistivity
Without some basic knowledge about electricity, it is difficult to imagine how electrical appliances work, why they work at all, why you need to plug in the TV to make it work, and why a flashlight only needs a small battery to shine in the dark.
And so we will understand everything in order.
Electricity
Electricity is a natural phenomenon that confirms the existence, interaction and movement of electrical charges. Electricity was first discovered back in the 7th century BC. Greek philosopher Thales. Thales noticed that if a piece of amber is rubbed on wool, it begins to attract light objects. Amber in ancient Greek is electron.
This is how I imagine Thales sitting, rubbing a piece of amber on his himation (this is the woolen outerwear of the ancient Greeks), and then with a puzzled look he watches as hair, scraps of thread, feathers and scraps of paper are attracted to the amber.
This phenomenon is called static electricity. You can repeat this experience. To do this, rub a regular plastic ruler thoroughly with a woolen cloth and bring it to the small pieces of paper.
It should be noted that this phenomenon has not been studied for a long time. And only in 1600, in his essay “On the Magnet, Magnetic Bodies and the Great Magnet - the Earth,” the English naturalist William Gilbert introduced the term electricity. In his work, he described his experiments with electrified objects, and also established that other substances can become electrified.
Then, for three centuries, the most advanced scientists in the world research electricity, write treatises, formulate laws, invent electrical machines, and only in 1897 Joseph Thomson discovers the first material carrier of electricity - the electron, a particle that makes electrical processes in substances possible.
Electron– this is an elementary particle, has a negative charge approximately equal to -1.602·10 -19 Cl (Pendant). Designated e or e –.
Voltage
To make charged particles move from one pole to another, it is necessary to create between the poles potential difference or - Voltage. Voltage unit – Volt (IN or V). In formulas and calculations, voltage is denoted by the letter V . To obtain a voltage of 1 V, you need to transfer a charge of 1 C between the poles, while doing 1 J (Joule) of work.
For clarity, imagine a water tank located at a certain height. A pipe comes out of the tank. Water under natural pressure leaves the tank through a pipe. Let's agree that water is electric charge, the height of the water column (pressure) is voltage, and the speed of water flow is electricity.
Thus, the more water in the tank, the higher the pressure. Similarly from an electrical point of view, the greater the charge, the higher the voltage.
Let's start draining the water, the pressure will decrease. Those. The charge level drops - the voltage decreases. This phenomenon can be observed in a flashlight; the light bulb becomes dimmer as the batteries are discharged. Please note that the lower the water pressure (voltage), the lower the water flow (current).
Electricity
Electricity is a physical process of directed movement of charged particles under the influence of an electromagnetic field from one pole of a closed electrical circuit to the other. Charge-carrying particles can include electrons, protons, ions and holes. Without a closed circuit, no current is possible. Particles capable of carrying electrical charges do not exist in all substances; those in which they exist are called conductors And semiconductors. And substances in which there are no such particles - dielectrics.
Current unit – Ampere (A). In formulas and calculations, current strength is indicated by the letter I . A current of 1 Ampere is generated when a charge of 1 Coulomb (6.241·10 18 electrons) passes through a point in an electrical circuit in 1 second.
Let's look again at our water-electricity analogy. Only now let’s take two tanks and fill them with an equal amount of water. The difference between the tanks is the diameter of the outlet pipe.
Let's open the taps and make sure that the flow of water from the left tank is greater (the diameter of the pipe is larger) than from the right. This experience is clear evidence of the dependence of flow speed on pipe diameter. Now let's try to equalize the two flows. To do this, add water (charge) to the right tank. This will give more pressure (voltage) and increase flow rate (current). In an electrical circuit, the pipe diameter is played by resistance.
The experiments carried out clearly demonstrate the relationship between voltage, electric shock And resistance. We'll talk more about resistance a little later, but now a few more words about the properties of electric current.
If the voltage does not change its polarity, plus to minus, and the current flows in one direction, then this is D.C. and correspondingly constant pressure. If the voltage source changes its polarity and the current flows first in one direction, then in the other, this is already alternating current And AC voltage. Maximum and minimum values (indicated on the graph as Io ) - This amplitude or peak current values. In home sockets, the voltage changes its polarity 50 times per second, i.e. the current oscillates here and there, it turns out that the frequency of these oscillations is 50 Hertz, or 50 Hz for short. In some countries, for example in the USA, the frequency is 60 Hz.
