1 Practical training Topic: Calculation of electrical circuits in the phenomenon of voltage resonance. Calculation of electric circuits in the phenomenon of current resonance

1 - Practical training
Topic: Calculation of electrical circuits in the phenomenon of voltage resonance. Calculation of electric circuits in the phenomenon of current resonance.
The purpose of the work: to learn how to calculate the phenomenon of resonance that occurs in this circuit when inductive and capacitive elements are connected in series or parallel in electric circuits. To learn how to calculate the phenomenon of resonance that occurs in this circuit when inductive and capacitive elements are connected in series or parallel in electric circuits.
Plan:

1. 
   Basic theoretical concepts.
   

2. Voltage resonance.
3. Current resonance.
4. Resonance frequency.


Basic theoretical concepts.
In electric current circuits consisting of reactive elements, inductance and capacitance resistance, the current and voltage vectors fall on top of each other, and if the angle between the particles is , a resonance phenomenon occurs.

1. 
   Resonance of voltages in the R, L, C circuit connected continuously.
   

During the resonance condition in this circuit X_L = X_C, or:
This is the resonant frequency:
So, the phenomenon of resonance is achieved by changing the parameters of alternating current frequency f, inductance and capacity.
Resistances of reactive elements during resonance:
or It is called wave resistance and is measured in (OM).
At resonance, the current reaches its maximum value:
Voltage in reactive elements:
Resonance contour frequency (ω), circuit parameters, current and voltage dependence function is called frequency characteristic. (I_(U) ,U_(ω), U_L(ω), U_C(ω), X_L(ω),X_C(ω), z_(ω))
When analyzing these characteristics, it is more convenient to express the current or frequency by a specific relative value, and the coefficient is taken as
In this: ;


Resonance of currents in parallel connected g, L, C chain.

In parallel connected current circuits
in a resonant state resonance
frequency:
or:
Conductivity of reactive elements:

- is equal to
is called wave permeability.
Total current at resonance: I₀ = Ug.
Currents in reactive elements: I_Lo = I_Co = U
If g < the current in the reactive resistors is greater than the total current: - it is called contour fading. In the formulation of the frequency characteristics for the resonance condition, the equation obtained relative to the current and frequency values was used:

Resonant frequency extinction limits from the given characteristic It was expressed by d = h1 – h2.

Even during the resonance of currents, the fluctuation of the energy of the electromagnetic field is similar to the state of resonance of voltages and remains unchanged.


Exercises
1. Parameters of the current chain connected to the chain bo’lib, U=10 B. Resonance frequency f₀, voltage in reactive elements U_L,U_C, wave resistance , contour nobility Q and determine the extinction coefficient d.
Solution:
Resonant frequency:

From this:
Resonant state current:
Reactive resistances:

Voltages in reactive resistors:

Wave resistance:
Coefficient of authenticity:
Extinction coefficient:

Current resonance

1.

Parameters of a current circuit connected in a parallel circuit connected to voltage . Resonant frequency f₀ , currents I, I_L, I_C extinction coefficient d and determine the wave permeability.

Solution: Resonant frequency:
or:
current:
Inductive and capacitive reactive conductivities:

Current flowing through inductance and capacitance:

Wave permeability:
Contour nobility:
Contour fading coefficient:
2. The electrical circuit presented in the diagram is connected to an alternating current source of frequency f=400 Gs. If the active resistance is R=5 Ohm, and the capacitance parameter is S=10.5 μF, at what value of the inductance will the resonant state occur.




Solution:
The resonance condition for this circuit is that the sum of the reactive conductances is equal to zero.
That is:
In this:
or:
we set the reactive conductivity equation to zero in this formula:

If divided by the common denominator:

The roots of the solution of the equation with respect to inductance:

So, the inductance values at which a resonance state can occur in the circuit are: