Linear Circuit Elements

In Power Electronics, Linear circuit elements are those elements that are not changed with respect to the voltage and current. Elements that follow ohm’s law are called linear circuit elements. Linear circuit elements mainly resist, store, or control the flow of electric current or voltage in a circuit without actively amplifying or generating signals.

Linear Circuit Elements can be used to connect together within the circuit in a series combination or parallel combination to control the current flow in complex circuits. In this article, we will learn about the role of Linear Circuit Elements in power electronics, their properties, working, advantages, disadvantages, and applications of linear circuit elements in power electronics.

What are Linear Circuit Elements ?

In power electronics, Linear circuit elements refer to the components in an electrical circuit that exhibit a linear relationship between the current input and the voltage output.

An element is said to be linear, where V-I characteristics follow only one equation of the straight line passing through the origin all the time. Linear elements are those whose characteristics are straight lines passing through the origin. Linear Circuit Elements do not require any external power supply to operate in the electrical circuit. Linear Circuit Elements receive the electrical energy and either convert it or store it in the form of a magnetic field or electric field. Linear circuit elements are important because they can amplify and process electronic signals without distortion.

In linear circuits, these linear elements is also known as electrical elements in the electric circuit and there will be a linear relationship between the voltage and current. The main examples of the linear circuit elements in power electronics are resistors, capacitors ,inductors, transformers, etc.

Properties of Linear Circuit Elements

• Linear elements obeys the super-position and homogenous principle.
• Linear Circuit Elements do not require any electrical power to function in a circuit.
• Linear Circuit Elements cannot increase the power of a signal nor are they able to amplify in the circuit.
• Linear elements are those which follows the ohms law.
• Linear element is one whose plot between voltage across it and the current through it, comes out be straight line.

Working of Linear Circuit Elements

Linear circuit elements are those, where V-I characteristics follows only one equation of straight line passing through origin for all the time. Linear elements are those that characteristics are straight line and passing through the origin.

Working of Linear circuit elements include, these Linear circuit elements follows ohm’s law:

Ohm’s Law

The potential difference in volts V, across the terminals of a given metallic wire in an electric circuit is directly proportional to the current flowing I through it, given its temperature remains the same.

This is known as Ohm’s law. In other words, it can be written as: Potential difference across the ends ∝ Current

or

V ∝ I

The linear circuit elements which obeys ohm’s law is resistor, capacitor, inductor, transformer and many other components.

Linear Circuit Elements

Types of Linear Circuit Elements

In power electronics, linear circuit elements are mainly divided into four basic electronic components which include:

• Resistors
• Capacitors
• Inductors
• Transformers

Resistor

Resistor is an type of linear circuit elements. Resistors control the flow of current by offering resistance. They are used to limit current, divide voltage, and set biasing conditions in electronic circuits.

• V = I R, where R is constant of proportionality called Resistance.
• Resistance is a property that opposes (resists) the flow of current, or it can be said that the flow of electrons in a conductor. It controls the magnitude (value) of the current flowing through the circuit.
• The SI unit of resistance is measured in ohm, which is denoted by Ω.
• Resistors oppose the flow of electrical charge or electrical current.
• Resistance is measured in ohm.
• The opposition to the flow of electrical current through the material is known as the resistance of that material.
• Resistors are made up of materials like Tungsten, Bronze, and Constantan.

Mathematically, Resistance can be defined as:

R = V / I

Here I is the current and V is the potential difference.

Resistor voltage equation:

V= I x R

• where V stands for Voltage
• I stands for Current
• R stands for Resistance

Resistor Circuit

Applications of Resistors

• It is used in Potential Divider.
• It helps in Biasing Circuits.
• It is used in Feedback Networks.
• It is used in Amplifiers.

Capacitors

Capacitors is a type of linear circuit elements. Capacitors store and release electrical energy. They are commonly used for decoupling, filtering, and energy storage in electronic circuits. A Capacitor is a two terminal electronic device that has the ability to store electrical energy in the form of electric charge in an electric field. It is a physical object.

• It is used to pass AC and block DC.
• It opposes the flow of direct current.
• It consists of two conducting parallel plates separated by dielectric.
• Dielectric is made up of ceramic, mica, glass, waxed paper, and bakelite.

Capacitor current equation with respect to time:

[Tex]I(t) = C \frac{dV(t)}{dt} [/Tex]

• I(t) stands for current in capacitor with respect to time
• C stands for capacitance
• V(t) stand for voltage across the capacitor with respect to time t.