Resistance
Electrical resistance– a physical quantity that determines the property of a conductor to impede (resist) the passage of current. Resistance unit – Ohm(denoted Ohm or the Greek letter omega Ω ). In formulas and calculations, resistance is indicated by the letter R . A conductor has a resistance of 1 ohm to the poles of which a voltage of 1 V is applied and a current of 1 A flows.
Conductors conduct current differently. Their conductivity depends, first of all, on the material of the conductor, as well as on the cross-section and length. The larger the cross-section, the higher the conductivity, but the longer the length, the lower the conductivity. Resistance is the inverse concept of conductivity.
Using the plumbing model as an example, resistance can be represented as the diameter of the pipe. The smaller it is, the worse the conductivity and the higher the resistance.
The resistance of a conductor manifests itself, for example, in the heating of the conductor when current flows through it. Moreover, the greater the current and the smaller the cross-section of the conductor, the stronger the heating.
Power
Electric power is a physical quantity that determines the rate of electricity conversion. For example, you have heard more than once: “a light bulb is so many watts.” This is the power consumed by the light bulb per unit of time during operation, i.e. converting one type of energy into another at a certain speed.
Sources of electricity, such as generators, are also characterized by power, but already generated per unit of time.
Power unit – Watt(denoted W or W). In formulas and calculations, power is indicated by the letter P . For alternating current circuits the term is used Full power, unit - Volt-amps (VA or V·A), denoted by the letter S .
And finally about Electric circuit. This circuit is a certain set of electrical components capable of conducting electric current and interconnected accordingly.
What we see in this image is a basic electrical device (flashlight). Under voltage U(B) a source of electricity (batteries) through conductors and other components with different resistances 4.59 (220 Votes)
In physics, electrical resistance is a physical quantity that characterizes the ability of a conductor to prevent the flow of electric current.
What is electrical resistance
Every body, every substance has electrical resistance. If you apply the same voltage to different bodies, different currents will flow through them, because they have different resistance. There are substances through which current will not flow at all. Such substances are called dielectrics, and substances that transmit electric current are called conductors.
As you know, current is the directed movement of electrons. Electrons from the negative pole of the voltage source enter the conductor, where they knock out other electrons from the conductor molecule, taking their place. Electrons seem to pass the baton from molecule to molecule.
In addition, conductors also have their own free electrons that are not associated with any specific atom. All these particles move along the conductor. Since free electrons are present throughout the conductor, when a voltage is applied, the electrons instantly reach the positive pole.
Molecules of different substances hold their electrons with different strengths. For example, it is easier to knock out particles from gold than from copper, and there are more free electrons in it, which means that the resistance of gold is less. Dielectric molecules give up their electrons extremely reluctantly, so no current flows through them.
How to determine the resistance value
The ability of a conductor to resist the passage of current is called resistance and is denoted by the letter R. Resistance is strictly related to current and voltage. If a voltage U is applied to the ends of a conductor with a resistance R, a current I will flow through it. R = U/ I. This is called Ohm's law.
In Omaha. 1 Ohm is the resistance through which a current of 1 Ampere flows at a voltage of 1 Volt.
Any conductor is characterized by a resistivity ρ. For each conductor this value is unchanged; it is indicated in reference books. Specific resistance is the resistance possessed by a conductor with a length of l=1 m and a cross-sectional area of S=1 sq.m. This means that the resistance is R=ρl/S. The longer the conductor, the greater the resistance, and as the cross-sectional area increases, the resistance decreases.
It should be borne in mind that when the conductor is heated, the resistance increases, and when it cools, on the contrary, it decreases. At absolute zero (-273°C) the resistance is close to zero. This phenomenon is called superconductivity. The resistivity indicated in reference books is measured under normal conditions, i.e. at room temperature.
Internal and external resistance
Not only conductors and elements of electrical circuits have resistance, but also voltage sources. The source's own resistance r is called internal, and the load resistance R is called external. Current I through the load from the source flows from minus to plus, and inside the source from plus to minus, i.e. the load current is equal to the current inside the source.
