A. John Mallinckrodt   Professor of Physics, Cal Poly Pomona
LRC
Circuits
Animated graphs of LRC circuit properties
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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.

Voltages [22K]

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.

Voltages vs. Frequency
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.
 
Phase vs. Frequency
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.
Normalized Power vs. Frequency
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.
Normalized power vs. Frequency

©2001 by A. John Mallinckrodt
ajm at csupomona.edu
http://www.csupomona.edu/~ajm

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The space for this page is provided by Cal Poly Pomona and is subject to its policies. Nevertheless, the opinions expressed here are my own and do not necessarily represent official policy of the University. I take full responsibility for the information presented and will appreciate being informed of errors or inaccuracies.

Last modified on 25 March, 2004