Please answer all questions in the lab. For pages 1, 4, and 5. The chart on page 4 provides the information you need. Thank you.

Phys 3B - E&M AC Circuits Experiment 8: Resonance in RLC Resonance In this lab, you will be observing the effects of resonance in an RLC circuit. Similar to resonance in a mechanical system, resonance in an electrical system causes the current (or the amplitude) to sharply increase Pre-Lab Questions The key characteristic of resonance is that the reactance of the capacitor equals the reactance of the inductor, XL = Xc. For this case ... A) Draw the phase diagram for the voltage of the inductor, resistor, capacitor and total voltage (stay roughly to scale) Va = Vmax VL B) What will be the impedance of the circuit? Derive the equation, starting with Z = VR2 + (XL - XC)2 2 = JR 2+ (o)2 C) Derive the expression of the current in terms of R, L, C, and Vo, where Vo is the voltage from the power supply. (Hint: you will only need two of the above parameters when done correctly). I = 2 D) Explain why current is maximum at resonance. Imax a may at reasonance I is maximized XL = XC Z TTf. L = - 2 TTFIC E) Derive the expression of the resonance frequency from X1 = Ac. f ~ ZAVLCPhys 3B - E&M AC Circuits Experiment 8: Resonance in RLC Resonance Measuring AC Voltage You will be using the amplifier to produce an alternating current through the provided LRC circuit. The Voltage Sensor will be used to measure the voltage drop (potential difference) across the resistor in the circuit. The goal here is to determine the resonant frequency experimentally. To do this, we will need to observe how the current changes with frequency. The frequency that gives us the maximum current will be the resonant frequency. You will also be observing the phase relationship between the applied voltage and the resistor's voltage at varying frequencies. For the following procedure, use PASCO Capstone to record and display both the applied voltage and the resistor voltage. PART I: Computer Setup 1. Connect the ScienceWorkshop interface to the computer, turn on the interface, and turn on the computer. 2. Connect the Voltage Sensor to Analog Channel A. 3. Open the Capstone program and go to the Hardware Setup tab on the left side. To Channel B - Click on Channel A and set it to Voltage sensor. - Click on the output voltage. You should see a line appear with a "lightning bolt" symbol under channel A as well as the output voltage. PART II: Sensor Calibration and Equipment Setup The following setup shows the AC/ DC Electronics Board (EM-9656) using a 10-0 resistor and a 100-uF capacitor . 1. Put the iron core inside the inductor coil. 2. Connect the alligator clips of the Voltage Sensor to the wires at both ends of the 10-0 resistor. The voltage measured at Analog Channel A is related to the current through the To Interface resistor by I =-R Rphys 3B - E&M Experiment 8: Resonance in RLC AC Circuits Resonance 3. Connect banana plug cords from the banana jacks on the edge of the AC/ DC Electronics Lab Board to the 'OUTPUT' ports on the ScienceWorkshop interface. Part III: Data Recording 1. Click on the Signal Generator tab and set the waveform to "sine". Set the output voltage to 3 volts. Set the output frequency to 10 Hz and click "ON." 2. Click on the data tab and drag one of the voltage sensors to "Scope" on the right side. Then drag the other voltage sensor to the same graph so that you see two y-axes, one for each sensor. 3. Start measuring data. Click Record at the bottom of the page and set the sample rate to 10 kHz. Stop the data after a short time. If you receive any error message, you need to lower the sample rate. This frequency can be found on the below the graph near the record button. The Scope should display shows the 'Output' voltage, V, from the interface, and the voltage, VR, across the resistor (Channel A). V.B V.A 1.2 Run #3 1.0 0.8 0. 6 0.4 0.2 - Voltage IN -1.0 -1.2 0.05 0.20 0.25 0.00 0.10 0.15 0.30 Time (s) [Scope title here! 4. In the Scope display, determine the voltage, VR, across the resistor (i.e., voltage from Channel A). Click the 'Smart Tool' button ( . ) in the Scope display toolbar. Move the cursor/ cross-hair to a peak of the signal that shows the voltage across the resistor, VR (Channel A).Phys SB E&M AC Circuits Ex eriment 8: Resonance in RLC Resonance 4, Record the voltage, VR, in the Data Table on the next page. 5. Adjust the function generator to 20 HZ. Repeat the process to find the new value of voltage and record it in the Data Table next to 20 Hz. Save the graph for future reference (Remember to click the start button) 6, Increase the frequency in 10 Hz increments until 150 Hz. Repeat the process of using the Smart Cursor to find each new value for the resistor voltage, VR. Record each voltage value in the Data Table. Save the graphs for 50 Hz, 100 Hz, and 150 Hz. You will use these graphs to analyze the phase relationship of VR and the amplifier's voltage. Data Table l'x: 10 IL Determining Resonance Frequency 1. Draw a graph of the amplitude of the current versus frequency (1 vs f). 2. How can you identify the resonance frequency by looking at your graph? Write down your estimated resonance frequency below. -\"-\\_ Phys 3B - E&M AC Circuits Experiment 8: Resonance in RLC Resonance 3. To better determine the resonance frequency, you will look at the phase between the output voltage and the capacitor's voltage. What do you expect to see at resonance? 4. Connect Channel A to your capacitor. Try a couple of frequencies surrounding your resonance frequency from question (2) above. At what frequency do you observe resonance? 5. Calculate the value for the inductance using your resonance frequency you found in the previous step. 6. How should you expect the phase between VR and the amplifier's voltage to change as the frequency approaches resonance? Is this what you observed