Experiment_11 - Experiment #11: LRC Circuit (Power...

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Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor) Concept: circuits Time: 30 m SW Interface: 750 Windows file: RLC.SWS EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor Decade Resistance, Capacitance, and Inductance Boxes (3) Patch Cords FROM AC/DC ELECTRONICS LAB* capacitor, 100 microfarad (100 μ F) PURPOSE The purpose of this laboratory activity is to study resonance in an inductor-resistor- capacitor circuit (LRC circuit) by examining the current through the circuit as a function of the frequency of the applied voltage. THEORY The amplitude of the AC current ( I m ) in a series LRC circuit is dependent on the amplitude of the applied voltage ( ε m ) and the impedance ( Z ). Z I m m ! = (1) Since the impedance depends on frequency, the current varies with frequency:
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2 2 ) ( C L X X R Z ! + = (2) where X L = inductive reactance = ω L, X C = capacitive reactance = C ! 1 , R = resistance, and ω = angular frequency = 2 πν ( ν = linear frequency). The current will be maximum when the circuit is driven at its resonant frequency: C L 1 = (3) One can show that, at resonance, X L = X C and thus the impedance ( Z ) is equal to R. At resonance, the impedance is the lowest value possible and the current will be the largest value possible. The phase difference φ between the current and the applied voltage is given by tan R X X C L ! = " (4) PROCEDURE In this activity the Power Amplifier produces an alternating current through the LRC circuit. The amplitude of the current depends on the impedance in the circuit, which varies with frequency. The Signal Generator controls the frequency. If the current is a maximum at the resonant frequency and is less than maximum for greater or lesser frequencies, the current should peak at the resonant frequency. The current can be determined from the ratio of the resistor voltage to the resistance. The Voltage Sensor measures the voltage drop (potential difference) across the resistor in the circuit. You will use the Signal Generator to change the frequency of the applied voltage. You will investigate the phase relationship between the applied voltage and the resistor voltage as you vary the frequency. You will also determine the amplitude of the current through the resistor and then plot current vs. frequency. The Science Workshop program collects and displays both the applied voltage and the resistor voltage. You will compare the theoretical resonant frequency to your measured resonant
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This note was uploaded on 08/05/2009 for the course PHY 2049 taught by Professor Ujj during the Spring '09 term at W. Florida.

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Experiment_11 - Experiment #11: LRC Circuit (Power...

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