a) the active resistance R, R is an idealized element of a chain, which occurs irreversible transformations of electrical energy into thermal:
BUT.
b) Inductance L is an idealized element of a chain, which is characterized by the ability to accumulate the magnetic field energy. The inductance is numerically equal to the ratio of streaming to the current, which this streaming is due to:
,
(3.6)
where 
- the clutch flow of the inductance coil,
N. -Theus turns coil,
F.- Magnetspot.
.
c) Capacity C- Idealized element electrical chainwhich characterizes the equipment to accumulate the energy of the electric field.
,
(3.7)
where 
- charge on plates or capacitor plates,
- The potential difference between the plates of the capacitor.
Capacity C - does not depend on 
, but is determined by the dimensions, the form of the condenser, as well as the dielectric properties of the medium located between the condenser plates.
.
Actual AC value
The fluctuations arising under the influence of an external periodically changing EMF are called forced electromagnetic oscillations. Installed forced electromagnetic oscillations can be considered as flowing alternating current In a chain containing a resistor, inductor inductor and a condenser.
In fig. 3.5 shows a graph of alternating sinusoidal current.
Fig. 3.5. Schedule of alternating current
The active value of alternating current is equal to such a value. direct currentwhich in the time equal to the period of alternating current is distinguished in the same resistance the same amount of heat as the current current. Determined by formula 3.8.
. (3.8)
Active, reactive and impedance in alternating current circuits
Current in active resistance
,
(3.9)
where I. r. , U. r. - Active values \u200b\u200bof current and voltage on the active resistance R.
The phase shift between the current and the voltage on the resistor is zero (see Fig. 3.6).
Fig. 3.6. Vector current and voltage diagram on resistor
Current in inductance
,
(3.10)
where I. L. , U. L. - existing values \u200b\u200bof current and voltage in inductive resistance h. L. .
,
(3.11)
where ω – The cyclic frequency is zero, so at constant current, the inductance coil has no resistance.
In the electrical engineering, active and reactive resistance is called a value that characterizes the strength of countering the area of \u200b\u200bthe electrical circuit to the directional (ordered) movement of particles or quasiparticles - media electric charge. This opposition is formed by the method of transformation of electricity to other forms of energy. In case of irreversible changes in the electrical energy of the chain link in other types of energy, the opposition will be active.
Feature of active and reactive resistance
A variable current network has an irreversible transformation and energy transmission elements of an electrical circuit. Exercising the exchanged electricity process with the chain components and the power source, the resistance will be reactive.
If the microwave oven is considered as an example, the electrical energy in it is irreversibly converted into heat, as a result of which the microwave oven receives an active opposition, as well as elements transforming electric energy in light, mechanical, etc.
Alternating current passing through focused electrical elements, forms a reactive resistance, which is caused mainly inductance and capacity.
Active resistance is directly dependent on the number of complete cycles of changes in the electromotive force (EMF) that occurred in one second. The larger this amount, the higher the active resistance.
However, many consumers have inductive and capacitive properties at the time of passing through them alternating current . These include:
- capacitors;
- chokes;
- electromagnets;
- transformers.
It should be taken into account both active and reactive resistance, which is due to the presence in the electromotive of the capacitive and inductive sign. The interrupting and closing chain of the DC passing through any of the windings, in parallel with the current conversion, the magnetic flux inside the winding itself will occur, as a result, an electromotive self-induction force appears in it.
A similar situation will be manifested in the winding, connected to an alternating current chain, with the only difference that in this case the current is constantly changing both by parameter and in the direction. From here it follows that the parameter of the magnetic flux penetrating into the winding will continuously, in which the electromotive power of self-induction is induced.
At the same time, the vector of electromotive force is invariably that it prevents the current transformation. Consequently, when increasing inside the winding, the electromotive power of self-induction will be to pause the increase in the current, and with a decrease - on the contrary, will try to keep the decrease in the current.
It turns out that the EMF appears inside the conductor (winding), activated in the AC circuit, will constantly counteract current, preventing its change. In other words, the EMF can be regarded as an auxiliary resistance, which, together with the active resistance of the coil, creates a synergistic effect of counteringly running through the coil of the variable current.
Electrotechnical law reactant
The formation of reactive resistance occurs with the help of a decline reactive powerspent on creating electromagnetic field In the electrical circuit. The reactive power decline is formed by the method of connecting to the apparatus converter with active resistance.
Two-pole connected to the chain, it turns out to accumulate only the limited share of the charge before changing the voltage polarity to the diametrically opposite. Thanks to this, the electrotocks are not lowered to zero mark, as in DC circuits. The accumulation of charge by the capacitor directly depends on the frequency of the electric flow.
The formula of the reactive resistance is determined by the impedance impedance:
Z \u003d R + jx, where Z is a complex electrical resistance, R is an active electrical resistance, X - reactive electrical resistance, J - imaginary unit.