If there is voltage E at the poles of the source, then it can be determined by the formula E = IR + Ir. From here you can calculate both internal and external resistance.
When an electrical circuit is closed, at the terminals of which there is a potential difference, an electric current occurs. Free electrons, under the influence of electric field forces, move along the conductor. In their movement, electrons collide with conductor atoms and give them a supply of their kinetic energy. The speed of electron movement continuously changes: when electrons collide with atoms, molecules and other electrons, it decreases, then under the influence of an electric field it increases and decreases again during a new collision. As a result, a uniform flow of electrons is established in the conductor at a speed of several fractions of a centimeter per second. Consequently, electrons passing through a conductor always encounter resistance to their movement from its side. When electric current passes through a conductor, the latter heats up.
Electrical resistance
The electrical resistance of the conductor, which is denoted by the Latin letter r, is the property of a body or medium to convert electrical energy into thermal energy when an electric current passes through it.
In the diagrams, electrical resistance is indicated as shown in Figure 1, A.
Variable electrical resistance, which serves to change the current in a circuit, is called rheostat. In the diagrams, rheostats are designated as shown in Figure 1, b. In general, a rheostat is made of a wire of one resistance or another, wound on an insulating base. The slider or rheostat lever is placed in a certain position, as a result of which the required resistance is introduced into the circuit.
A long conductor with a small cross-section creates a large resistance to current. Short conductors with a large cross-section offer little resistance to current.
If you take two conductors from different materials, but the same length and cross-section, then the conductors will conduct current differently. This shows that the resistance of a conductor depends on the material of the conductor itself.
The temperature of the conductor also affects its resistance. As temperature increases, the resistance of metals increases, and the resistance of liquids and coal decreases. Only some special metal alloys (manganin, constantan, nickel and others) hardly change their resistance with increasing temperature.
So, we see that the electrical resistance of a conductor depends on: 1) the length of the conductor, 2) the cross-section of the conductor, 3) the material of the conductor, 4) the temperature of the conductor.
The unit of resistance is one ohm. Om is often represented by the Greek capital letter Ω (omega). Therefore, instead of writing “The conductor resistance is 15 ohms,” you can simply write: r= 15 Ω.
1,000 ohms is called 1 kiloohm(1kOhm, or 1kΩ),
1,000,000 ohms is called 1 megaohm(1mOhm, or 1MΩ).
When comparing the resistance of conductors from different materials, it is necessary to take a certain length and cross-section for each sample. Then we will be able to judge which material conducts electric current better or worse.
Video 1. Conductor resistance
Electrical resistivity
The resistance in ohms of a conductor 1 m long, with a cross section of 1 mm² is called resistivity and is denoted by the Greek letter ρ (ro).
Table 1 shows the resistivities of some conductors.
Table 1
Resistivities of various conductors
The table shows that an iron wire with a length of 1 m and a cross-section of 1 mm² has a resistance of 0.13 Ohm. To get 1 Ohm of resistance you need to take 7.7 m of such wire. Silver has the lowest resistivity. 1 Ohm of resistance can be obtained by taking 62.5 m of silver wire with a cross section of 1 mm². Silver is the best conductor, but the cost of silver excludes the possibility of its mass use. After silver in the table comes copper: 1 m of copper wire with a cross section of 1 mm² has a resistance of 0.0175 Ohm. To get a resistance of 1 ohm, you need to take 57 m of such wire.
Chemically pure copper, obtained by refining, has found widespread use in electrical engineering for the manufacture of wires, cables, windings of electrical machines and devices. Aluminum and iron are also widely used as conductors.
The conductor resistance can be determined by the formula:
Where r– conductor resistance in ohms; ρ – specific resistance of the conductor; l– length of the conductor in m; S– conductor cross-section in mm².
Example 1. Determine the resistance of 200 m of iron wire with a cross section of 5 mm².
Example 2. Calculate the resistance of 2 km of aluminum wire with a cross section of 2.5 mm².
From the resistance formula you can easily determine the length, resistivity and cross-section of the conductor.
Example 3. For a radio receiver, it is necessary to wind a 30 Ohm resistance from nickel wire with a cross section of 0.21 mm². Determine the required wire length.
Example 4. Determine the cross-section of 20 m of nichrome wire if its resistance is 25 Ohms.
