Laboratory #5-2023

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School

University of Cincinnati, Main Campus *

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Course

2051C

Subject

Electrical Engineering

Date

Apr 3, 2024

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pdf

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Network Analysis 2051C Laboratory #5: Current-Sensing and Impedance Objectives: To learn how to use current-sensing resistors to measure current and to measure the frequency dependence of the magnitude of impedance of a reactive component. Background - Current sensing resistor: Current can be measured using Ohm’s Law by inserting a known -value resistor into the circuit and then measuring the voltage across that resistor. Engineers call that resistor a Current-Sensing (or Current-Sense) resistor. For example, if we measure 5V across a 1000 Ω current-sense resistor, the current is 5 mA. In this laboratory, you will measure the frequency dependence of the impedance of a capacitor. If you measure the voltage across a component and the current through that component, you can then calculate the impedance Z = V/I for that component. Using a function generator as an AC sinusoidal voltage source, you will construct a series RC circuit consisting of a current-sense resistor in series with a capacitor. Pre-Laboratory - to be completed before coming to the laboratory: 1. For each frequency in Hz (3,000; 6,000; and 12,000 Hz): Calculate the magnitude of the impedance of the 0.1- μ F capacitor. Remember that ω (rad/sec) = 2 π x f(Hz). Enter your impedance values here: ⎢ X C ⎢ (3000 Hz) = ____________ ⎢ X C ⎢ (6,000 Hz) = _____________ ⎢ X C ⎢ (12,000 Hz) = ___________ 2. Simulate your series RC circuit. Connect an AC voltage source to the series resistor-capacitor circuit. Use a frequency of 6,000 Hz, a 330 Ω current-sense resistor, and a 0.1 μ F capacitor; set the AC output to 4 V peak. Click-and-drag a Tektronix oscilloscope. Connect channel 1 across the function generator. Connect channel 2 across the capacitor. Set the trigger to A/Single. Set the time base to 20 μ s/div and adjust both input channel y-scales to 1.5 V/Div for both channels. Run your simulation. You should see two waveforms on the oscilloscope screen. Carefully adjust the vertical positions so that the waveforms are symmetrical about the horizontal axis. Now click on the Math Function and select subtraction ( – ) and Ch1 - Ch2. You should see a third waveform, which is the voltage across the resistor. Use Ohm's law, I = V/R, to calculate the peak AC current through the resistor. Enter that value here: I peak = __________________ 530.50 18.10 mA 265.25 132.69

Next, on the oscilloscope screen, measure the peak AC voltage across the capacitor. Using the peak AC capacitor voltage, the peak current value, and Ohm's law (Z = V/I), derive the magnitude of the capacitor impedance ⎢ X C ⎢ = V C peak / I peak . Enter that value here: ⎢ X C ⎢ = __________________ 3. Attach a screenshot showing the function generator, the current-sense resistor, the capacitor, and the Oscilloscope with three traces on the oscilloscope screen. Question: The voltages across the function generator and the capacitor are not in phase with each other. Why does this happen? Laboratory Exercise: to be completed in the laboratory 1. Measure the value of your resistor and record that value. Use this value in your calculations for the rest of the lab. R = ________________________ 2. Construct the RC circuit consisting of a 330 Ω current-sense resistor in series with a 0.1 uF capacitor. Make sure that one end of the capacitor is attached to the ground terminal of the function generator. Connect Channels 1 and 2 of the oscilloscope as shown in the figure above. Connect the probe grounds to the function generator ground. Set the timebase to 20 μ sec/Div and both channels to 1.5 V/Div. Three frequencies will be used: 3,000 Hz; 6,000 Hz; and 12,000 Hz. 3. Set the frequency of the function generator to 3,000 Hz. Connect the waveform generator across the series RC network. Set the amplitude of the waveform generator to 4 volts peak on the oscilloscope screen. Table 1: RC Series Network Freq (Hz) Calculated X C Measured V R peak Measured V C peak Derived I peak = V R /R Derived ⎢ X C ⎢ = V C /I % Diff X C meas /X C calc 3,000 Hz 6,000 Hz 12,000 Hz 4. Enter your calculated ⎢ X C ⎢ value from your pre-lab into Column 2 of Table 1. 5. Measure the peak voltage across the resistor (V R = Ch1 - Ch2). Record that peak voltage in column 3 of Table 1. 6. Measure the peak voltage across the capacitor (V C = Ch2) on the oscilloscope screen. Record that peak voltage in column 4 of Table 1. 7. Use Ohm's law to calculate the peak current I peak . Enter that value into column 5 of Table 1. 8. Using the peak capacitor voltage, the peak current value, and Ohm's law, derive the magnitude of the capacitor impedance ⎢ X C ⎢ = V C peak / I peak . Enter that value into column 6 of Table 1. 9. Calculate the % difference between the value of ⎢ X C ⎢ that you just derived and the value of ⎢ X C ⎢ from your simulation in the pre-lab. Enter that % difference into column 7 of Table 1. 10. Repeat this procedure for frequencies of 6,000 Hz and 12,000 Hz. NOTE: Each time you adjust the frequency, you will need to measure the waveform generator voltage and adjust for 4 V peak. Question: Do your calculated and measured values of X C agree? If not, why not. 530.50 265.25 330 0.748 1.10 1.305 3.33 mA 3.95 mA 2.267 mA 1.20 0.883 0.524 529.40 265.16 132.65 132.50 This indicated that there is a phase shift between the two waveforms. 0.207 based on the small percentage difference, the calculated and measured values agree with each other. 0.0033 132.69 0.030

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