## Illustration 31.8: Impedance and Resonance, RLC Circuit

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The impedance of a circuit is the relationship between the voltage and the current, V = I Z, where Z is the impedance. In a purely resistive circuit, Z = R and the voltage and current are in phase. When capacitors and inductors are included, the relationship between voltage and current is more complicated. Calculating the impedance means taking the phase shift between voltage and current into account. In a series RLC circuit, the impedance is given by

Z = (R2 + (ωL - 1/ωC)2)1/2.

Notice that the impedance will be the smallest when ωL = 1/ωC. If the impedance is smallest, what does that mean for the current at a given voltage? The frequency associated with this condition is called the resonant frequency. In the graph above you can see how the impedance changes as a function of frequency for different values of the resistance, the capacitance, and the inductance. If you change R, does the resonant frequency change? What if you increase C? What if you increase L? Using the equation, you should be able to predict what will happen as you change the values. At resonance, the power dissipated is the greatest and the impedance is said to be purely ohmic because Z = R (since ωL = 1/ωC). Restart.

Illustration authored by Anne J. Cox.
Script authored by Morten Brydensholt.
Applet authored by Harry Broeders and modified by Wolfgang Christian.