Physics Lesson 16.16.4 - Resonance in a Series RLC Circuit

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Welcome to our Physics lesson on Resonance in a Series RLC Circuit, this is the fourth lesson of our suite of physics lessons covering the topic of The Series RLC Circuit, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Resonance in a Series RLC Circuit

As stated earlier, resonance is a state of a RLC circuit in which the current and net emf are in phase. This occurs when X_L = X_C. The graph of voltage and current versus time in a situation involving resonance for a complete cycle is shown below.

Physics Tutorials: This image provides visual information for the physics tutorial The Series RLC Circuit

The amplitudes may be different from those shown in the above graph; they depend on the corresponding values. This means the current graph may be above the voltage graph or they may have the same height, no matter which graph is higher. The graph above is only for illustration purpose.

We will show below the corresponding phasor diagram as well.

In absence of resonance, the graphs of current and voltage do not have their peak at the same time because either current is ahead of voltage (when the phase constant is negative, i.e. when the circuit is more capacitive than inductive), or it is behind the voltage (when the phase constant is positive, i.e. when the circuit is more inductive than capacitive). In such cases, the voltage and current phasors are not collinear, as discussed earlier.

Giving that during resonance X_L = X_C, we have after substitutions:

ω_d ∙ L = 1/ω_d ∙ C
ω_d² = 1/L ∙ C
ω_d = √1/L ∙ C = 1/√L ∙ C

This is the known equation obtained earlier for natural angular frequency of free oscillations. In this case, the oscillations are forced (driven) by the power source. This makes possible the generation of long-lasting (sustainable) oscillations, for which we can apply the approach used in free oscillations, as they do not fade with time.

As for the frequency of RLC circuit oscillations, we have (giving that ωd = 2π ∙ f):

2π ∙ f = 1/√L ∙ C

Hence,

f = 1/2π ∙ √L ∙ C

You have reached the end of Physics lesson 16.16.4 Resonance in a Series RLC Circuit. There are 5 lessons in this physics tutorial covering The Series RLC Circuit, you can access all the lessons from this tutorial below.

More The Series RLC Circuit Lessons and Learning Resources

Magnetism Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
16.16	The Series RLC Circuit
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
16.16.1	Recap on the Series RLC Circuit
16.16.2	The Current Amplitude
16.16.3	The Phase Constant
16.16.4	Resonance in a Series RLC Circuit
16.16.5	Effective Values of Alternating Current and Voltage

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