12-1-11 Resonant Response of RLC Circuits

# Eq 1 the equation to find the resonant frequency eq 2

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Eq 1. The equation to find the resonant frequency Eq 2. The equations for the reactances of a capacitor and inductor

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Procedure I. Series RLC Circuit In this procedure, we were to build the circuit in Figure 1. Our function generator was set to output a , , sine wave initially. We were then to step up the frequency in steps to find the resonance frequency by experimentally. We also calculated the resonance frequency in order to compare the two. Figure 1. The RCL circuit for part 1. The additional resistor (R2) is the internal resistance of the function generator. Figure 2. The simulated oscilloscope at a frequency close to resonance, 16 kHz
Next, we were to calculate the resonance frequency by hand: Then, to show the equivalence between the reactances: Thus, in series, these two reactances will cancel out as their equivalent is: Next, to confirm the voltage is zero, we use Ohm’s Law: Table 1. The values measured Frequency Input () Frequency Output () Voltage Input () Voltage Output () 5 5 1.02 0.96 6 6 1.02 0.96 7 7 1.02 0.94 8 8 1 0.92 9 9 1.04 0.88 10 10 1 0.84 11 11 1.02 0.82 12 12 1 0.744 13 13 1 0.682 14 14 0.98 0.574 15 15 1 0.49 16 16 1 0.332 17 17 0.96 0.216 18 18 0.94 0 19 19 0.97 0 20 37.5 0.96 0.248 21 39 0.96 0.344 22 31 0.96 0.4 23 32 0.96 0.47 24 24 0.96 0.536 25 25 0.96 0.6 Figure 3. A graph of the above data, showing the measured resonant frequency to be 19.5 kHz

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