ECE 2004 Lab 2 Power Measurements and Bridge Circuits Rev 2_0

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ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 1 Lab 2 Rev 2.0 09/16/2022 Lab #2 Power Measurements and Bridge Circuits I. Experimental Procedure A. Equipment List ± Tektronix CDM250 Digital Multimeter (DMM) (for voltage and resistance measurements) ± Fluke 8010A Digital Multimeter (DMM) (as an ammeter) ± Tektronix CPS250 Power Supply ± Banana to Alligator Clip, Red (quantity 3) ± Banana to Alligator Clip, Black (quantity 3) ± 100 Ω, 5%, 1 watt resistor ± 2.7 kΩ, 5%, 1 watt resistor ± 10 kΩ, 5%, ½ watt resistor ± Resistance Decade Box, 1 Ω to 10 M Ω Resistance Range, 1% Accuracy, AEMC BR07 ± 1 kΩ, 5%, ½ watt resistor (quantity 2) ± 1 kΩ, 0.1%, ¼ watt resistor (quantity 2) ± 2 kΩ, 5%, ½ watt resistor (quantity 3) ± 2 kΩ, 0.1%, ¼ watt resistor (quantity 2) ± 200 Ω, 5%, ½ watt resistor ± Unknown resistor B. Power Dissipation in a Resistor Connect a 100 ohm, 1‐Watt resistor to the +/‐ terminals on one‐channel of the DC power Supply. Using the DMM, set the DC power supply voltage to 5V (it’s always the safest to start with the power supply voltage turn down to 0 V, connect the circuit, then while measuring the output voltage, increase the power supply voltage until the DMM reads the desired voltage). Using Ohm’s Law, calculate the current flowing through the 100 ohm resistor enter the value on Table 1. Calculate the absorbed power and enter the value on Table 1. Are you able to touch the resistor without burning your fingers? On Table 1, describe the temperature of the resistor when touching the body of the resistor, cool, warm, hot or very hot. Repeat the test for power supply voltages up to 8 V. Caution, at the higher dissipated power ሺ൐ 0.5 𝑊ሻ , the resistor will very become hot so lightly tap the resistor when estimating its temperature. What do you think will happen if the 1‐Watt power rating is exceeded? Table 1 Calculated and Absorbed Power for 100 ohm Resistor Power Supply Voltage (V) Calculated current (A), based on R=100‐ohm Calculated Power Dissipated in R (W) Temperature (cool, warm, hot, very hot?) 5 6 7 8

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 2 Lab 2 Rev 2.0 09/16/2022 Replace the 100 ohm resistor with a 2.7 kohm, 1‐Watt resistor. Repeat the experiment and enter the values on Table 2. Table 2 Calculated and Absorbed Power for 2.7 kohm Resistor Power Supply Voltage (V) Calculated current (A), based on R=2.7 kohm Calculated Power Dissipated in R (W) Temperature (cool, warm, hot, very hot?) 5 6 7 8 Approximately, how large would the supply voltage need to be before the resistor would begin to heat up and you could no longer touch it. The power supply is rated for a maximum output voltage of +20 V on each channel. Switching the power supply into “Series” mode, will place the A‐channel and B‐channel in series. In this case, the total output voltage will reach +40 Volts. Switch the supply to “Series” mode. Connect the 2.7 kohm resistor between the red terminal of channel A and the black terminal in channel B. Using the DMM, measure the total output voltage across these terminals and increase the power supply voltage to the maximum value. Enter the maximum voltage on the last line in Table 2 above. Calculate the current and power for this configuration. Is the resistor hot? Enter your observation on the table. Would you say that the current flow or the power dissipation is related to the amount of heating? Compare the parameter in each resistor that relates to heating. Turn down the power supply voltage and return to “Independent” mode. C. Maximum Power Transfer in a Resistive Load Using the breadboard, connect the power supply, 10 k  resistor and Decade Resistance Box as shown in Fig. 1. A Decade Resistance Box is an instrument with discrete resistance steps in factors of ten. Examine the knobs on your Box to understand how the resistance can be adjusted. Set your Resistance Box to 1 ohm . Set the DMM to measure the voltage. Using the DMM, adjust the power supply voltage to +20 V and turn on the voltage output. Using the DMM, connect the test probes across the Resistance Box as shown in Fig. 1. Note: for each setting on the Box, you may need to adjust the scaling on the DMM to properly read the voltage with the most digits displayed. Adjust the Resistance Box settings to the values shown on Table 3 and record the measured voltage across the Resistance Box (load). Calculate the power dissipated ൬ 𝑉 ௅ை஺஽ ଶ 𝑅 ൗ ൰ in the load resistance and enter on Table 3. For your lab report and using Microsoft® Excel®, plot the Power Dissipated (Y‐axis) versus the Load Resistance (box setting, X‐axis). It is best to use the X‐Y scatter plot in Excel®. Change the X‐Axis to a logarithmic scale. Looking for the peak in your plot, what is the value in the load resistance that achieves the maximum power transfer to the load (relative to the 10 k  source resistor)? If the source resistance was

