Lab 6 Phases, AC circuits

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University of Utah *

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2200

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Electrical Engineering

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Dec 6, 2023

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ECE 2200/2210 Lab 6: AC Circuits, Phasors Possible Points: 61 Lab Equipment List:  1 kΩ resistor  0.1 μF (104) & 0.01 μF (103) capacitors  Inductor, 2 to 4 mH (probably 3.3mH)  Function generator  Oscilloscope  LCR meter Partnering:  Everyone must create their own lab report (fill out this document).  Everyone must build their own circuits, but you may use the same measurement equipment.  Discussions are encouraged, and you are also encouraged to answer each other’s questions!  Seek out the TA if you get stuck or need help. Lab Procedures: The objectives of this lab are to observe the phase relationship between the current and voltage in a capacitor vs. in an inductor. Part 1: Predict Whether a Capacitor causes a Phase (Time) Delay in the Current (13pts). 1. Consider the circuit shown in Fig. 1. Notice that the source is sinusoidal. Let’s predict the capacitor voltage waveform relative to the capacitor current waveform. Assume that there is a current flowing through the circuit that has the following form: i = A cos ( ωt ) Amps. Write an expression for the voltage across the capacitor. Make sure to write your answer with a cosine reference (use cos rather than sin ) so that both the current and voltage expressions are written in terms of cosine. Hint: v C = 1 C ∫ − ∞ ∞ i C dt (The source is on for all time, so that we can assume the current waveform is a true, infinitely long cosine.) (5pts) <Vc = 1/0.6Acos(wt – 90) i = Acos(wt)> 1 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 Fig. 1 An RC circuit connected to a sinusoidal source. 2. What is the phase difference (in degrees) between the capacitor current and the capacitor voltage? Hint: Compare the arguments of the cosine expression for the current vs. the voltage. (5pts) <90> 3. Is there a time-delay between the capacitor current and the capacitor voltage? (Remember, if there is a phase difference then this means there is a time difference between the two signals.) If so, which one is lagging behind the other? (3pts) <Voltage lags behind> Part 2: Measure Whether a Capacitor Causes a Phase (Time) Delay in the Current (23pts). 1. Now let’s measure the phase difference between the voltage and current of the capacitor in the RC circuit of Fig. 1. How would you set up this experiment with the oscilloscope probes? Remember, oscilloscopes only measure voltage, not current. Also, the grounds of the oscilloscope probes should be connected to ground. Create a sketch of your plan below before going on to the next page. (3pts) <add your sketch here> 2 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

ECE 2200/2210 Fig. 2 Diagram showing one way to measure the phase difference between the current and voltage of a capacitor in the RC circuit. The edge of the function generator is shown on the left. 2. One way to perform this measurement is shown in Fig. 2. Since the ground of the scope probes should be connected to ground, and because the oscilloscope measures only voltage, we must be a bit creative in how we measure the phase of the voltage and current for the capacitor. First, CH1 of the oscilloscope in Fig. 2 measures the source voltage. The capacitor voltage will be in phase with the source voltage. We want to see if the current through the capacitor experiences a phase delay relative to the phase of the voltage. The current through the capacitor is the same as the current through the resistor (according to KCL). And since V R = IR (there is a linear relationship between the resistor voltage and current), if CH2 measures the resistor voltage, V R , that will also provide us the phase of the capacitor current. You can either move ahead using the above description (use CH1, the source voltage, to determine the phase of the capacitor voltage). Or, if you want to explore your oscilloscope, you can also try inverting CH2 and adding it to CH1 to get the actual capacitor voltage. 3. Let’s see if we can observe the expected time delay between the capacitor voltage and current. Build the circuit shown in Fig. 2. Make sure to set up the scope probes. Attach your oscilloscope and circuit set-up below (10pts). <add pictures and leave this line highlighted> 3 UNIVERSITY OF UTAH DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 50 S. Central Campus Dr | Salt Lake City, UT 84112-9206 | Phone: (801) 581-6941 | Fax: (801) 581-5281 | www.ece.utah.edu

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