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Physics Lesson 16.15.1 - What is a RLC Circuit? Damped Oscillations in a RLC Circuit

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Welcome to our Physics lesson on What is a RLC Circuit? Damped Oscillations in a RLC Circuit, this is the first lesson of our suite of physics lessons covering the topic of Introduction to RLC Circuits, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

What is a RLC Circuit? Damped Oscillations in a RLC Circuit

By definition, a RLC circuit is a circuit that contains at least a resistor, a capacitor and an inductor. The simplest RLC circuits are series RLC circuits, like the one shown in the figure below.

Physics Tutorials: This image provides visual information for the physics tutorial Introduction to RLC Circuits

As stated in the previous tutorial, when the resistance of circuit is considered, the total energy (electric plus magnetic) in the circuit does not remain constant but it rather decreases with time as some of this energy converts into thermal energy and is therefore dissipated in the form of heat by the resistor. As a result, the energy in the circuit will decrease after each cycle; the oscillations fade and becomes less visible until they disappear completely.

Due to this decrease in the electromagnetic energy of the system, all related quantities such as current, charge and potential difference will decrease too, as there is a continuous decrease in the amplitude of oscillations. We say the oscillations are damped, exactly as occurs in a real block-and-spring oscillation system, in which the amplitude of oscillations decreases after each cycle because of friction.

In tutorial 10.2 "Energy in Simple Harmonic Oscillations" we have provided a general overview on what damped oscillations are. Let's recall a passage from the core paragraph of that tutorial:

"If we make a system oscillate, the amplitude of oscillations would decrease until it becomes zero if energy is not provided continuously to the system. In this case, the oscillations fade away with time. Such oscillations are known as damped oscillations the amplitude of which decreases with time. Look at the graph below. ,/i>

Physics Tutorials: This image provides visual information for the physics tutorial Introduction to RLC Circuits

The "envelope" that surrounds the graph of damped oscillations represents a decreasing exponential function of the form x(t) = A0 ∙ e-γ ∙ t where A0 is the initial amplitude and γ is a constant. Despite the amplitude decreases with time, this is still a simple harmonic motion because the other quantities such as period and frequency remain unchanged. This kind of SHM has the equation

x(t) = A0 ∙ e-γ ∙ t cos⁡(ω ∙ t + φ)

On the other hand, in sustainable SHM, the amplitude of oscillations does not change with time. The envelope shows a horizontal function of the type x(t) = A0."

In the next paragraph, we will see that a RLC circuit without a sustainable energy supply from outside, represents a system of damped oscillations because the energy of system decreases with time. This occurs because part of the total energy of the system converts into thermal energy and is therefore dissipated in the form of heat from the resistor to the environment. This brings a continuous decrease in the total energy of the system.

You have reached the end of Physics lesson 16.15.1 What is a RLC Circuit? Damped Oscillations in a RLC Circuit. There are 4 lessons in this physics tutorial covering Introduction to RLC Circuits, you can access all the lessons from this tutorial below.

More Introduction to RLC Circuits Lessons and Learning Resources

Magnetism Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
16.15Introduction to RLC Circuits
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
16.15.1What is a RLC Circuit? Damped Oscillations in a RLC Circuit
16.15.2Equation of the Damped Oscillations in a RLC Circuit
16.15.3Forced Oscillations. Alternating Current and Emf in a RLC Circuit caused by Forced Oscillations
16.15.4Resistive, Inductive and Capacitive Load

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