Name____________________________________ Date____________ Partner(s)_________________________ __________________________ Physics Laboratory The RLC Series Circuit In this experiment, we will record and graph how the current amplitude in an RLC series circuit responds as the frequency of the inputted signal changes, and will use the graph to determine the experimental resonant frequency of the circuit.. Through our analysis, we know that the current amplitude is a maximum at the resonant frequency of the system. This experimental value will then be compared to the theoretical value. I. Relationship between the Current Amplitude Im and frequency f in the RLC Series Circuit A. A circuit consisting of a resistor R, inductor L, and capacitor C are connected in series and R C then connected to a function generator L producing a sinusoidal signal with a constant voltage amplitude Vm . We know that the relationship between the current amplitude and the voltage amplitude is Vm = ImZ , where Z is the impedance of the RLC series v = Vm sin t circuit. The current amplitude can then be written as Vm Im . R 2 L 1 C 2 Rewrite this in terms of the frequency f. Find the frequency at which the current amplitude is a maximum. The frequency is called the resonant frequency of the circuit. Show and explain how you found this value. B. Draw the graph of how the current amplitude Im varies with frequency f. Be sure to show the resonant frequency. Im f II. The Experimental Set-up A. Equipment: oscilloscope w/ two BNC leads inductor function generator w/ one BNC lead capacitance box two wire connectors decade resistance box B. Connect a function generator, inductor, capacitance box and decade resistance box as an RLC series circuit. Be sure that the resistance box is connected to the ground terminal of the AC generator. Connect Channel Inductor Channel 2 1 of the oscilloscope across the resistance box and Channel 2 across the entire RLC circuit. Remember the ground of the AC generator and the ground of the oscilloscope must be connected to the same location. (Do you know why? If not ask your instructor.) Set Function the decade resistance box at 100 ohms (500 ohms) and Generator Capacitance Box the value of capacitance to between 0.006 and 0.060 F. Have your instructor check your circuit. Channel 1 C. Instead of measuring the current amplitude directly, we will measure the voltage amplitude across the Decade Resistance decade resistance box. In this case remember that the Box voltage amplitude across the resistor is proportional to the current amplitude (VmR = ImR). We will also divide this value by the voltage amplitude coming from the function generator (Vm) in order to eliminate any effects caused by variations in the voltage supplied by the function generator. This is referred to as “normalizing.” D. Data: Report your values of resistance, capacitance, and inductance. Adjust the frequency of your function generator to 1000 Hz and record the subsequent voltages on channel 1 (V1 = VmR) and channel 2 (V2 = Vm). Repeat these measurements at 2000, 4000, 7000, 10000, 20000, 40000, 70000, and 100000 Hz. Make more measurements close to and around the resonant frequency so that you can draw a smooth curve through the points. L = _______________ mH, RL = _______________ ohms; C = _______________ F Trial 1 – R = 100 ohms Trial 2 – R = 500 ohms Frequency (Hz) Ch-1 voltage Ch-2 voltage Ch-1 voltage Ch-2 voltage V1/V2 V1/V2 V1 (volts) V2 (volts) V1 (volts) V2 (volts) 1000 2000 4000 7000 10000 20000 40000 70000 100000 E. Graph these two sets of data on the same sheet of two cycle semilog graph paper, and draw a smooth curve through your points. F. Calculations and Results: Locate the resonant frequency for each set of data on your graph and report these values as your experimental values of the resonant frequency. Calculate your theoretical value from the values of your circuit elements and report this value. Find the percentage error between the experimental values and the theoretical value. Experimental Value of Theoretical Value of Resonant Frequency Resonant Frequency Percentage Error (Hz) (Hz) Trisl 1 Trial 2 III. Questions A. Does changing the value of resistance in the circuit affect the value of the resonant frequency? Explain. B. Which of the two circuits above when connected to an antenna would make a better receiver for a radio? Why?
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