Example 5. A wire with a cross section of 0.5 mm² and a length of 40 m has a resistance of 16 Ohms. Determine the wire material.
The material of the conductor characterizes its resistivity.
Based on the resistivity table, we find that lead has this resistance.
It was stated above that the resistance of conductors depends on temperature. Let's do the following experiment. Let's wind several meters of thin metal wire in the form of a spiral and connect this spiral to the battery circuit. To measure current, we connect an ammeter to the circuit. When the coil is heated in the burner flame, you will notice that the ammeter readings will decrease. This shows that the resistance of a metal wire increases with heating.
For some metals, when heated by 100°, the resistance increases by 40–50%. There are alloys that change their resistance slightly with heating. Some special alloys show virtually no change in resistance when temperature changes. The resistance of metal conductors increases with increasing temperature, while the resistance of electrolytes (liquid conductors), coal and some solids, on the contrary, decreases.
The ability of metals to change their resistance with changes in temperature is used to construct resistance thermometers. This thermometer is a platinum wire wound on a mica frame. By placing a thermometer, for example, in a furnace and measuring the resistance of the platinum wire before and after heating, the temperature in the furnace can be determined.
The change in the resistance of a conductor when it is heated per 1 ohm of initial resistance and per 1° temperature is called temperature coefficient of resistance and is denoted by the letter α.
If at temperature t 0 conductor resistance is r 0 , and at temperature t equals r t, then the temperature coefficient of resistance
Note. Calculation using this formula can only be done in a certain temperature range (up to approximately 200°C).
We present the values of the temperature coefficient of resistance α for some metals (Table 2).
table 2
Temperature coefficient values for some metals
From the formula for the temperature coefficient of resistance we determine r t:
r t = r 0 .
Example 6. Determine the resistance of an iron wire heated to 200°C if its resistance at 0°C was 100 Ohms.
r t = r 0 = 100 (1 + 0.0066 × 200) = 232 ohms.
Example 7. A resistance thermometer made of platinum wire had a resistance of 20 ohms in a room at 15°C. The thermometer was placed in the oven and after some time its resistance was measured. It turned out to be equal to 29.6 Ohms. Determine the temperature in the oven.
Electrical conductivity
So far, we have considered the resistance of a conductor as the obstacle that the conductor provides to the electric current. But still, current passes through the conductor. Therefore, in addition to resistance (obstacle), the conductor also has the ability to conduct electric current, that is, conductivity.
The more resistance a conductor has, the less conductivity it has, the worse it conducts electric current, and, conversely, the lower the resistance of a conductor, the more conductivity it has, the easier it is for current to pass through the conductor. Therefore, the resistance and conductivity of a conductor are reciprocal quantities.
From mathematics it is known that the inverse of 5 is 1/5 and, conversely, the inverse of 1/7 is 7. Therefore, if the resistance of a conductor is denoted by the letter r, then the conductivity is defined as 1/ r. Conductivity is usually symbolized by the letter g.
Electrical conductivity is measured in (1/Ohm) or in siemens.
Example 8. The conductor resistance is 20 ohms. Determine its conductivity.
If r= 20 Ohm, then
Example 9. The conductivity of the conductor is 0.1 (1/Ohm). Determine its resistance
If g = 0.1 (1/Ohm), then r= 1 / 0.1 = 10 (Ohm)
It's time to find out what resistance is. Now imagine an ordinary crystal lattice. So... The closer the crystals are located to each other, the more charges will be retained in them. This means, in simple terms, the greater the resistance of the metal. By the way, the resistance of any ordinary metal can be temporarily increased by heating it. “Why?”, ask. Yes, because when heated, metal atoms begin to vibrate intensely near their position fixed by bonds. Therefore, moving charges will collide with atoms more often, and therefore will be more often and more delayed in the nodes of the crystal lattice. Figure 1 shows a visual assembly diagram, so to speak, for the “uninitiated,” where you can immediately see how to measure the voltage across the resistance. In exactly the same way, you can measure the voltage on a light bulb. By the way, if, as can be seen from the figure, our battery has a voltage of, say, 15V (Volt), and the resistance is such that 10V “settles” on it, then the remaining 5V will go to the light bulb.
This is what Ohm's law looks like for a closed circuit.