Capacitor Circuit

Applications of Capacitors

• Capacitors are used for Energy Storage
• Capacitors are used for Power Conditioning
• Capacitors are used as Sensors
• Capacitors are used for Signal Processing

Inductors

Inductors is a type of linear circuit elements. Inductors store and release magnetic energy. They are used for applications such as filtering, energy storage, and impedance matching.

• All inductors are coiled structures and insulated wire wrapped around the area.
• Inductors work on electromagnetic induction.
• It is used to decrease the electric spikes in electronic circuits.
• Inductance can be found in many electrical and electronic systems, as well as circuits.

Formula for Inductance:

Following is the inductance formula,

L = μN²A/l

Where,

• L = Inductance (H),
• μ = Permeability (H/m or N/(Amp^2)),
• N = The coil’s number of turns,
• A = The coil’s cross sectional area,
• l = Length of coil (m).

Inductor Current equation with respect to time:

[Tex]V(t) = L\frac{di(t)}{dt} [/Tex]

• V(t) stand for voltage across the inductor with respect to time t
• L stands for inductance
• i(t) stand for current through the inductor with respect to time t

Inductor Circuit

Applications of Inductors

• It is used in minimizing alternating current in the circuits.
• It is used in RF choke in the oscillator.
• It is used in LC resonance.
• It is used in Radio Transmitter and receiver.

Transformers

Transformer is a type of linear circuit elements. A transformer is used to transfer electrical power from one circuit to another via magnetic media i.e. magnetic core.

• It has two windings on a core. The winding to which input power is given is called the primary winding.
• The winding which delivers power to the load is the secondary winding.
• When transformers step up or step down voltage, power, and energy remain the same on the primary and secondary sides. As energy is not being amplified.
• Transformers are often used to raise voltage levels and keep the power constant.

Transformer current Equation :

[Tex]\frac{I1}{I2} =\frac{N2}{N1} [/Tex]

• I1 stands for primary current in transformer
• I2 stands for primary current in transformer
• N1 stands for number of turns in primary winding
• N2 stands for number of turns in secondary winding

Transformer Circuit

Applications of Transformers

• It is used to raise voltage levels.
• It is used in power generation
• It is used in transmission and distribution.
• It is used in lighting, audio systems, and electronic equipment.

Other Linear circuit elements in power electronics include controllers, sensors, diodes, thermistors, varactors, transducers, and many other common components. These components follows ohms law.

Advantages and Disadvantages of Linear Circuit Elements

There are some list of Advantages and Disadvantages of Linear Circuit Elements given below :

Advantages of Linear Circuit Elements

• Linear Circuit Elements can store energy.
• Linear Circuit Elements can provide power conversion.
• Linear Circuit Elements offer isolation.
• No extra power supply needed from outside.
• They are available at low cost.
• Linear Circuit Elements are easy to design.

Disadvantages of Linear Circuit Elements

• Sometimes they have response issues.
• They provide less functionality.
• We have less control on linear circuit elements.
• Linear Circuit Elements cannot amplify the signal in the circuit.

Conclusion

In this article we have learnt about Linear Circuit Elements, these can easily handle energy in the electrical circuit by storing it in the form of a magnetic or electric field or converting it into some other form of energy. We have seen the properties of Linear Circuit Elements and different types of linear circuit elements and we have the applications and advantages and disadvantages of linear circuit elements. In power electronics, linear circuit elements play an important role in storing and handling energy in the electrical circuits.

FAQs on Linear Circuit Elements

1. When do we say an element is linear circuit element?

We can say an element is linear circuit element (such as resistance, capacitance, inductance, gain, etc.) when it does not change with the level of voltage or current in the circuit.

2. What are the classification of linear circuit elements in power electronics?

The components which do not change with the level of voltage or current in the circuit. are called linear circuit elements. Resistors, capacitors, inductors, transformers, etc. are classified into linear circuit elements in power electronics.

3. What are linear circuit elements and non linear circuit elements in power electronics?

Linear Circuit Elements are the elements that show a linear relationship between voltage and current. Examples: Resistors, Inductors ,capacitors ,Transformers ,etc. Non-Linear Circuit Elements are those that do not show a linear relation between voltage and current. Examples: Voltage sources and current sources.

4. Are sensors and controllers is a type of Linear Circuit Elements ?

Yes, Sensors and controllers are type of Linear Circuit Elements in power electronics. Because they follow superposition principle. Sensors and controllers are important parts of the control system; without information from the sensor, the controller cannot make a decision and instruct the valve to move.