Physics 241 Lab: RLC Circuit â AC Source

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Section 6: Extra lab technique tips.An RLC circuit has a resonant driving frequency f resonance that maximizes the circuit currentamplitude. Therefore, a plot of the current amplitude vs. driving frequency will show peak currentamplitude at the resonant driving frequency. However, this graph can appear different depending onthe resistance used in the circuit:The sharpness of the resonance peak is measure by the quality factor Q. The larger the qualityfactor, the sharper the peak. Q is found to be given as Q resonance Lfor an RLC circuit in seriesRdriven sinusoidally.In today’s lab you usually want to use as small of a resistance as possible (while still beingsafe) in order to obtain a nice sharp peak in the current amplitude. This will make it easier to find theresonance frequency. However, it is not always desirable to have a large quality factor. In somemechanical systems (bridges, buildings, etc.) a pronounced response to a driving frequency can causedestruction.The most accurate way to find f resonance is to utilize the fact that at resonance, V R (t) and V source (t)are exactly in phase with each other with equal amplitudes. You should place each of these voltageson your oscilloscope channels and examine an XY formatted display. The resonance frequency iseasily found because you will see an ellipse when V R (t) and V source (t) are out of phase and a diagonalline when they are in phase. You see a straight line when they are in phase because both voltages mustreach zero simultaneously.Note that if R is chosen small enough, the resistance of the very long wire of the solenoid maybecome an appreciable resistance of the circuit. When this occurs, the amplitude of the resistor voltagewill be smaller than the source voltage amplitude so that you will see a different angle of tilt (not 45 o )of the in phase resonance line shown above. This is because V source V R V resistance of solenoid V L V C.
Section 7: Construct an RLC circuit driven by a sinusoidal driving voltage of V source 5 Voltsamplitudewith f drive = 3,500 Hz, R 1 k , C 0.1 F, and L 50 mH. You must keep this drivingfrequency the same until 7.8 of this section of the lab.7.1. Quickly measure the voltage amplitudes of each component separately using a single channelof your oscilloscope. Double check that your source voltage amplitude is 5 Volts first. Record yourobservations:7.2. Now use two-channel observations to simultaneously measure the resistor voltage and theinductor voltage to determine their respective phase shift. Your observed inductor voltage phaseshift:7.3. Now use two-channel observations to simultaneously measure the resistor voltage and thecapacitor voltage to determine their respective phase shift. Your observed capacitor voltage phaseshift:7.4. Now use two-channel observations to simultaneously measure the inductor voltage and thecapacitor voltage to determine their respective phase shift. Your observed capacitor voltage phaseshift:7.5. Now use two-channel observations to simultaneously measure the resistor voltage and thesource voltage to determine their respective phase shift. Note that a phase shift of /2 corresponds to ashift along the time axis of ¼ of oscillation cycle T. Therefore, if t shift is the amount of time lag or timelead that you measure between the resistor amplitude and the source amplitude, you can set up thefollowing equivalent ratios to find the phase shift of the source source ,t shift14 T source. 2This gives source 2 t shift drive t shift.TAnother way to think about how to measure the source voltage phase shift is to examine theextra amount of time it would take for the resistor voltage to come into phase with the source voltage ifthe source voltage was frozen in time:sin drive t t shift sin drivet source .For these sine functions to be equal, their arguments must be equal so that you find source drive t shift.Use this equation to experimentally determine the source voltage phase shift source from theresistor voltage. Your observed source voltage phase shift:7.6. Theoretical calculations: Use the labeled values for inductance, capacitance and resistance thatyou have in your circuit as well as your actual driving frequency to calculate the following RLCcircuit parameters in SI units. Your work and answers: C L Z resonancef resonance
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Physics 241 Lab: RLC Circuit â AC Source