Profile
Settings
Refer your friends
Sign out
A series LCR circuit is a circuit that consists of an inductor, resistance, and capacitor connected in series. To understand the LCR circuit deeply, you should get familiar with phasors.
What are phasors?
To draw a phasor diagram, you need to combine the phasor diagram of resistance, capacitor, and inductor. The phasor diagram represents the position of current and voltage in a circuit. These diagrams can be used efficiently to understand LCR topics easily.
Components of LCR circuit
There are three components of an LCR circuit which are
Resistor
The function of a resistor is to oppose the flow of current in a circuit. It is present in both the AC and DC circuits. You can define resistance mathematically as
R=V/I
Capacitor
The main function of this device is to store energy and release it accordingly. To prevent heavy current flow from the inductor, the capacitor releases the energy in a controlled manner. The mathematical expression of the capacitor is
C=Q/V
Inductor
To resist the change in the flow of current, the inductor is used. The mathematical expression of the inductor is as follows.
V = Ldi/dt
Importance of LCR circuit
LCR circuit is present everywhere in your daily life, right from your cell phones to your computers. Some important applications of series LCR circuits are given below.
- LCR circuit plays the role of the variable tuned circuit.
- The main function of the series LCR circuit is the oscillator.
- Sometimes it also acts as a voltage multiplier.
Reactance and Impedance
Broadly speaking, you will deal with three types of reactance in this topic. All three types of reactance are significant to create a series LCR circuit. This reactance forms the basics of the LCR series circuit.
Types of Reactance
Three types of reactance are listed as follows:
- Capacitive Reactance
- Inductive Reactance
- Electrical Reactance
Capacitive Reactance
This stores the energy of a capacitor in the form of changing electric fields. Whenever you bring two conducting plates close to each other and fill the space between them with a dielectric medium, then there is the generation of capacitance. Here, the current stays ahead of the voltage by 90 degrees. To explain this in mathematical forms, its formula is as follows.
Xc= 12fc=1/C
Where,
XC is the capacitive reactance
fc is the frequency of the capacitor
C is the capacitance of capacitor
is the natural frequency
Inductive Reactance
When the energy is present in the form of a changing magnetic field, it’s known as inductive reactance. Here, the voltage stays ahead of the current by 90 degrees. Mathematically, the equation of inductive reactance is
Where,
XL is the inductive reactance
fL is the frequency of the inductor
L is the inductance of the inductor
is the natural frequency
Electrical reactance
The tendency to oppose the flow of current in a circuit is known as electrical reactance. The energy generated in this process gets expelled out in the form of heat. The mathematical expression for this is
R=V/I
Where,
R is the electrical reactance
V is the voltage of the resistor
I is the current of the resistor
What is Impedance?
The combination of electrical reactance, inductive reactance, and capacitive reactance is known as impedance. Have you heard about complex numbers, where you find both the real and imaginary parts?
Impedance also comprises the real and imaginary parts in it. If you want to know the magnitude as well as the direction of the current, then impedance is your answer. To define impedance mathematically, the formula is
Z =VI
Where,
Z is the impedance of the circuit and in series LCR circuit, it is given by
Z=R2+(XL–XC)2
Resonance in series LCR circuit
A series LCR circuit is known to be in resonance when the magnitude of both the capacitive reactance and inductive reactance are equal, but being 180 degrees opposite to each other, they cancel out. In a series LCR circuit, the impedance is stated as.
Where,
W the resonant frequency
L is the inductance
C is the capacitance
Conclusion
While having a tour through the series LCR circuit, the different types of reactance, and the resonance in the series LCR circuit, don’t forget that the only key to learning any topics is practice. In this article we learned about the series LCR circuit and its impedance. We also learned about the resonance condition of a series LCR circuit and the reactance of each of its components.
