Resonant Circuit Series Behavior The behavior of the

Resonant Circuit

Series Behavior ] The behavior of the series RLC i R circuit is governed by the impedance. • Magnitude and phase v L C

Perfect Match ] There is special behavior when XC = XL. • Vectors cancel • Impedance only from resistor ] This is called resonance. VL=IXL VR=IR VC=IXC

Resonant Frequency ] The requirements for resonance come from the reactances. ] There is a resonant frequency w 0 associated with the circuit. • Angular frequency w • Can be converted into frequency f in Hz

Vector Sum ] The total impedance is the magnitude of Z. XC XL Z f R ] The phase between the current and voltage is the angle f between Z and the x-axis.

Peak Performance ] At resonance the current is at maximum for the voltage.

Circuit Example ] Find the resonant frequency in the following circuit in Hz. 100 W ] The problem requires the formula for the frequency f. ] Only the inductance and capacitance matter. 10 V 250 m. H 0. 1 m. F • 1/2 p (0. 25 H 10 -7 F)1/2 = 1 k. Hz

Circuit Example ] The behavior of the series RLC 100 W circuit is governed by the impedance. • Magnitude and phase 10 V 250 m. H 0. 1 m. F

Resonant Reactance ] In the preceding circuit the voltage across each component can be found. • Current due to resistor only ] The voltage across the inductor has an amplitude of 158 V. • So does the capacitor ] They are each 90° out of phase and cancel out. next