PHYS208 PHYS208 5/8 Class

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ac Circuits (contd.)

Reworking the formula for the current resulting from an ac emf applied to an RLC series circuit leads to the universal resonance formula.

[RLC series resonance]

Universal resonance with quality factor:

[universal resonance]

Quality factor for RLC series ac circuit:

[quality factor]

Resonance in an RLC Series Circuit

Resonance occurs in a circuit when the maximum value of the current is achieved. Examining the numerous formulas associated with the RLC series circuit, we find that the following conditions are synonymous with resonance:

Note that at resonance, VL = VC, so that the net voltage across the reactive elements is zero (added as phasors). However, each reactive element itself may have a very large voltage. In a high-Q circuit, the voltage across the reactive elements may be many times larger than the applied emf.

Concept Check

An Interesting Application of Phasors

Quiz: LC Circuits - (Solution)

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Last updated May 6, 1998.
Copyright George Watson, Univ. of Delaware, 1997.