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 3 Lab 2 Rev 2.0 09/16/2022 changed to 1 k  , what load resistance is now required for maximum power transfer? In your report, briefly discuss the relationship between source resistance and load resistance. Figure 1 Circuit for measuring maximum power transfer Table 3 Measured Voltage as a function of load resistance Resistance Box Setting (ohm) Measured Voltage (V) Calculate Power in R load (W) 1 10 100 1 k 10 k 100 k 1 M D. Node Voltage and Equivalent Resistance, Circuit #1 Using your breadboard, connect the circuit using the schematic shown in Fig. 2. Use 5% tolerance resistors for this circuit. The first DMM will be used to measure voltage and resistance. The second DMM will be configured to measure current (ammeter). The ammeter is inserted in series between the Power Supply and Node A, as shown in Fig. 2. Verify that the DMM’s “+” lead (Red Probe) is connected to the instrument’s current (A) port and set this instrument to measure current.

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ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 4 Lab 2 Rev 2.0 09/16/2022 Figure 2 Circuit #1 Using the DMM, adjust the power supply voltage until V AD = +20 VDC. Using Node D as the reference ( V D = 0 VDC), measure the voltage at the other two nodes and record on Table 4. Using any analysis technique that you prefer (nodal, mesh, etc.), calculate the theoretical values for these two node voltages and record on Table 4. Also, calculate the percent error between your measurement and the theory, record these percentages on Table 4. In your lab report, discuss why there could be differences between the measured and the theoretical voltages. Table 4 Measurement of Node Voltages for Circuit #1 Node Voltage Measurement (V) Theoretical (V) % 𝐸𝑟𝑟𝑜𝑟 ൌ ሺ𝑇ℎ𝑒𝑜𝑟𝑦 െ 𝑀𝑒𝑎𝑠ሻ 𝑇ℎ𝑒𝑜𝑟𝑦 𝑥100 V AD 20 20 0% V BD V CD V D 0 0 0% Using the ammeter (DMM), measure the total source current, I S , and record on Table 5. Calculate R TOTAL using this measured current and knowing that V AD = +20 V, enter on Table 5. Lastly, using any analysis technique that you prefer (series/parallel resistors, nodal, mesh, etc.), compute the theoretical total resistance, R TOTAL , across nodes A to D and record on Table 5. Calculate the % error and enter on Table 5. In your report, discuss the reasons for the measurement error. Table 5 Measured and Theoretical Resistance for Circuit #1. Measurement using Ohms Law

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 5 Lab 2 Rev 2.0 09/16/2022 Measured I S Calculate 𝑅 ்ை்஺௅ ൌ 𝑉 ஺஽ 𝐼 ௌ ൗ Theoretical 𝑅 ்ை்஺௅ % 𝐸𝑟𝑟𝑜𝑟 ൌ ሺ𝑇ℎ𝑒𝑜𝑟𝑦 െ 𝐷𝑀𝑀ሻ 𝑇ℎ𝑒𝑜𝑟𝑦 𝑥100 Disconnect the power supply and ammeter from Node A and Node D. Measure the total resistance across nodes A to D using the DMM (set to measure resistance) and record on Table 6. Enter the theoretical total resistance, R TOTAL , on Table 6 (previously calculated and entered on Table 5). Calculate the % error between the and enter on Table 6. In your report, discuss the reasons for the measurement error. Also compare the % errors between Table 5 and Table 6. Is one measurement technique more accurate than the other, discuss? Table 6 DMM Measured and Theoretical Resistance for Circuit #1. Measurement using DMM Resistance DMM Measured 𝑅 ்ை்஺௅ Theoretical 𝑅 ்ை்஺௅ % 𝐸𝑟𝑟𝑜𝑟 ൌ ሺ𝑇ℎ𝑒𝑜𝑟𝑦 െ 𝐷𝑀𝑀ሻ 𝑇ℎ𝑒𝑜𝑟𝑦 𝑥100 E. Node Voltage and Equivalent Resistance, Circuit #2 Continue using 5% tolerance resistors. You will be repeating the steps from Part D (above) for the Circuit #1 but now modified to include a shorting wire between Node B to Node C. Reconnect the power supply and ammeter between Node A and Node D. Verify that your modified circuit is the same as shown in Figure 3. Figure 3 Circuit #2 Using the DMM, set to measure voltage, confirm that the applied voltage across the bridge, V AD , = +20 VDC. As before, use Node D as the reference ( V D = 0 VDC) and adjust the power supply voltage if necessary. Measure the voltage at the other two nodes (B and C) and record on Table 7. Using any analysis technique that you prefer, calculate the theoretical values for these two node voltages and record on Table 7. In your lab report, discuss why there could be differences between the measured voltages and the theoretical voltages.