The magnitude of the reactive electrical resistivity can be expressed through the values \u200b\u200bof the capacitive and inductive counteraction.
Electric impedance
The full resistance of the AC circuit or impedance is the reflection of the current transforming current. In the electrical literature, the Latin letter Z is denoted by the Latin letter Z. The impedance is a two-dimensional (vector) value, which includes two independent scalar one-dimensional characteristics: active and reactive anti-alternating electrotok. Simply put, full resistance is active and reactive in total.
The active component of the impedance, denoted by the letter R, is a level criterion with which the material counteracts the stream of negatively charged particles among its atoms. By low-level materials, it is considered:
- gold;
- silver;
- copper.
High-resistance materials are called dielectrics or insulators. The list of such materials can be attributed:
- polyethylene;
- mica;
- plexiglas.
Substances with an intermediate degree of opposition refer to the semiconductor group. This group includes:
Full resistance is calculated by the formula: z \u003d √ R 2 + (XL - XC) 2, where: R is an active electrical resistance; XL - inductive resistance, unit of measurement; XC - Capacitive Counteraction, Unit of measurement OM. Full opposition is calculated step by step. Initially draw a scheme, then the equivalent counteraction is calculated individually for the active, inductive and capacitive components of the load and the complete opposition of the electrical circuit is calculated.
So, inductors and capacitors prevent the flow of alternating current. Such a variable current resistance is called reactive resistance X and measured in Omah. Reactance It depends on both the value of inductance and capacity and the frequency of the signal.
Inductance coil has inductive VL reactive resistance equal
where F is the frequency in Hertz, A L is the inductance in Henry.
Since ω \u003d 2πf, you can write XL \u003d Ωl. For example, the reactive resistance of the coil with an inductance of 10 mPN, which is supplied to a frequency of 1 kHz, equal to
XL \u003d 2π * 1 * 103 * 10 * 10-3 \u003d 62.8 Ohm.
The reactive resistance of the inductance coil increases with increasing signal frequency (Fig. 4.26).
The capacitor has an XC capacitive resistance equal
where C is a container in the Farades. For example, the condenser reactive resistance with a capacity of 1 μF, which is supplied with a frequency of 10 kHz, equal to
Fig. 4.26. The dependence of inductive rice. 4.27.
resistance from frequency.
Fig. 4.28. Capacitive vector sum (XC)
and inductive (XL) resistance.
Fig. 4.29.
(a) inductance coil connected sequentially with R. resistor
(b) vector representation R, XL and their vector sum z
The condenser reactive resistance decreases with increasing signal frequency (Fig. 4.27).
The resulting chain resistance includes capacitive resistance XC and inductive resistance XL, equal to the vector sum XC and XL. Vectors XC and XL, as seen from fig. 4.28 (b) are in antiphase, i.e. the phase difference between them is 1800. Therefore, the resulting resistance is simply equal to the difference between XC and XL. For example, let xl \u003d 100 ohm, and xc \u003d 70 ohms. Then the resulting reactive resistance x \u003d 100 - 70 \u003d 30 ohms and is inductive as XL is greater than XC.
Impedance
The resulting resistance of the chain containing both active and reactive (inductive or capacitive) resistance is the name of the impedance or the total resistance of the chain.
Impedance Z is a vector of the amount of reactive resistance and active resistance R.
Consider, for example, the circuit shown in Fig. 4.29. It includes an inductive resistance XL connected in series with a resistor R. As can be seen from fig. 4.29 (b), vector XL is ahead of the vector R 90 °. Impedance is equal
If xl \u003d 400 ohms and r \u003d 300 ohms, then z \u003d 500 ohms.
Reactance - Electrical resistance to variable current due to power transmission with a magnetic field in inductors or electric field in capacitors.
Elements possessing reactive resistance are called reactive.
Reactive resistance of inductance coil.
When the flow of alternating current I. In the coil, the magnetic field creates an EDC in its turns, which prevents the change in current.
As the current increases, the EMF is negative and prevents the increase in current, with a decrease - positive and prevents its decrease, in this way the resistance to the change in current throughout the entire period.
As a result of the created opposition, the conclusions of the inductor inductance in the antiphase are formed voltage U., the overwhelming EMF equal to the amplitude and the opposite sign.
When passing the current through zero, the AMC amplitude reaches maximum valuethat forms the discrepancy in the current time and voltage in 1/4 period.
If applied to the conclusions of the inductance coil voltage U., the current can not start instantly because of the opposition of EDC, equal -U.Therefore, the current in inductance will always lag behind the voltage at an angle of 90 °. Shift with lagging current is called positive.
We write the expression instant voltage value u. Based on EMF ( ε
), which is proportional to inductance L. and current changes: u \u003d -ε \u003d L (di / dt).
