Lab experiment report, Lab Reports of Circuit Theory

Download Lab experiment report and more Lab Reports Circuit Theory in PDF only on Docsity! Exrerimen? Name 71 bt Impedance of Series AC Circuits Objectives: 1, Measure the impedance of a series R-L circuit and the phase between the ac voltage and current and compare your measured values with the calculated values. 2. Measure the impedance of a series R-C circuit and the phase between the ac voltage and current and compare your measured values with the calculated values. 3. Measure the impedance of a series R-L-C circuit and the phase between the ac voltage and current and compare your measured values with the calculated values. 4. Calculate the expected ac rms voltage across each element in a series R-L-C circuit and compare your calculated voltages with the measured values. 5. Demonstrate how Kirchhoff’s voltage law applies to a series ac impedance using phasors. 6. Demonstrate the effect of frequency changes on the ac rms current and voltages in a series R-L-C circuit. * Materials: One dual-trace oscilloscope One function generator One 0-10 mA ac milliammeter Four 0-10 V ac voltmeters One 0.1 uF capacitor One 100 mH inductor One 1 kQ resistor Theory: Complete Experiments 19 and 20 on inductive and capacitive reactance before attempting this experiment. When an ac sinusoidal voltage is applied across a series R-L, R-C, or R-L-C circuit, as shown in Figures 21-1, 21-2, and 21-3, there is an opposition to the ac current flow called impedance (Z), and its unit of measurement is the ohm (©). The voltage across each element and the current in each element are also sinusoidal and have the same frequency as the applied voltage. However, the ac voltage across the inductor will lead the ac current by 90 degrees, the ac voltage across the capacitor will lag the ac current by 90 degrees, and the ac voltage across the resistor will be in-phase with the ac current. This will cause a phase difference (8) between the ac voltage applied to the circuit and the ac circuit current. This phase difference can be between 0 degrees and 90 degrees, depending on the relationship between the total reactance and total resistance in the circuit. 141 162 Part IV Alternating Current (AC) Circuits | As ina de resistive circuit, Ohm’s law determines the relationship between the ac rms voltage applied to the series circuit and the ac rms circuit current. In an ac circuit, the impedance (Z) of the circuit replaces the resistance of a resistor in the Ohm’s law equation. Therefore, V=ZI where Z is the circuit impedance in ohms (2), V is the ac rms voltage applied to the circuit, and I is the ac rms circuit current. Because the rms voltage and current are both equal to the peak value times 0.707, Ohm's law can also be applied to the peak ac voltage (V,) and peak ac current (I,) as follows: Vp=Zlp Ohm's law can be used to find the voltage across an inductive reactance (X_), a capacitive reactance (X,), and a resistance (R). Therefore, VHX, for an inductor, Vo=IX for a capacitor, and V,=IR for a resistor. When applying Kirchhoff's voltage law to a series circuit ac impedance, the ac voltages must be added using phasor addition because they are out-of-phase with each other. Both the magnitude and the phase of each voltage must be taken into account. The ac voltage across the circuit reactance (IX) is 90 degrees out-of-phase with the ac circuit current, and the ac voltage across the circuit resistance (IR) is in phase with the ac circuit current. Therefore, IR and IX must be added as if they are separated by 90 degrees. From right angle trigonometry (Pythagorean theorem), Kirchhoff’s voltage law, and Ohm’s law, the ac rms voltages around the closed path can be represented by V = {dR +(x) = JPR? +X?) = WR? +X? = IZ Based on this equation, the series circuit impedance (Z) can be determined from Z= VR? +x? where X is the circuit reactance in ohms, and R is the circuit resistance in ohms. | Experiment 21 165 nN ” Notice that the phasor sum of V, and Vx is equal to V. From the triangle, | Va JVEt Va 1 M. | _ | Note: If you do the experiment in a real laboratory environment (hardwired), see the end of the Theory section of Experiment 19 regarding the inductor resistance (R,). Figure 21-1 Impedance—Series R-L Circuit * [woo cone ; 100mH : L + 0.000|v worm 166 PartIV Alternating Current (AC) Cir: : Figure 21-2 lmpedance—Series R-C Circuit 0.000/V Experiment 21 167 . ny “Procedure: Step L. Pull down the File menu and open FIG21-1. Bring down the oscilloscope enlargement and make sure that the following settings are selected: Time base (Scale = 100 j1s/Div, Xpos = 0, Y/T), Ch A (Seale = 5 V/Div, Ypos = 0, AC), Ch B (Scale = 5 V/Div, Ypos = 0, AC), Trigger (Pos edge, Level = 1 'V, Nor, A). Bring down the function generator enlargement and make sure that the following settings are selected: Sine Wave, Freq = 2 kHz, Ampl = 10 V, Offset = 0. Click the On-Off switch to run the simulation. Click “Pause” after ten screen displays on the oscilloscope. The red curve is plotting the voltage across the impedance of the R-L circuit (V), and the blue curve is plotting the current (I) because the voltage across the 1 kQ resistor is proportional to the current (1 V is equivalent to 1 mA on the oscilloscope vertical axis). Draw the curve plots for the voltage (V) and current (I) in the space provided. Record the ac rms voltage (V) and current (1) readings on the ac voltmeter and ammeter. Step 2. Step 3. Step 4. v= mms i= mms Based on the curve plots in Step 1, determine the phase difference (0) between the voltage and current. Based on the ac rms voltage (V) and current (1), calculate the magnitude of the impedance (Z) of the R-L circuit. Based on the value of the inductance (L) and the sinusoidal frequency (f), calculate the inductive reactance (X,) of the inductor. 