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Concept of alternating current

Preface.

Before you start talking about the meters, remember that these are electrical appliances, and in the following description I will rush into all sorts of clever terms. Of course, if you have an electrical engineering education, then this part can be skipped immediately. And if you only know about electricity, that if you plug the iron into the socket, it starts to warm up, then I strongly recommend reading this chapter so that you do not feel like a stranger at a general celebration of life. The chapter is taken from the site Voropayev EG "Electrical Engineering" , there are still many of these, I recommend reading for self-education, it is written quite popularly (at the level of the first year of an electrical engineering technical school).

So:

Definition: Variables are called currents and voltages that vary in time, in magnitude and direction. Their value at any given time is called the instantaneous value. Denoted by instantaneous values ​​in small letters: i, u, e, p.

Currents whose values ​​are repeated at regular intervals are called periodic. The smallest time interval, after which their repetitions are observed, is called the period and is denoted by the letter T. The reciprocal of the period is called the frequency, i.e.
and is measured in hertz (Hz). Magnitude called the angular frequency of the alternating current, it shows the change in the phase of the current per unit of time and is measured in radians divided by seconds

The maximum value of alternating current or voltage is called amplitude. It is denoted by large letters with the index '' m '' (for example, I m ). There is also the concept of the effective value of alternating current (I). Quantitatively, it is equal to:

it should be noted that the effective value of the voltage is less than the maximum.

Alternating current can be mathematically written in the form:

Here the index expresses the initial phase. If the sine wave starts at the intersection of the coordinate axes, then = 0, then


The initial value of the current can be left or right of the ordinate axis. Then the initial phase will be advanced or lagging.

1.2. RESISTANCE IN AC CIRCUITS.

The electric current in the conductors is continuously connected with the magnetic and electric fields.
Elements that characterize the conversion of electromagnetic energy into heat are called active resistances (denoted by R).
Elements associated with the presence of a magnetic field only are called inductances.
Elements associated with the presence of an electric field are called capacitances.
Typical representatives of active resistance are resistors, incandescent lamps, electric furnaces, etc.
Inductance have coil relays, windings of electric motors and transformers. Inductive resistance is calculated by the formula:

where L is the inductance.
Capacitors have capacitors, long power lines, etc.
Capacitive resistance is calculated by the formula:

where C is the capacity.
Real consumers of electrical energy may have a complex value of resistance. In the presence of R and L, the value of the total resistance Z is calculated by the formula:

Similarly, the calculation is carried out Z and for the chain R and C:

Consumers with R, L, C have total resistance:

1.3. SERIAL CONNECTION OF ACTIVE RESISTANCE R,
CAPACITOR C AND INDUCTIVITY L

Consider a circuit with active, inductive and capacitive impedances connected in series (Fig. 1.3.1).

To analyze the circuit, decompose the mains voltage U into three components:
U R - the voltage drop across the active resistance,
U L - voltage drop on inductive resistance,
U C - the voltage drop across the capacitance.

The current in the circuit I will be common to all elements:


Check produced by the formula:

It should be noted that the voltages on individual sections of the circuit do not always coincide in phase with the current I.
So, on active resistance, the voltage drop coincides in phase with the current, on the inductive one it is ahead in phase of the current by 90 ° and on capacitive - it is 90 ° behind it.
Graphically, this can be shown on a vector diagram (Fig. 1.3.2).

The three voltage drop vectors shown above can be geometrically added to one (Fig. 1.3.3).

In such a combination of elements, active-inductive or active-capacitive nature of the load of the circuit is possible. Therefore, the phase shift has both positive and negative signs.
An interesting mode is when = 0.
In this case

This mode of operation of the circuit is called voltage resonance.
Impedance at voltage resonance has a minimum value:
, and at a given voltage U, the current I can reach a maximum value.
From the condition determine the resonant frequency

The phenomenon of voltage resonance is widely used in radio engineering and in individual industrial installations.

1.4. PARALLEL CONNECTION OF CAPACITOR AND COIL,
HAVING ACTIVE RESISTANCE AND INDUCTIVITY

Consider a parallel circuit including a capacitor and a coil with active resistance and inductance (Fig. 1.4.1).

In this scheme, the common parameter for the two branches is the voltage U. The first branch, the inductive coil, has the active resistance R and the inductance L. The resulting resistance Z 1 and the current I 1 are determined by the formula:

where

Since the resistance of this branch is complex, the current in the branch lags in phase from the voltage by an angle.

Let's show it on the vector diagram (fig. 1.4.2).

We project the current vector I 1 on the coordinate axis. The horizontal component of the current will be the active component of I 1R , and the vertical component of I 1L . The quantitative values ​​of these components will be equal to:

Where

The second branch includes a capacitor. His resistance

This current leads the phase of the voltage by 90 °.
To determine the current I in the unbranched part of the circuit, we use the formula:

Its value can be obtained graphically by adding the vectors I 1 and I 2 (Fig. 1.4.3)
The angle of shift between current and voltage is denoted by j .
Here various modes are possible in the operation of the circuit. At = + 90 °, the capacitive current will prevail, at = -90 ° - inductive current.
The mode is possible when = 0, i.e. the current in the unbranched part of circuit I will be active. This will happen in the case when I 1L = I 2 , i.e. with equal reactive components of the current in the branches.

On the vector diagram it will look like this (Fig. 1.4.4):

This mode is called current resonance. Also as in the case of voltage resonance, it is widely used in radio engineering.
The above case of parallel connection of R, L and C can also be analyzed in terms of increasing cos j for electrical installations. It is known that cos j is a technical and economic parameter in the operation of electrical installations. It is determined by the formula:

where

Р - active power of electrical installations, kW,
S is the total power of electrical installations, kW.
In practice, cos j is determined by taking the readings of active and reactive energy from the meters, and by dividing one indication by another, we get tg j .
Further, according to the tables, find cos j .
The more cos j , the more economically the power system works, since with the same values ​​of current and voltage (which the generator is designed for) it is possible to get more active power from it.
Reducing cos j leads to incomplete use of equipment and at the same time decreases the efficiency of the installation. Electricity tariffs provide for a lower cost of 1 kilowatt-hour at high cos j , compared to low.
The cos enhancement activities include:
- prevention of idling of electrical equipment,
- full loading of electric motors, transformers, etc.
In addition, cos j is positively affected by the connection to the network of static capacitors.