# PHYS208 11/26 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.

### 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:

• Im is a maximum.
• Z is at a minimum; Z = R; Z is purely resistive.
• XL = XC; 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, 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.

Solution