Without going into details, this law says that the voltage of the power source is equal to the sum of the voltage drops in all its sections. Those. in our case, 15V = 10V + 5V. But... if you delve a little into the details, you need to know that what we called the battery voltage is nothing more than its value when a consumer is connected (in our case, this is a light bulb + resistance). If you disconnect the light bulb with the resistance and measure the voltage value on the battery, it will turn out to be slightly more than 15V. This will be the open circuit voltage and it is “called” the EMF of the battery - electromotive force. In reality the circuit will work as shown in Fig. 2. In reality, a battery can be imagined as some other battery with a voltage of, say, 16V, which has its own internal resistance Rin. The value of this resistance is very small and is determined by the technological features of manufacturing. It can be seen from the figure that when a load is connected, part of the battery voltage will “settle” on its internal resistance and its output will no longer be 16V, but 15V, i.e. 1B will be “absorbed” by its internal resistance. Ohm’s law for a closed circuit also applies here. The sum of the voltages in all sections of the circuit will be equal to the emf of the battery. 16V = 1V + 10V + 5V. The unit of resistance is a value called Ohm. It was named after the German physicist Georg Simon Ohm, who was involved in this work. 1 Ohm is equal to the electrical resistance of a conductor (it could, for example, be a light bulb) between the ends of which a voltage of 1 volt occurs at a direct current of 1 ampere. To determine the resistance of the lamp, it is necessary to measure the voltage on it and measure the current in the circuit (see Fig. 5). And then divide the resulting voltage value by the current value (R=U/I). Resistances in electrical circuits can be connected in series (the end of the first with the beginning of the second - in this case they can be designated arbitrarily) and in parallel (beginning with the beginning, end with the end - and in this case they can be designated arbitrarily). Let's consider both cases using light bulbs as an example - after all, their filaments are made of tungsten, i.e. represent resistance. The case of a serial connection is shown in Fig. 3.
The result is a garland known to everyone (and, therefore, we will consider it understandable). With such a connection, the current I will be the same everywhere, regardless of whether these are identical lamps with the same voltage or different ones. We must immediately make a reservation that lamps on which:
- the same voltage and current are indicated (like light bulbs from a flashlight);
- The same voltage and power are indicated (similar to lighting lamps).
In this case, the voltage U of the power source “spreads” over all lamps, i.e. U = U1 + U2 + U3. Moreover, if the lamps are the same, the voltage on all of them will be the same. If the lamps are not the same, then depending on the resistance of each specific lamp. In the first case, the voltage across each lamp can be easily calculated by dividing the source voltage by the total number of lamps. In the second case, you need to delve into the calculations. We will consider all this in the tasks of this section. So, we found out that when connecting conductors (in this case, lamps) in series, the voltage U at the ends of the entire circuit is equal to the sum of the voltages of the conductors (lamps) connected in series - U = U1 + U2 + U3. According to Omadl's law of the circuit section: U1 = I*R1, U2 = I*R2, U3 = I*R3, U = I*R where R1 is the resistance of the filament of the first lamp (conductor), R2 - the second and R3 - the third, R - impedance of all lamps. Replacing the value of U with I*R, U1 with I*R1, U2 with I*R2, U3 with I*R3 in the expression “U = U1 + U2 +U”, we get I*R = I*(R1+R2+R3 ). Hence R = R1+R2+R3. Conclusion: when conductors are connected in series, their total resistance is equal to the sum of the resistances of all conductors. Let's conclude: sequential connection is used for several consumers (for example, New Year's garland lamps) with a supply voltage lower than the source voltage.
The case of parallel connection of conductors is shown in Fig. 4.
When conductors are connected in parallel, their beginnings and ends have common connection points to the source. In this case, the voltage on all lamps (conductors) is the same, regardless of which of them and what voltage they are designed for, since they are directly connected to the source. Naturally, if the lamp is at a lower voltage than the voltage source, it will burn out. But the current I will be equal to the sum of the currents in all lamps, i.e. I = I1 + I2 + I3. And the lamps can be of different power - each will take the current for which it is designed. This can be understood if, instead of a source, we imagine a socket with a voltage of 220V, and instead of lamps, we imagine, for example, an iron, a table lamp and a phone charger connected to it. The resistance of each device in such a circuit is determined by dividing its voltage by the current it consumes... again, according to Ohm's law for a section of the circuit, i.e.
