12-1-11 Resonant Response of RLC Circuits

A graph of the above data showing the measured

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Figure 3. A graph of the above data, showing the measured resonant frequency to be 19.5 kHz II. Parallel RLC Circuit For this portion of the lab, we did the same thing, but observed resonance with a parallel connection. This circuit is shown in Figure 1. For consistency’s sake, this section will match the above.
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Figure 4. The RCL circuit for part 2. The additional resistor (R2) is the internal resistance of the function generator. Figure 5. The simulated oscilloscope at a frequency close to resonance, 16 kHz As the calculation for the resonant frequency is not dependent on a series or parallel connection, the resonant frequency is the same: Again, to show the equivalence between the reactances:
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Next, in parallel, their combined reactances are: This undefined value results in a voltage very close to the input voltage, as seen in Figure 5. Table 2. The values measured Frequency Input () Frequency Output () Voltage Input () Voltage Output () 5 5 0.96 0.368 6 6 0.96 0.44 7 7 0.96 0.512 8 8 0.98 0.568 9 9 0.98 0.632 10 10 0.98 0.712 11 11 0.98 0.76 12 12 0.98 0.84 13 13 0.98 0.88 14 14 1 0.9 15 15 1 0.96 16 16 1.02 1 17 17 1 1 18 18 1 1.02 19 19 1 1 20 20 1 1 21 21 1 1 22 22 1 1 23 23 1 0.98 24 24 1 0.92 25 25 1 0.92 Figure 3. A graph of the above data, showing the measured resonant frequency to be 18.5 kHz Conclusion All things considered, this lab managed to show the applications of the resonant frequency very well. We were able to observe its effects as both a voltage dampener and as a
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voltage follower. Mathematically, we were also able to explain these effects, with a 0 resistance or a resistance of effectively infinity. Our results were rather close to the calculated value of 15.9 kHz, with a 22.6% and 16.4% error for series and parallel circuitry, respectively. Error, as always, was present in this lab. Our results were not as close to the calculated value as we would have liked, but given the components lack of precision and the fact that the oscilloscope shut down the second channel if the voltage was sufficiently low could be to blame. Again, for the equipment and components at our disposal, we were able to show the resonance frequency effect very well.
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