Alternating Current

Resonance (continued)

fo =

fo is known as the resonance frequency of the circuit. At resonance frequency in an electrical system, the amplitude of the current becomes maximum.

As the frequency is changed -- either increased or decreased -- from the resonance frequency, the current decreases as shown here.

At resonance, with the (XL - XC) term in this equation,

I = V / Z =

equal to zero, the current is determined solely by the resistance

Ires = V / R

so 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 = I2 R

the 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 like we have seen in class.

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

fo =

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 fo 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.

Return to Resonance

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(c) Doug Davis, 2002; all rights reserved