Let us immediately state the fact that there is a quantity that is the reciprocal of resistance and it is called conductivity. It is designated Y. In the SI system it is designated as Cm (Siemens). The inverse of resistance means that
Without going into mathematical conclusions, we will immediately say that when connecting conductors in parallel (be it lamps, irons, microwaves or TVs), the reciprocal of the total resistance is equal to the sum of the reciprocals of the resistances of all parallel-connected conductors, i.e.
Considering that
Sometimes in problems they write Y = Y1 + Y2 + Y3. It is the same. There is also a more convenient formula for finding the total resistance of two parallel-connected resistances. It looks like this:
Let us conclude: the parallel switching method is used to connect lighting lamps and household electrical appliances to the electrical network.
As we found out, collisions of free electrons in conductors with atoms of the crystal lattice inhibit their forward motion... This is opposition to the directional movement of free electrons, i.e. direct current, constitutes the physical essence of conductor resistance. The mechanism of resistance to direct current in electrolytes and gases is similar. The conductive properties of a material determine its volumetric resistivity ρv, equal to the resistance between opposite sides of a cube with an edge of 1 m, made of this material. The reciprocal of volume resistivity is called volume conductivity and is equal to γ = 1/ρv. The unit of volume resistance is 1 Ohm*m, volume specific conductivity is 1 S/m. The resistance of a conductor to direct current depends on temperature. In the general case, a rather complex dependence is observed. But when the temperature changes within a relatively narrow range (about 200°C), it can be expressed by the formula:
where R2 and R1 are resistances at temperatures T1 and T2, respectively; α is the temperature coefficient of resistance, equal to the relative change in resistance when the temperature changes by 1°C.
Important Concepts
An electrical device that has resistance and is used to limit current is called a resistor. An adjustable resistor (i.e., it is possible to change its resistance) is called a rheostat.
Resistive elements are idealized models of resistors and any other electrical devices or parts thereof that resist direct current, regardless of the physical nature of this phenomenon. They are used in drawing up equivalent circuits and calculating their modes. When idealizing, currents through the insulating coatings of resistors, frames of wire rheostats, etc. are neglected.
A linear resistive element is an equivalent circuit for any part of an electrical device in which the current is proportional to the voltage. Its parameter is resistance R = const. R = const means that the resistance value is unchanged (const means constant).
If the dependence of current on voltage is nonlinear, then the equivalent circuit contains a nonlinear resistive element, which is specified by the nonlinear I-V characteristic (volt-ampere characteristic) I(U) - read as “And from Y”. Figure 5 shows the current-voltage characteristics of linear (line a) and nonlinear (line b) resistive elements, as well as their designations on equivalent circuits.
Ohm's law is the fundamental law of electrical circuits. At the same time, it allows us to explain many natural phenomena. For example, you can understand why electricity does not “hit” birds that are sitting on wires. For physics, Ohm's law is extremely significant. Without his knowledge, it would be impossible to create stable electrical circuits or there would be no electronics at all.
Dependence I = I(U) and its meaning
The history of the discovery of the resistance of materials is directly related to the current-voltage characteristic. What it is? Let's take a circuit with a constant electric current and consider any of its elements: a lamp, a gas tube, a metal conductor, an electrolyte flask, etc.
By changing the voltage U (often denoted as V) supplied to the element in question, we will monitor the change in the current strength (I) passing through it. As a result, we obtain a dependence of the form I = I (U), which is called the “volt-ampere characteristic of the element” and is a direct indicator of its electrical properties.
The current-voltage characteristic may look different for different elements. Its simplest form is obtained by examining a metal conductor, which is what Georg Ohm (1789 - 1854) did.
The current-voltage characteristic is a linear relationship. Therefore, its graph is a straight line.
Law in simple form
Ohm's studies on the current-voltage characteristics of conductors showed that the current strength inside a metal conductor is proportional to the potential difference at its ends (I ~ U) and inversely proportional to a certain coefficient, that is, I ~ 1/R. This coefficient became known as “conductor resistance,” and the unit of measurement of electrical resistance is Ohm or V/A.
Another thing worth noting is this. Ohm's law is often used to calculate resistance in circuits.
