Open your browser and go to the simulation. You will see three things: PART 2: Voltage vs. time graph In this part we shall focus on the voltages shown in the bottom-left graph. 1) Bottom-left you see a graph of voltage (in volts, V) vs. time (in milliseconds, ms) for the four components Start with the initial settings: R = 50 ohm, C = 4 UF, L = 40 mH, and the frequency set to 500 Hz. in our circuit o Red curve = voltage VR (t) across the resistor R V (V) QUESTION 1: With the frequency set to 500 Hz, what is the amplitude of the resistor voltage? 400 o Blue curve = voltage VL(t) across the inductor L 200 o Green curve = voltage Vc(t) across the capacitor C t (ms) Purple curve = voltage Vsrc(t) delivered by the AC -200 QUESTION 2: Make a prediction: to maximize the amplitude of the resistor voltage by changing source. If you can't see the purple curve, it is probably -400 only the frequency of the AC source, will you need to increase or decrease the frequency? What are hidden underneath the red curve. you basing your prediction on? 2) Bottom-right you see a graph of the current max (in A) vs. frequency f 1 (A) Adjust the frequency until you have maximized the resistor voltage. (in Hz). The red dot indicates the current for the selected values of 4 resistance R, inductance L, capacitance C, and frequency f. w QUESTION 3: The frequency at which the resistor voltage is maximized has a name - what is the name of this particular frequency? There is also an equation that predicts what this frequency Just like all the voltages, the current has the shape of a sine (or cosine). N should be. What is the equation, and does the frequency given by the equation match the The current that is shown is the amplitude of the current, max- frequency you found in the simulation? 0 f (Hz) 300 400 500 600 700 QUESTION 4: Does anything else special happen at this particular frequency? Do you notice anything about the voltage across the inductor compared to the voltage across the capacitor at this frequency? If so, what? What about the phase relationship between the input voltage 3) Top-right you see a "phasor diagram" which is a mathematical description of what is going and the three output voltages? on in the voltage-vs-time graph at the bottom-left. You will learn more about phasors in Part 3 of today's lab. XC QUESTION 5: State two ways of changing the circuit to double the resonance frequency. N 3PART 3: Phasors Change the settings back to R = 50 ohm, C = 4 uF, L = 40 mH, and set the frequency to 500 Hz. In this part we focus on the phasor diagram at the top-right of the simulation. QUESTION 10: Make a screenshot of the simulation at 500 Hz, showing the voltage-vs-time and the phasor diagram. If you run into any issues, please contact your instructor for assistance. When we wanted to understand a DC circuit with three resistors in series we would generally find the equivalent resistance of the circuit by simply adding the three resistance values together. The AC circuit we're using here, with three circuit elements in series, is somewhat similar. Again, it is helpful to find the equivalent resistance of the circuit; we call this the impedance, Z. Because of the phase relationship between the voltage and the current, however, we add the effective resistances of the different circuit elements as vectors. Now adjust the frequency to the resonance frequency. Keep R = 50 ohm, C = 4 UF, L = 40 mH. The resistance goes on the x-axis: voltage and current are in phase for the resistor. QUESTION 11: As you adjust the frequency, what do you look for on the screen to tell you that you have found the resonance frequency? The effective resistance of the inductor (the inductive reactance X1) is drawn on the y-axis: voltage leads the current by 90 for the inductor The effective resistance of the capacitor (the capacitive reactance Xc) is drawn on the negative y- axis: voltage lags the current by 90 for the capacitor. QUESTION 12: A plot of the current as a function of time is not shown, but one of the voltage signals mirrors the current in (i.e., is in phase with) the circuit at all frequencies (not just at resonance). Which voltage signal mirrors the current? QUESTION 6: Add the three vectors shown on the right to find the impedance Z. Each square is (1 ohm) x (1 ohm). XL QUESTION 13: Make a screenshot of the simulation at resonance, showing the voltage-vs-time and the phasor diagram. If you run into any issues, please contact your instructor for assistance. QUESTION 7: The angle between the impedance and the resistance equals the phase angle between the voltage and the current in the circuit. Calculate what that angle is in the situation shown on the right. Does the voltage lead the current Xc in this case or does the current lead the voltage? QUESTION 14: What does the phasor diagram tell you about how the phase of the input voltage (from the AC source) compared to the phase of the current at resonance (i.e. does it lead or lag the current)? Does this match what you observe in the voltage-vs-time graph? QUESTION 8: If you know the frequency and the inductance, how do you find the inductive reactance? Now change the frequency to 300 Hz. Keep R = 50 ohm, C = 4 uF, L = 40 mH. QUESTION 15: Make a screenshot of the simulation, showing the voltage-vs-time and the phasor diagram at 300 Hz. If you run into any issues, please contact your instructor for assistance. QUESTION 9: If you know the frequency and the capacitance, how do you find the capacitive reactance? 5QUESTION 16: What does the phasor diagram tell you about how the phase of the input voltage (from the AC source) compared to the phase of the current at 300 Hz (i.e. does it lead or lag the current)? Does this match what you observe on the screen? QUESTION 17: The maximum current in the circuit is given by max = Vmax/Z. Compare the phasor diagram of 300 Hz to the phasor diagrams at resonance and see how the impedance (Z) compare. How should the maximum currents at the two frequencies compare? Is this what you observe? Now change the frequency to 700 Hz. . Keep R = 50 ohm, C = 4 UF, L = 40 mH. QUESTION 18: Make a screenshot of the simulation, showing the voltage-vs-time and the phasor diagram at 700 Hz. If you run into any issues, please contact your instructor for assistance. QUESTION 19: What does the phasor diagram tell you about how the phase of the input voltage (from the AC source) compared to the phase of the current at 700 Hz (i.e. does it lead or lag the current)? Does this match what you observe on the screen? QUESTION 20: Now compare the phasor diagrams of 300 Hz, 700 Hz, and at resonance. At which frequency is the impedance Z the least? At which frequency is the impedance Z the greatest