Resonant Circuit.

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Presentation transcript:

Resonant Circuit

Series Behavior The behavior of the series RLC circuit is governed by the impedance. Magnitude and phase i R L v 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 w0 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. The phase between the current and voltage is the angle f between Z and the x-axis. XL XC Z f R

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

Circuit Example Find the resonant frequency in the following circuit in Hz. The problem requires the formula for the frequency f. Only the inductance and capacitance matter. 1/2p (0.25 H 10-7 F)1/2 = 1 kHz 100 W 250 mH 10 V 0.1 mF

Circuit Example The behavior of the series RLC circuit is governed by the impedance. Magnitude and phase 100 W 250 mH 10 V 0.1 mF

Resonant Reactance next 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