#
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.

### Universal resonance with quality factor:

### Quality factor for RLC series ac circuit:

### 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:

- I
_{m} is a maximum.
- Z is at a minimum; Z = R;
Z is purely resistive.
- X
_{L} = X_{C};
inductive reactance cancels capacitive reactance;
net reactance is zero.
- The phase angle is zero;
the current is perfectly in phase with the applied emf;
the tangent of the phase angle is zero.
- The driving frequency is identical to the natural frequency.
- The power factor is unity (see next class).

Note that at resonance, V_{L} = V_{C}, 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.

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"http://www.physics.udel.edu/~watson/phys208/clas0508.html"

Last updated May 6, 1998.

Copyright George Watson, Univ. of Delaware, 1997.