Statement of the law
Ohm's law says that the current strength (I) of a single section of a circuit is proportional to the voltage in this section and inversely proportional to its resistance.
It should be noted that in this form the law remains true only for a homogeneous section of the chain. Homogeneous is that part of the electrical circuit that does not contain a current source. How to use Ohm's law in an inhomogeneous circuit will be discussed below.
Later, it was experimentally established that the law remains valid for electrolyte solutions in an electrical circuit.
Physical meaning of resistance
Resistance is the property of materials, substances or media to prevent the passage of electric current. Quantitatively, a resistance of 1 ohm means that a conductor with a voltage of 1 V at its ends is capable of passing an electric current of 1 A.
Electrical resistivity
It was established experimentally that the resistance of the electric current of a conductor depends on its dimensions: length, width, height. And also on its shape (sphere, cylinder) and the material from which it is made. Thus, the formula for resistivity, for example, of a homogeneous cylindrical conductor will be: R = p*l/S.
If in this formula we put s = 1 m 2 and l = 1 m, then R will be numerically equal to p. From here the unit of measurement for the conductor resistivity coefficient in SI is calculated - this is Ohm*m.
In the resistivity formula, p is the resistance coefficient determined by the chemical properties of the material from which the conductor is made.
To consider the differential form of Ohm's law, it is necessary to consider several more concepts.
As is known, electric current is a strictly ordered movement of any charged particles. For example, in metals the current carriers are electrons, and in conducting gases they are ions.
Let's take a trivial case when all current carriers are homogeneous - a metal conductor. Let us mentally select an infinitesimal volume in this conductor and denote by u the average (drift, ordered) speed of electrons in this volume. Next, let n denote the concentration of current carriers per unit volume.
Now let’s draw an infinitesimal area dS perpendicular to the vector u and construct an infinitesimal cylinder with a height u*dt along the velocity, where dt denotes the time during which all current velocity carriers contained in the volume under consideration will pass through the area dS.
In this case, the electrons will transfer a charge through the area equal to q = n*e*u*dS*dt, where e is the charge of the electron. Thus, the electric current density is a vector j = n*e*u, denoting the amount of charge transferred per unit time through a unit area.
One of the advantages of the differential definition of Ohm's law is that it is often possible to do without calculating resistance.
Electric charge. Electric field strength
Field strength, along with electric charge, is a fundamental parameter in the theory of electricity. Moreover, a quantitative idea of them can be obtained from simple experiments available to schoolchildren.
For simplicity of reasoning, we will consider the electrostatic field. This is an electric field that does not change over time. Such a field can be created by stationary electric charges.
A test charge is also necessary for our purposes. We will use a charged body as it - so small that it is not capable of causing any disturbances (redistribution of charges) in surrounding objects.
Let us consider in turn two taken test charges, sequentially placed at one point in space, which is under the influence of an electrostatic field. It turns out that the charges will be subject to constant influence on his part over time. Let F 1 and F 2 be the forces acting on the charges.
As a result of generalizing the experimental data, it was found that the forces F 1 and F 2 are directed either in one or in opposite directions, and their ratio F 1 / F 2 is independent of the point in space where the test charges were alternately placed. Consequently, the ratio F 1 / F 2 is a characteristic exclusively of the charges themselves, and does not depend in any way on the field.
The discovery of this fact made it possible to characterize the electrification of bodies and was later called an electric charge. Thus, by definition, it turns out q 1 /q 2 = F 1 /F 2, where q 1 and q 2 are the magnitude of the charges placed at one point of the field, and F 1 and F 2 are the forces acting on the charges from the field.
From similar considerations, the charges of various particles were experimentally established. By conditionally putting in the ratio one of the test charges equal to one, you can calculate the value of the other charge by measuring the ratio F 1 / F 2.
Any electric field can be characterized through a known charge. Thus, the force acting on a unit test charge at rest is called the electric field strength and is denoted by E. From the definition of charge, we find that the strength vector has the following form: E = F/q.
Relationship between vectors j and E. Another form of Ohm's law
Also note that the definition of cylinder resistivity can be generalized to wires consisting of the same material. In this case, the cross-sectional area from the resistivity formula will be equal to the cross-section of the wire, and l - its length.
