[Physics Class Notes] on LCR Circuit Pdf for Exam

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. 

A Brief Explanation of LCR Circuit

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. 

The three Components of an LCR circuit work together to Produce different Effects

Resistor: 

The resistor limits the current flow. It helps in controlling the power or voltage that is applied to the LCR circuit. The resistor is a component in an electronic device that limits the flow of electric current. The resistor helps control the amount of power or voltage that is applied to the LCR circuit. This is important because it prevents too much current from flowing through the other components in the circuit

Capacitor:

A capacitor stores energy and releases it in a controlled manner- It helps in controlling the voltage or power that is applied to the LCR circuit. The capacitor stores energy and releases it in a controlled manner, which prevents too much current from flowing through the L resistor.

Inductor:

An inductor resists change in current flow- It helps in controlling the fluctuations in current flow. The inductor resists change in current flow, which helps to stabilize the LCR circuit. The LCR circuit is used as a part of electronic devices such as cellphones, televisions, and computers to regulate the intensity of light emitted from these devices.

LCR Circuit Diagram

This diagram consists of all the components of the module, such as inductance, capacitance, and resistance. It fulfills along with its 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 [V_{s}] 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 [X_{L}] is smaller or higher than the capacitive reactance [X_{C}]. Diagrams can illustrate this.

As per the above diagram, one can infer that:

[ V^{2} = V_{R}^{2} + (V_{L} – V_{C}) ^{2} —(1)]

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

[V_{C} = I_{R}] —(2)

[V_{L} = I X _{L}] —(3)

[V_{C} = I X _{C}]—-(4)

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

[ I = frac{V}{sqrt{R^{2} + (X_{L} – X_{C})^{2}}}]

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

[tan phi = frac{V_{L} – V_{C}}{R}],

In terms of impedance, it is represented as,

[tan phi = frac{X_{L} – X_{C}}{R}],

Three Possibilities Arise Depending upon the Values of [X _{C} and X_{L}]. 

1. If [X _{L}> X_{c}], then [tan phi > 0], in this case, the voltage leads the current, and the LCR circuit is said to be an inductive circuit.

2. If [X _{L} <  X_{c}], then [tan phi < 0], in this case, the current leads the voltage, and the LCR circuit is said to be a capacitive circuit.

3. If [X _{L} =  X_{c}], then [tan phi = 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.

Importance of LCR Circuit

LCR circuits are important in various applications. LCR circuits help reduce power consumption by controlling too much current flow through a device or component, causing it to overheat. LCR circuits also help reduce voltage fluctuations that can damage electronic devices.

Stores energy and releases it in a controlled manner which prevents too much current from flowing throughout the L resistor. It consists of three components L resistor, capacitor, and L inductor

Helps in controlling the fluctuations of current flow, which stabilizes the LCR circuit.