From here we express a sinusoidal current.
Integral function sIN (T) will be --SS (T)or equal to her function sIN (T-π / 2).
Differential dt. Functions sin (ωt) will come out of the sign of the integral multiplier 1 /ω
.
As a result, we obtain an instant current expression 
with a shift from the voltage effect π / 2. (90 °).
For rms values U. and I. In this case, you can record 
.
As a result, we have the dependence of the sinusoidal current from the voltage according to the Ohm's law, where in the denominator instead R. expression ωLwhich is reactive resistance:
The reactive resistance of inductors is called inductive.
Condenser reactive resistance.
The electrical current in the capacitor is a part or a set of processes of its charge and discharge - the accumulation and returns of energy by an electric field between its plates.
In the AC circuit, the capacitor will be charged to a certain maximum value until the current change the direction to the opposite. Consequently, at the moments of the amplitude value of the voltage on the condenser, the current in it will be zero. Thus, the voltage on the condenser and the current will always have a discrepancy in time in a quarter of a period.
As a result, the current in the chain will be limited to the voltage drop on the condenser, which creates a reactive resistance to the variable current, a reverse-proportional speed of current change (frequency) and capacitor capacity.
If applied to the condenser voltage U., the current will instantly begin from the maximum value, further decreasing to zero. At this time, the voltage on its conclusions will grow from zero to the maximum. Consequently, the voltage on the plates of the phase capacitor lags behind the current at an angle of 90 °. Such a phase shift is called negative.
The current in the condenser is the derivative of the function of its charge i \u003d dq / dt \u003d c (du / dt).
Derived from sIN (T) will be cOS (T) or equal function sIN (T + π / 2).
Then for sinusoidal voltage u \u003d u amp sin (ωt) We write the expression instant current value as follows:
i \u003d u amp ωcsin (ωt + π / 2).
From here Express the ratio of rms values 
.
Ohm's law suggests that 1 / Ωc. There is nothing but a reactive resistance for sinusoidal current.
For the calculations of stresses and currents through the elements of the electrical circuit, you need to know their overall resistance. Energy sources are divided into two types:
- direct current (batteries, rectifiers, batteries), the electromotive force (EMF) of which does not change in time;
- alternating current (Household and industrial networks), the EDC of which varies according to the sinusoidal law with a certain frequency.
Active and reactive resistance
The load resistance is active and reactive. Active resistance (R) does not depend on the frequency of the network. This means that the current in it changes synchronously with the voltage. This is the resistance that we measure the multimeter or tester.
Reactance It is divided into two types:
— inductive (transformers, chokes);
— capacitive (condensers).
A distinctive feature of the reactive load is the presence of ahead or a current lag from the voltage. In the capacitive load of the current, the voltage is ahead, and in inductive - lags behind it. Physically it looks like this: if the discharged capacitor is connected to the DC source, then at the time of turning on the current through it maximum, and the voltage is minimal. Over time, the current decreases, and the voltage increases until the capacitor charges. If you connect the capacitor to the AC source, it will be constantly recharged with the frequency of the network, and the current is to increase earlier than the voltage.
By connecting inductance to the DC source, we obtain the opposite result: the current through it will increase some time after the voltage is connected.
The magnitude of the reactive resistance depends on the frequency. Capacitance:
Corner frequency associated with the frequency of the network f. Formula:
As can be seen from the formula, with an increase in frequency, the capacity decreases.
Full resistance of the electrical circuit of alternating current
In the AC network there is no load only active or just reactive. The heating element besides active contains inductive resistance, in the electric motor, the inductive resistance prevails over active.
The amount of impedance that takes into account all the active and reactive components of the electrical circuit is calculated by the formula:
Calculation of equivalent resistance of chain elements
A multiple resistance can be connected to one power source. To calculate the source load current, the equivalent load resistance is calculated. Depending on the connection of the elements between them, two methods are used.
Consecutive resistance connection.
In this case, their values \u200b\u200bfold:
The more resistance is connected in series, the greater the equivalent resistance of this chain. Household example: if the contact in the plug will deteriorate, it is equivalent to the connection sequentially with the load of additional resistance. Equivalent load resistance will grow, and the current through it will decrease.
Parallel resistance connection.
The calculation formula looks much more complicated:
The case of applying this formula for two parallel connected resistance:
Connection case n. identical resistance R.:
The more resistance to connect in parallel, the outcome resistance of the chain is less. We are observing both in everyday life: the more to the network to connect consumers, the smaller the equivalent resistance and the longer load current.
In this way, calculation of the total resistance of the electrical circuit It happens in stages:
- A chain substitution scheme containing active and reactive resistance is drawn.
- Equivalent resistance are calculated separately for active, inductive and capacitive components of the load.
- The total resistance of the electrical circuit is calculated
- Current currents and voltages in the power supply circuit are calculated.