MM0704; Lesson 1
Mechanical Analogies
Many electrical principles can be better understood when they are compared to mechanical devices. A device closely
related to the resonant circuit is the pendulum. As in the case of a free-swinging pendulum, the frequency of the
resonant circuit is practically independent of the amplitude of the force applied and there is but a single resonant
frequency. However, both reach large amplitudes with very small amounts of power applied, both can be made to
oscillate with a push along a small part of each cycle, and both continue to oscillate for many cycles after the driving
force has been removed.
The only energy required to keep a pendulum going is friction. A large amount of energy is stored in the moving
pendulum in two forms: kinetic energy when the pendulum falls and potential energy as the pendulum rises. A similar
continuous exchange of energy goes on in the resonant circuit. Imagine a capacitor connected across an inductor.
Assume the capacitor is to be charged by some outside force that is no longer active (a generator that has just been
disconnected). Energy is stored in the electrostatic field of the capacitor, which must discharge through the coil. This
takes time because the inductor opposes a change in current. As the capacitor discharges, its energy is stored in the
magnetic field built up by the flow of current in the coil. When the voltage across the capacitor is gone, current
continues to flow in the same direction because of the collapse of the magnetic field about the coil. This current
charges the capacitor and current flows in the opposite direction for a half cycle. Except for resistance losses, which
convert this circulating energy into heat, it could be made to oscillate forever from a single pulse of electrical energy.
In practice, these oscillations are not detectable after a few hundred cycles; the exact rate of dying out (damping) is
determined by the Q of the circuit. As with the pendulum, the only energy required by the resonant circuit is that
amount that is wasted by the electrical equivalent of friction, which is resistance.
Summary of Series and Parallel Resonance
Series resonant circuits have in common the following:
The current is maximum at resonance.
XL = XC at resonance.
Power factor is one (unity) at resonance.
When the applied voltage is below the resonant frequency of the LC circuit, the circuit reactance is capacitive.
When the applied voltage is above the resonant frequency of the LC circuit, the circuit reactance is inductive.
Frequency of resonance equals
Parallel resonant circuits have in common the following:
XL = XC at resonance.
Power factor is one at resonance.
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