If inductors and capacitors are connected in series to an AC circuit, they will act in their own way on the generator that powers the circuit and the phase relationship between current and voltage.
Inductors introduce a phase shift, where the current causes the voltage to lag by a quarter of a cycle, while capacitors cause the voltage and current in the circuit to lag by a quarter of a cycle. Therefore, the effect of inductance and resistance on the phase shift between current and voltage in a circuit is opposite to that of capacitive resistance.
This leads to the fact that the total phase shift between current and voltage in a circuit depends on the ratio of inductive resistance to capacitive resistance.
If the capacitive resistance value of a circuit is greater than the inductive value, then the circuit is essentially capacitive, which means that the voltage lags behind the phase of the current. On the contrary, if the inductance and resistance of the circuit are greater than the capacitive inductance, the voltage is before the current, so the circuit is inductive.
Due to the opposite effects of these resistors in the circuit, one of the resistors Xc is designated as a negative sign, while the total reactance is determined by the following formula:
Applying Ohm's law to this chain, we obtain:
This formula can be converted as follows:
The effective value of the total voltage component in the XL circuit can overcome the inductance and resistance of the circuit, while the effective value of the total voltage component in the IX C circuit can overcome the capacitive resistance.
Therefore, the total voltage of a circuit composed of a series connection of coils and capacitors can be considered as consisting of two terms, whose values depend on the inductance and capacitance resistance of the circuit.
We believe that this circuit does not have active resistors. However, if the active resistance of the circuit is very small and can be ignored, the total resistance of the circuit is determined by the following formula:
Where R is the total active resistance of the circuit, and X L - X C is its total reactance. We have the right to write the formula for Ohm's Law:
Communication resonance
The inductive and capacitive resistors connected in series will result in a smaller phase shift between current and voltage in an AC circuit compared to being included separately in the circuit.
In other words, due to the simultaneous action of these two reactors with different properties in the circuit, compensation for phase shift occurs (mutual destruction).
Complete compensation, that is, when the induced resistance is equal to the circuit, that is, when the capacitance resistance of X undergoes a complete elimination of the phase shift between the current and the voltage in this circuit XL=X. This is the same when ω L=1/ω C.
In this case, the circuit will behave as a pure active resistor, as if there were no coils or capacitors present. The value of this resistor is determined by the sum of the effective resistance of the coil and the connecting wire. In this case, the effective current value in the circuit will be maximum and determined by the formula I=U/R of Ohm's Law, where R. is now set instead of R.
At the same time, the proxy voltage will become equal between the coil Ø L=me X L and the capacitor Uc=me X C, and will be as large as possible. In the case where the active resistance of the circuit is small, these voltages may exceed several times the total voltage U on the circuit terminals. This interesting phenomenon is called series resonance in electrical engineering.
In the picture. The figure shows the voltage, current, and power curves of series resonance in the circuit.
It should be remembered that the impedances XL and XC are variable depending on the frequency of the current, and there is at least a slight modification to their frequency, for example, increasing to XL=ω L will increase, and X is C ^=1/ω S will decrease. Therefore, the resonance of the voltage is immediately destroyed in the circuit, and along with the active resistance, reactance appears in the circuit. If the size of the inductance or capacitance of the circuit is changed, the same situation will occur.
Through series resonance, the power of the current source will only be used to overcome the active resistance of the circuit, that is, to heat the conductor.
In fact, in a circuit with an inductor, there exists energy resonance, which refers to the periodic transition of energy from the generator to the magnetic field of the coil. In circuits with capacitors, the same thing occurs, but due to the energy of the capacitor's electric field. In a circuit with capacitors and inductors during series resonance (X L=X C), the energy released by the circuit is periodically transferred from the coil to the capacitor, and vice versa. Only the energy consumption required to overcome the active resistance of the circuit falls on the current source. Therefore, in the absence of a generator, energy is exchanged between capacitors and coils.
Only the resonance of price pressure needs to be overcome, as the energy of the coil magnetic field becomes unequal to the energy of the capacitor electric field, and there will be excess energy during the energy exchange between these magnetic fields, which will periodically flow from the power source to the circuit or back to the circuit.
This phenomenon is very similar to that in a mainspring. If it were not for the frictional force hindering its movement, the pendulum may resonate continuously without the help of a spring (or clock load).
The spring informs the pendulum of a portion of its energy at the appropriate time, helping it overcome friction and ensure the continuity of vibration.
Similarly, in a circuit, when resonance exists, the current source only consumes energy to overcome the active resistance of the circuit, thereby supporting the resonance process.
Therefore, our conclusion is that under certain conditions, X L=X C, an AC circuit consisting of a generator and a series connected inductor and capacitor becomes a resonant system. This type of circuit is called a resonant circuit.
From the equation X L=X C, we can determine the frequency value of the generator where series resonance occurs:
The capacitance and inductance values of a circuit experiencing series resonance
Therefore, changing any of these three quantities (f res, L, and C) may cause series resonance in the circuit, turning it into a resonant circuit.