170 Part IV Alternating Current (AC) Circuits Question: How did your calculated impedance magnitude in Step 11 compare with the impedance from the measured ac rms voltage and current in Step 9? Step 12. Based on the calculated capacitive reactance (X,) and the value of resistance R, calculate the expected phase difference (6) between the current and voltage sinusoidal functions. Question: How did the calculated value for the phase difference in Step 12 compare with the measured phase difference between the current and voltage curve plots in Steps 7 and 8? Is the voltage leading or lagging the current? Is this what you expected? : Step 13. Pull down the File menu and open FIG21-3. Bring down the oscilloscope enlargement and make sure that the following settings are selected: Time base (Scale = 200 ps/Div, Xpos = 0, Y/T), Ch A (Scale 5 V/Div, Ypos = 0, AC), Ch B (Scale = 5 V/Div, Ypos = 0, AC). Trigger (Pos edge, Level = 1 pV, Nor, A). Bring down the function generator enlargement and make sure that the following settings are selected: Sine Wave, Freq = 1 kHz, Amp! = 10 V, Offset = 0. Click the On-Off switch to run the simulation. Click “Pause” after ten screen displays on the oscilloscope. The red curve is plotting the voltage across the impedance of the R-L-C circuit (V), and the blue curve is plotting the current (I) because the voltage across the 1 kQ resistor is proportional to the current (1 V is equivalent to 1 mA on the oscilloscope vertical axis). Draw the curve plots for the voltage (¥) and current (1) in the space provided on the nexf page. Record the ac rms input voltage (V), circuit current (1), inductor voltage (V,), capacitor voltage (V), and resistor voltage (Vp) on the ac voltmeters and ammeter. Experiment 21 171 Step 14. Sa Step 15. Step 16. Step 17. Based on the curve plots in Step 13, determine the phase difference (8) between the voltage and current. Based on the ac rms input voltage (V) and circuit current (I), calculate the magnitude of the impedance (Z) of the R-L-C circuit. Based on the value of the capacitance (C) and the sinusoidal frequency (f), calculate the capacitive reactance (X_) of the capacitor. Based on the value of the inductance (L) and the sinusoidal frequency (f), calculate the inductive reactance (X,) of the inductor. 172 Part {V_ Alternating Current (AC) Circuits ‘ Step 18. Based on the value of resistance R, the capacitive reactance (X_) of capacitor C, and the inductive reactance (X,) of inductor L, calculate the expected magnitude of the impedance (Z) of the R-L-C circuit. Question: How did your calculated impedance magnitude in Step 18 compare with the impedance from the measured ac rms voltage and current in Step 15? Step 19. Based on the calculated capacitive reactance (X_), the calculated inductive reactance (X,), and the value of resistance R, calculate the expected phase difference (8) between the current and voltage sinusoidal functions. phon, Question: How did the calculated value for the phase difference in Step 19 compare with the measured phase difference between the current and voltage curve plots in Steps 13 and 14? Is the voltage leading or lagging the current? Is this what you expected? Explain. Step 20. Based on the inductive reactance (X,) calculated in Step 17 and the ac rms circuit current (D, calculate the expected ac rms voltage across the inductance (V,). ane Experiment 21 175 # “Question: How did your calculated ac rms circuit current compare with the measured value in Step 25? Step 30. Based on the inductive reactance (X,) calculated in Step 26 and the ac rms circuit current (1), calculate the expected ac rms voltage across the inductance (V,). Question: How did your calculated value for V, in Step 30 compare with the measured value in Step 25? Step 31. Based on the capacitive reactance (X,) calculated in Step 27 and the ac rms circuit current (J), calculate the expected ac rms voltage across the capacitance (V,). Question: How did your calculated value for V_ in Step 31 compare with the measured value in Step 25? ee" Step 32. Based on the resistance (R) and the ac rms circuit current (1), calculate the expected ac mms voltage across the resistance (Vz). Question: How did your calculated value for V, in Step 32 compare with the measured value in Step 25? Step 33. Add the phasor sum of the ac rms voltages across the inductor, capacitor, and resistor, taking the phase difference between the voltages into account. Draw the phasor diagram. _Question: Does the phasor sum of the voltages equal the ac rms voltage (V) applied across the total ‘impedance? Did the sum satisfy Kirchhoff's voltage law? 176 Part IV Altemating Current (AC) Circuits é Troubleshooting Problems Note: Exercises 5 and 6 are challenging problems for more advanced students. 1. Pull down the File menu and open FIG21-4. Click the On-Off switch to run the simulation. Based on the oscilloscope curve plots, which component is shorted (R, L, or C)? Explain why. 2, Pull down the File menu and open FIG21-5. Click the On-Off switch to run the simulation. Based on the oscilloscope curve plots, which component is shorted (R, L, or C)? Explain why. 3. Pull down the File menu and open FIG21-6. Click the On-Off switch to run the simulation. The red curve is plotting the voltage across X and the blue curve is plotting the current in X. Based on the oscilloscope curve plots, determine the component in X (R, L, or C). Explain why. 4. Pall down the File menu and open FIG21-7. Click the On-Off switch to run the simulation. The red curve is plotting the voltage across X and the blue curve is plotting the current in X. Based on the oscilloscope curve plots, determine the component in X (R, L, or C). Explain why. Experiment 21 177 ‘ ‘5. Pull down the File menu and open FIG21-8. Click the On-Off switch to run the simulation for ten screen displays, then click “pause.” Based on the oscilloscope curve plots, determine the value of L and R. L= R=