 # LCR Circuit

## What is LCR Circuit?

An electronic LCR circuit contains a resistor of R ohms, a capacitor of C farad, and an inductor of L Henry, all connected in a series combination with each other. Since all the three elements of the LCR circuit are connected in series, the current passing through each of them is the same and is equivalent to the total current I passing through the circuit.

A circuit that contains L, R and C components at some particular frequencies can make the L and C ( or some of their electrical effects ) disappear completely. The LCR circuit can act as just a capacitor, just a resistor, or just an inductor individually. The LCR circuit is also used to enhance the voltage to increase the voltage passing through the individual components of the circuit.

This voltage can be much larger than the external voltage applied to the circuit. LCR circuits are also useful to change the impedance of the circuit, to increase or decrease the resistance to the current of different frequencies. All these effects can either be used separately or can be used all together to get the desired results in electronic devices.

### LCR Circuit Diagram

This diagram consists of all the components of the module, such as inductance, capacitance, and resistance. It fulfills along with their properties like Reactance, Impedance, and Phase.

This module discusses the overall effect of L, C, and R when connected in series and supplied by an alternating voltage. In such arrangements, the current provided passes through all the elements of the circuit equally. VR, VC, and VL symbolize the amount of individual voltage across the register, capacitor, and inductor, respectively.

There is some internal resistance on the applied voltage, which is measured across the inductor. In the LCR circuits, the internal and external resistance is usually there in the circuit. Therefore, it is easy to know that the voltage across VR is the total voltage across the circuit which inhibits the internal resistance L accompanied by a fixed resistor. Here VS is the applied supplied voltage.

The phase relationship between the current of the circuit IS, and the supplied voltage VS depends on both, the relative values of the capacitance, inductance, and frequency of the applied voltage. Various conditions arise depending upon whether the inductive reactance XL is smaller or higher than the capacitive reactance XC. Diagrams can illustrate this.

As per the above diagram, one can infer that:

V² = (VR)^2 + (VL – Vc)^2 —– (1)

Since it is an LCR circuit, the equal current will pass through all components. Therefore,

VR = IR—– (2)

VL = IXL —– (3)

Vc = IXc —– (4)

Using equation (1), (2), (3) and (4)

I = V√R^2 + (XL − XC)^2

The angle between I and V is known as phase constant,

tan ∅ = VL − VCVR

In terms of impedance, it is represented as,

tan ∅ = XL − XCR

### Three Possibilities Arise Depending upon the Values of XC and XL.

1. If XL>Xc, then tan∅>0 in this case, the voltage leads the current, and the LCR circuit is said to be an inductive circuit.

2. If XL<Xc, then tan∅<0, in this case, the current leads the voltage, and the LCR circuit is said to be a capacitive circuit.

3. If XL =Xc, then tan ∅ = 0 and the current is in phase with the voltage, and the circuit is known as a resonant circuit.

## Overview

This module gives a brief introduction to some of the most beneficial and most creative circuits of the electronic world. The circuits are elementary, containing two or three components that are connected in series with each other. They perform various complex functions and have a broad range of circuit applications.

Electronic circuits are used to connect an indicator, a resistor, or a capacitor either in parallel or in series. Some previous modules of this series talk about the capacitors and inductors, and their connection with the resistors exclusively. This creates some useful circuits like filters, integrators, and differentiators.

Capacitors and Inductors have different purposes in an AC circuit. This module talks about the cumulative properties of reactance, the impedance of the capacitors, and the inductors with various frequencies to generate amazing effects.

### 1. What is the Impedance of LCR Circuit?

In electrical engineering, impedance is the measure of the resistance that a circuit exerts to current with the application of voltage. Impedance can be minimized by making the applied AC frequency equal to the resonant frequency of the LCR circuit.

When the frequencies are equalized, the inductive and capacitive reactance becomes almost zero, and only resistance remains. This is the only concept behind resonance.

If an external frequency of 1khz supplies a series of the resonant circuits with the resonance frequency of 200 kHz, then it will not let that additional frequency pass through it. But if we supply an external frequency of 200 kHz, the current in the circuit will become maximum.

So when an external frequency of equal resonant frequency of the LCR circuit is applied, then the circuit completely behaves like an R circuit (as if there is no inductor or capacitor ).

This means that resonance is a particular condition of the LCR circuit when the capacitive reactance XC is equal to inductive reactance XL.

At resonance, the impedance of the circuit equals the resistance of the resistors. This is because the capacitance and the inductance cancel out as per the mentioned formula.

Z²=R²+ (XL²−Xc²)Z²=R²+(XL²−Xc²)

As XL = Xc,

Z = R

Therefore, the Impedance of LCR circuit is equal to the resistance of resistors.

### 2. What is the Application of LCR Circuit?

The application of LCR circuit is given here below:

a. The LCR series circuit is also known as a tuned circuit or acceptor circuit. They have a wide range of applications in the field of oscillating circuits.

b. The series LCR has various uses in radio and communication engineering.

c. The LCR circuits are used to detect the frequencies of the narrow range in the broad spectrum of radio waves. LCR circuit is used to tune radio frequency of AM/FM radio.

d. It can be used as a low pass, band-pass, high pass, and band-stop filters based upon the type of frequency used.

e. The LCR circuit can be used as an oscillator.

f. The circuit is used to multiply voltage and in pulse discharge circuits.