Active resistance: basic information, formulas and dependencies for an alternating current circuit

For the design of electronic devices, various parameters should be calculated, one of which is the electrical conductivity or the resistance of the conductor. For circuits powered by direct current, it is easy to calculate. But in alternating current (AC) circuits, there are completely different ratios. To calculate the active resistance, you need to familiarize yourself with the basic formulas, as well as alternative methods for calculating it.

Basic information about electrical conductivity

Each substance conducts current in a different way. It all depends on the electronic configuration, which can be obtained from Table D. AND. Mendeleev. The electronic configuration shows the main parameter on which the resistance value R depends - the number of free electrons (Nse). A substance consists of atoms that form a crystal lattice (CR). Not all electrons are firmly held by the nucleus.

Classification of substances

In substances there are several electrons (E), which have a very weak interaction force with the nucleus. In addition, in metals, in addition to ordinary E, there is a certain Nse. When a small external energy is applied, electrons are detached from the nuclei of atoms, and this leads to the formation of ions. The metal remains uncharged, since the negative charge of all E is equal to the positive charge of the elementary particles (EF) that make up the nuclei. The nucleus consists of nucleons, namely:

• protons - positively charged EF;
• neutrons - neutral EC.

Free electrons move chaotically, but among them there are those that fly close to the surface of the metal, and they cannot fly out of the substance, since they are held by the force of attraction of ions and nuclei. Based on Nse, any substance can be divided into 3 groups by conductivity:

1. Conductors.
2. Semiconductors.
3. Dielectrics.

Conductors (P) include substances with a large Nse. These include metals, electrolytic solutions and ionized gases. In metals, free charge carriers (CHC) are free E, in electrolytes and ionized gases - ions, under the action of an electric field, the movement of the SNZ becomes ordered, as a result of which an electric current is formed (THIS).

In semiconductors, Nse depends on various external factors, under the action of which there is liberation of some E from the action of the force of attraction of the nucleus - the Coulomb force in the interaction of 2 or more particles. The place that E left is called the hole. The movement of holes and E is the opposite, and in this case, ET appears. Semiconductor-type substances include the following: silicon (Si), germanium (Ge), selenium (Se), etc.

The group of dielectrics or insulators includes substances that do not have SNC at all, and therefore, they do not conduct electric current at all. Under some conditions, the dielectric can become different from the P current, for example, if it is covered with droplets of an electrically conductive liquid. This moment is very important to avoid equipment failure or damage to ET. When flowing through P, ET has a thermal effect on it. This property is due to the fact that E interact with the nodes of the RR, and the kinetic energy E is converted into heat.

As a result, the speed of E decreases, and then it is completely restored when exposed to an electromagnetic field. This process is repeated a large number of times and is called electrical resistance, which denoted for DC circuits R, and for AC circuits (AC) there is a complete resistance - Z. R and Z are measured in ohms.

Dependence on various parameters

R is a value that depends on many factors. These factors can be divided into groups:

1. Physical properties: length, cross-sectional area (S) and deformation.
2. External environment: temperature.
3. Electric: I, U, e (electromotive force - EMF).

R is calculated according to Ohm's law: I = U / R. The formulation of this law is as follows: I, flowing in the section of the chain, is directly proportional to U and inversely proportional to R of the selected section.

Formulation for the entire circuit: I, flowing through the entire circuit, is directly proportional to the EMF and inversely proportional to R of the entire section, taking into account the internal resistance of the power source (PS). The formula is: I = e / (R + Rip). From the ratios for the complete and section of the chain, you can get R:

1. R = U / I.
2. R = (e / I) - Rip.

The type of substance is determined by the coefficient of resistivity p, which is taken from the reference book. However, it should be noted that the reference book contains its value at a temperature of +20 degrees. In addition, there is also specific conductivity, which is inversely proportional to p. It is denoted by σ and is equal to: p = 1 / σ.

At a smaller value of S, E flows through P and interactions with CR become more frequent, which illustrates the dependence of R on S. To calculate S, you need to use reference books or the Internet. If we consider that the conductor is a plane, then it is necessary to cut it using another plane (stereometry).

When cut, a flat figure is obtained in the form of a square, circle, ellipse, rectangle or triangle. Then you need to calculate the S of this figure. If P consists of a certain number of cores, then you need to measure S of one core, and then multiply by the number of cores.

R depends in direct proportion to the length P (L): the greater the length, the more interactions E makes when moving. Based on all the dependencies, R can be expressed by the formulas:

1. R = p * L / S.
2. R = L / (σ * S).

These ratios are valid at a temperature of +20 degrees, but this is not enough for accurate calculations. Some supersensitive elements may not work correctly due to low I values.

The value of p depends on t and is expressed by the following relationship: p = p20 * [1 + a * (t - 20)]. This ratio contains the following quantities:

1. p is the calculated resistivity.
2. p20 is the resistivity value taken from the reference literature at a temperature (temperature +20 degrees Celsius).
3. Temperature coefficient a, which is taken from reference literature. For metals, it is always greater than 1, and for electrolytic solutions, it is less.
4. Temperature P under specific operating conditions, temperature scale in Celsius - t.

In addition, p also depends on the level of deformation of the RR. Deformation is elastic and plastic. For elastic, p increases, and for plastic, decreases. This is due to the conditions of deformations, as well as to the degree of difficulty in movement of E. The final formula, taking into account the main factors, will take the following form: R = p20 * [1 + a * (t - 20)] * L / S.

AC ratios

In order to understand some terms, for example, what resistance is called active, and what it is, it is necessary to apply the formula for impedance: sqr (Z) = sqr® + sqr (Xc-Xl). The AC resistance is total and consists of active R, inductive (Xl) and capacitive (Xc).

Resistance formula

Resistance is called active if there is no inductance or capacitance in a section or in a complete circuit. For the calculation, it is necessary to measure the amplitude values ​​of the current and voltage. For these purposes, a voltmeter and ammeter for alternating current and voltage are used. However, the disadvantage of such measurements is to obtain not amplitude, but effective values. Amplitude values ​​are calculated using the formulas:

1. For U: Um = 1.4142 * Ud.
2. For I: Im = 1.4142 * Id.

Based on these ratios, the active resistance formula is calculated by the formula: R = Um / Im. Active resistance also depends on Um and Im.

Simple measurement methods

Accurate calculations of R are not always required, and for these purposes a device called an ohmmeter is used. With the growth of scientific progress, combined devices - multimeters - appeared on the market. They have many functions, but the main one is measuring I, R and U values. There are also specialized instruments for measuring large R values, which are called megohmmeters. A megohmmeter is used to measure the R insulation level between cable cores.

The ohmmeter is also used for troubleshooting electrical circuits, and also allows you to determine the radio component for serviceability. To measure the values ​​of R, as well as to identify malfunctions, it is necessary to follow the rules of electrical safety and de-energize the circuit section. It is also necessary to discharge the capacitors, since their charge can damage the device, which is in the R measurement mode.

Thus, the active resistance in the AC circuit is any load that is not capacitive or inductive, and depending on temperature, type of deformation, type of substance, Um, Im, length and S conductor.