Physics Lesson 16.15.3 - Forced Oscillations. Alternating Current and Emf in a RLC Circuit caused by Forced Oscillations

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Welcome to our Physics lesson on Forced Oscillations. Alternating Current and Emf in a RLC Circuit caused by Forced Oscillations, this is the third 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.

Forced Oscillations. Alternating Current and Emf in a RLC Circuit caused by Forced Oscillations

As stated in the previous paragraph, a RLC circuit needs an external sustainable source of emf to make it operate for a long time at steady values. This is made possible by connecting the circuit to an AC power supply, which on the other hand is supplied by an AC generator. An AC generator consists on a current-carrying loop placed inside an external magnetic field, as discussed in the tutorial 16.3 "Magnetic Force on a Current-Carrying Wire. Ampere's Force." Such a system produces forced oscillations in the circuit, which makes it operate for a long time with constant periodic values.

A simplified version of an AC generator is shown in the figure below. A conducting loop is placed inside an external magnetic field. The slip rings are used to create the contact with multiple coils. Each ring is connected to one end of the loop and to the rest of the circuit through metal brushes. As a result, the rings slip against the metal brush and are free to rotate. This brings an induced current I in the circuit.

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

As the conducting loop of the generator is forced to rotate in the external magnetic field B, an emf is induced in the loop. The equation of this induced emf is

ε(t) = ε_max ∙ sin ω_d ∙ t

where ε_max is the amplitude of the induced emf in the generator (usually the amplitude is the initial induced emf), while ωd is called the "driving angular frequency" because it drives an induced current in the circuit, the equation of which is given by

i(t) = i_max ∙ sin (ω_d ∙ t - φ)

where i_max is the amplitude of the driven current in the circuit. The induced current may not be in phase with the induced emf, so the inclusion in the formula of the initial phase φ is necessary.

In addition, we may express the driven angular frequency as

ω_d = 2π ∙ f_d

where f_d is the driven frequency of the induced current.

Thus, in circuits with no or very small resistance, the induced current (and emf) oscillate at angular frequency

ω = 1/√L ∙ C

which is known as the "natural angular frequency". Such oscillations are known as free oscillations.

On the other hand, when a resistor is present is the circuit, the oscillations are known as damped (when no external source is present) or forced (when an external source is needed to keep the values of the induced current and emf constant). The following rule is true for the forced oscillations:

"The induced current and emf in a circuit always occur according the angular frequency of the forced oscillations, regardless the value of the natural angular frequency."

You have reached the end of Physics lesson 16.15.3 Forced Oscillations. Alternating Current and Emf in a RLC Circuit caused by Forced Oscillations. 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 ID	Physics Tutorial Title	Revision Notes	Revision Questions
16.15	Introduction to RLC Circuits
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
16.15.1	What is a RLC Circuit? Damped Oscillations in a RLC Circuit
16.15.2	Equation of the Damped Oscillations in a RLC Circuit
16.15.3	Forced Oscillations. Alternating Current and Emf in a RLC Circuit caused by Forced Oscillations
16.15.4	Resistive, Inductive and Capacitive Load

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