An electric pendulum
Capacitors store energy in the form of an
electric field, and electrically manifest that stored energy as a
potential: static voltage. Inductors store energy in the form of
a magnetic field, and electrically manifest that stored energy as a
kinetic motion of electrons: current. Capacitors and inductors
are flip-sides of the same reactive coin, storing and releasing energy
in complementary modes. When these two types of reactive components are
directly connected together, their complementary tendencies to store
energy will produce an unusual result.
If either the capacitor or inductor
starts out in a charged state, the two components will exchange energy
between them, back and forth, creating their own AC voltage and current
cycles. If we assume that both components are subjected to a sudden
application of voltage (say, from a momentarily connected battery), the
capacitor will very quickly charge and the inductor will oppose change
in current, leaving the capacitor in the charged state and the inductor
in the discharged state:
The capacitor will begin to discharge,
its voltage decreasing. Meanwhile, the inductor will begin to build up a
"charge" in the form of a magnetic field as current increases in the
circuit:
The inductor, still charging, will keep
electrons flowing in the circuit until the capacitor has been completely
discharged, leaving zero voltage across it:
The inductor will maintain current flow
even with no voltage applied. In fact, it will generate a voltage (like
a battery) in order to keep current in the same direction. The
capacitor, being the recipient of this current, will begin to accumulate
a charge in the opposite polarity as before:
When the inductor is finally depleted of
its energy reserve and the electrons come to a halt, the capacitor will
have reached full (voltage) charge in the opposite polarity as when it
started:
Now we're at a condition very similar to
where we started: the capacitor at full charge and zero current in the
circuit. The capacitor, as before, will begin to discharge through the
inductor, causing an increase in current (in the opposite direction as
before) and a decrease in voltage as it depletes its own energy reserve:
Eventually the capacitor will discharge
to zero volts, leaving the inductor fully charged with full current
through it:
The inductor, desiring to maintain
current in the same direction, will act like a source again, generating
a voltage like a battery to continue the flow. In doing so, the
capacitor will begin to charge up and the current will decrease in
magnitude:
Eventually the capacitor will become
fully charged again as the inductor expends all of its energy reserves
trying to maintain current. The voltage will once again be at its
positive peak and the current at zero. This completes one full cycle of
the energy exchange between the capacitor and inductor:
This oscillation will continue with
steadily decreasing amplitude due to power losses from stray resistances
in the circuit, until the process stops altogether. Overall, this
behavior is akin to that of a pendulum: as the pendulum mass swings back
and forth, there is a transformation of energy taking place from kinetic
(motion) to potential (height), in a similar fashion to the way energy
is transferred in the capacitor/inductor circuit back and forth in the
alternating forms of current (kinetic motion of electrons) and voltage
(potential electric energy).
At the peak height of each swing of a
pendulum, the mass briefly stops and switches directions. It is at this
point that potential energy (height) is at a maximum and kinetic energy
(motion) is at zero. As the mass swings back the other way, it passes
quickly through a point where the string is pointed straight down. At
this point, potential energy (height) is at zero and kinetic energy
(motion) is at maximum. Like the circuit, a pendulum's back-and-forth
oscillation will continue with a steadily dampened amplitude, the result
of air friction (resistance) dissipating energy. Also like the circuit,
the pendulum's position and velocity measurements trace two sine waves
(90 degrees out of phase) over time:
In physics, this kind of natural
sine-wave oscillation for a mechanical system is called Simple
Harmonic Motion (often abbreviated as "SHM"). The same underlying
principles govern both the oscillation of a capacitor/inductor circuit
and the action of a pendulum, hence the similarity in effect. It is an
interesting property of any pendulum that its periodic time is governed
by the length of the string holding the mass, and not the weight of the
mass itself. That is why a pendulum will keep swinging at the same
frequency as the oscillations decrease in amplitude. The oscillation
rate is independent of the amount of energy stored in it.
The same is true for the
capacitor/inductor circuit. The rate of oscillation is strictly
dependent on the sizes of the capacitor and inductor, not on the amount
of voltage (or current) at each respective peak in the waves. The
ability for such a circuit to store energy in the form of oscillating
voltage and current has earned it the name tank circuit. Its
property of maintaining a single, natural frequency regardless of how
much or little energy is actually being stored in it gives it special
significance in electric circuit design.
However, this tendency to oscillate, or
resonate, at a particular frequency is not limited to circuits
exclusively designed for that purpose. In fact, nearly any AC circuit
with a combination of capacitance and inductance (commonly called an "LC
circuit") will tend to manifest unusual effects when the AC power source
frequency approaches that natural frequency. This is true regardless of
the circuit's intended purpose.
If the power supply frequency for a
circuit exactly matches the natural frequency of the circuit's LC
combination, the circuit is said to be in a state of resonance.
The unusual effects will reach maximum in this condition of resonance.
For this reason, we need to be able to predict what the resonant
frequency will be for various combinations of L and C, and be aware of
what the effects of resonance are.
- REVIEW:
- A capacitor and inductor directly
connected together form something called a tank circuit, which
oscillates (or resonates) at one particular frequency. At that
frequency, energy is alternately shuffled between the capacitor and
the inductor in the form of alternating voltage and current 90 degrees
out of phase with each other.
- When the power supply frequency for an
AC circuit exactly matches that circuit's natural oscillation
frequency as set by the L and C components, a condition of
resonance will have been reached.
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