22.8 Resonance

The current in a series RCL circuit is given by I = V / Z =

Notice that this has a maximum value for

X_L = X_C

since the (X_L - X_C) term in the denominator vanishes for X_L = X_C. From earlier equations for X_L and X_C, this means

2 f L =

Consider the capacitance and inductance to be fixed for a given circuit while the frequency can be varied. The current will be a maximum for the frequency that fits this equation; solving for the frequency and labeling it f_o, we have

f_o =

f_o is known as the resonance frequency of the circuit. At resonance frequency in an electrical system, the amplitude of the current becomes maximum. This corresponds to resonance in mechanical systems in which the amplitude of vibration becomes maximum at the resonance frequency.

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