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The following
movies show animated plots of various frequency-dependent electrical features
of sinusoidally driven, series LRC circuits. In each one the feature is
plotted as a function of frequency normalized with respect to the resonance
frequency, (1/LC)1/2, and running from 0 to 3. Each plot is
animated over the value of Q, (L/C)1/2/R, in 15 equal steps
of about 0.2 running from 0.01 to 3.00.
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Voltages
[22K]
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- This
movie plots the voltage amplitudes across the capacitor, resistor,
and inductor normalized with respect to the drive voltage amplitude.
The maximum normalized voltage amplitude across the resistor is
always unity and always occurs at the resonance frequency. As
Q increases, the "wings" of the VR curve are reduced. The capacitor
and inductor curves always approach unity as the frequency approaches
zero and infinity respectively, a result of their reactances dominating
the circuit in these respective limits. They show no peaks for
small Q-values. For larger Q-values, they peak at increasingly
large values and at frequencies slightly lower than and higher
than the resonance frequency respectively.
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Phases
[17K]
- This
movie plots the phase angle—the phase by which the drive
voltage waveform leads the circuit current waveform. The phase
is always negative for frequencies below resonance, zero at resonance,
and positive for frequencies above resonance. The phase changes
slowly for small values of Q and more quickly—over an increasingly
restricted range of frequencies near resonance—as Q increases.
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- Absorbed
power [17K]
- This
movie plots the power absorbed from the drive source normalized
with respect to the peak power when Q = 1. The power always
peaks at the resonance frequency. The power near resonance increases
with Q while the power far from resonance decreases with Q. For
any finite, non-zero frequency, the power increases with Q at
small values of Q. Eventually, however, the power at any non-resonant
frequency will begin to decrease with Q as the peak continues
to sharpen.
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- Normalized
absorbed power [20K]
- This
movie plots the power absorbed from the drive source normalized
with respect to the peak power for each value of Q. In
contrast to the previous plot which shows both growth and sharpening
of the peak, this plot emphasizes the sharpening only by normalizing
out the growth.
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