Ohm's law is the basic law of electrical circuits. Moreover, it allows explaining many natural phenomena. For example, you can understand why electricity does not βhitβ birds that sit on wires. For physics, Ohm's law is extremely significant. Without his knowledge, it would be impossible to create stably working electrical circuits or there would be no electronics at all.
Dependence I = I (U) and its value
The history of the discovery of the resistance of materials is directly related to the current-voltage characteristic. What it is? 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 "current-voltage 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 when considering a metal conductor, which was done by Georg Om (1789 - 1854).
The current-voltage characteristic is a linear relationship. Therefore, her schedule is a straight line.
Law in simple form
Ohm's research 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 some coefficient, that is, I ~ 1 / R. This coefficient became known as the "resistance of the conductor", and the unit of measurement of electrical resistance is Ohm or V / A.
It is worth noting one more thing. Ohm's law is often used to calculate resistance in circuits.
The wording of the law
Ohm's law says that the current strength (I) of a single section of the 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 the part of the electrical circuit that does not contain a current source. How to use Ohm's law in an inhomogeneous chain will be discussed below.
Later it was experimentally established that the law remains valid for solutions of electrolytes in an electric circuit.
Physical meaning of resistance
Resistance is the property of materials, substances or media to impede the passage of electric current. Quantitatively, a resistance of 1 Ohm means that an electric current of 1 A is capable of passing through a conductor at a voltage of 1 V at its ends
Electrical resistivity
It was established by an experimental method that the electrical current resistance of a conductor depends on its size: length, width, height. And also from its shape (sphere, cylinder) and the material from which it is made. Thus, the resistivity formula of, for example, 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 is calculated for the coefficient of resistivity of the conductor in SI - this is Ohm * m.
In the resistivity formula, p is the resistance coefficient determined by the chemical properties of the material of which the conductor is made.
To consider the differential form of Ohm's law, it is necessary to consider a few more concepts.
Current density
As you know, an electric current is a strictly ordered movement of any charged particles. For example, in metals, electrons act as current carriers, and ions in conductive gases.
Take the trivial case when all current carriers are homogeneous - a metal conductor. Mentally select an infinitesimal volume in this conductor and denote by u the average (drift, ordered) velocity of electrons in the taken volume. Next, let n denote the concentration of current carriers in a unit volume.
Now we draw an infinitesimal area dS perpendicular to the vector u and construct along the speed an infinitesimal cylinder with a height u * dt, where dt is the time during which all the current velocity carriers contained in the volume under consideration pass through the area dS.
In this case, the electrons will transfer a charge equal to q = n * e * u * dS * dt, where e is the electron charge. Thus, the electric current density is the vector j = n * e * u, which indicates the amount of charge transferred per unit time through a unit area.
One of the advantages of differential definition of Ohm's law is that you can often do without calculating the resistance.
Electric charge. Electric field strength
Field strength along with electric charge is a fundamental parameter in the theory of electricity. At the same time, a quantitative idea of ββthem can be obtained from simple experiments available to students.
For simplicity, we will consider the electrostatic field. This is an electric field that does not change with time. Such a field can be created by motionless electric charges.
Also for our purposes, a test charge is required. In its quality, we will use a charged body - so small that it is not able to cause any disturbances (redistribution of charges) in the surrounding objects.
Let us consider, in turn, two test charges taken, successively placed at one point in space under the influence of an electrostatic field. It turns out that the charges will be exposed to a constant effect from time on his part. Let F 1 and F 2 be the forces acting on the charges.
As a result of the generalization of 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 placed in turn. Therefore, the ratio F 1 / F 2 is a characteristic of the charges themselves, and does not depend on the field.
The discovery of this fact made it possible to characterize the electrification of bodies and was hereinafter called the electric charge. Thus, by definition, q 1 / q 2 = F 1 / F 2 is obtained, where q 1 and q 2 are the magnitudes 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 side of the field.
From such considerations, the charges of various particles were experimentally established. By conditionally putting one of the test charges in the ratio equal to unity, we can calculate the value of the other charge by measuring the ratio F 1 / F 2 .
Through a known charge, any electric field can be characterized. Thus, the force acting on a single test charge, which is at rest, is called the electric field strength and is denoted by E. From the definition of the charge, we obtain that the intensity vector has the following form: E = F / q.
The relationship of vectors j and E. Another form of Ohm's law
In a homogeneous conductor, the ordered motion of charged particles will occur in the direction of the vector E. And this means that the vectors j and E will be aligned. As in determining the current density, we select in the conductor an infinitesimal cylindrical volume. Then, a current equal to j * dS will pass through the cross section of this cylinder, and the voltage applied to the cylinder will be equal to E * dl. Also known is the cylinder resistivity formula.
Then, having written the formula of the current strength in two ways, we get: j = E / p, where the value 1 / p is called the electrical conductivity and is inverse to the electrical resistivity. It is customary to denote Ο (sigma) or Ξ» (lambda). The unit of conductivity is Sm / m, where Sm is Siemens. The unit is the inverse of ohms.
Thus, one can answer the question posed above about Ohm's law for an inhomogeneous chain. In this case, the current carriers will be affected by the force from the side of the electrostatic field, which is characterized by the strength E 1 , and other forces acting on them from the side of another current source, which can be designated E 2 . Then Ohm's law, as applied to an inhomogeneous part of the chain, will have the form: j = Ξ» (E 1 + E 2 ).
More on Conductivity and Resistance
The ability of a conductor to conduct electric current is characterized by its resistivity, which can be found through the formula of resistivity, or conductivity, calculated as the inverse of conductivity. The value of these parameters is determined both by the chemical properties of the material of the conductor, and by external conditions. In particular, ambient temperature.
For most metals, the resistivity at normal temperature is proportional to it, that is, p ~ T. However, at low temperatures, deviations are observed. For a large number of metals and alloys at temperatures close to 0 Β° K, the calculation of resistance showed zero values. This phenomenon is called superconductivity. For example, mercury, tin, lead, aluminum, and others have this property. Each metal has its own critical temperature T k at which superconductivity is observed .
We also note that the determination of the specific resistance of the cylinder can be generalized for wires consisting of one material. In this case, the cross-sectional area from the resistivity formula will be equal to the cross-section of the wire, and l is its length.