f _{o}=f

_{o}is known as theresonance frequencyof the circuit. At resonance frequency in an electrical system, the amplitude of the current becomesmaximum.As the frequency is changed -- either increased or decreased -- from the resonance frequency, the current decreases as shown here.

At resonance, with the (X

_{L}- X_{C}) term in this equation,I = V / Z = equal to

zero, the current is determined solely by the resistanceI _{res}= V / Rso the current at resonance will be greater in a circuit with small resistance and will be less in a circuit with large resistance.

Since the power used in a circuit is given by

P = I ^{2}Rthe power also depends very strongly on the frequency. A graph of power versus frequency looks similar to the current versus frequency graph of the figure above.

When you tune in a radio station you are probably rotating a variable capacitor somewhat like the ones shown here.

As the capacitance C of the tuning circuit is changed, the resonance frequency of a circuit

f _{o}=is changed. The antenna of the receiver acts as an AC source with all sorts of frequencies superimposed at the same time. The voltage -- called a signal -- that it provides at this resonance frequency f

_{o}will provide a relatively large current which provides the program you listen to. The voltages -- or signals -- at other frequencies will provide very little current. The sensitivity of a tuning circuit is directly related to the "sharpness" of its resonance curve, just as shown in the figure above.(c) Doug Davis, 2002; all rights reserved

Return to Ch 22 Home Page (ToC)