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 6 Lab 2 Rev 2.0 09/16/2022 Table 7 Measurement of Node Voltages for Circuit #2 Node Voltage Measurement (V) Theoretical (V) % 𝐸𝑟𝑟𝑜𝑟 ൌ ሺ𝑇ℎ𝑒𝑜𝑟𝑦 െ 𝑀𝑒𝑎𝑠ሻ 𝑇ℎ𝑒𝑜𝑟𝑦 𝑥100 V AD 20 20 0% V BD V CD V D 0 0 0% Using the ammeter (DMM), measure the total source current, I S , and record on Table 8. Calculate R TOTAL using this measured current and knowing that V AD = +20 V, enter on Table 8. Lastly, using any analysis technique that you prefer (series/parallel resistors, nodal, mesh, etc.), compute the theoretical total resistance, R TOTAL , across nodes A to D and record on Table 8. Calculate the % error and enter on Table 8. In your report, and as before, discuss the reasons for the measurement error (should be the same reasons). Table 8 Measured and Theoretical Resistance for Circuit #1. Measurement using Ohms Law Measured I S Calculate 𝑅 ்ை்஺௅ ൌ 𝑉 ஺஽ 𝐼 ௌ ൗ Theoretical 𝑅 ்ை்஺௅ % 𝐸𝑟𝑟𝑜𝑟 ൌ ሺ𝑇ℎ𝑒𝑜𝑟𝑦 െ 𝐷𝑀𝑀ሻ 𝑇ℎ𝑒𝑜𝑟𝑦 𝑥100 Disconnect the power supply and ammeter from Node A and Node D. Measure the total resistance across nodes A to D using the DMM (set to measure resistance) and record on Table 9. Enter the theoretical total resistance, R TOTAL , (from Table 8) and record on Table 9. Calculate the % error between the measured DMM resistance and the theory and enter on Table 9. In your report, and as before, discuss the reasons for the measurement error (should be the same reasons). Compare the % errors between Table 8 and Table 9. Table 9 DMM Measured and Theoretical Resistance for Circuit #1. Measurement using DMM Resistance DMM Measured 𝑅 ்ை்஺௅ Theoretical 𝑅 ்ை்஺௅ % 𝐸𝑟𝑟𝑜𝑟 ൌ ሺ𝑇ℎ𝑒𝑜𝑟𝑦 െ 𝐷𝑀𝑀ሻ 𝑇ℎ𝑒𝑜𝑟𝑦 𝑥100

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ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 7 Lab 2 Rev 2.0 09/16/2022 F. Measurement of Unknown Resistor, Circuit #3: Wheatstone Bridge Continue using the 2 k  resistors with 5% tolerance. Wire the circuit using the schematic shown in Figure 4. Note that R3 is now a 2 k  resistor. The Decade Box is located at R2. You will be given an unknown resistor to place in the location for R4. Using the DMM, set to measure voltage, confirm that the applied voltage across the bridge, V AD , = +20 VDC. As before, use Node D as the reference ( V D = 0 VDC) and adjust the power supply voltage if necessary. This circuit is known as the “Wheatstone Bridge”, or a “bridge” circuit. This is a balanced circuit where an unknown resistor is place in one of the four legs (R4 in this case) and R2 is a variable resistor (Decade Box) which is tuned until no current flows in R5, this is the “balanced” state. When balanced, the value of the variable resistor, R2, is also the value for the unknown resistor. Using the DMM, you will monitor the voltage across R5 while you adjust R2. When the R5 voltage = 0 ( V BC = 0 V), the circuit is balanced and the resistor setting on the Decade Box is the value for the unknown resistor. Figure 4 The Wheatstone Bridge, Circuit #3 Balance your bridge circuit. Read the resistance on the Decade Box, this is the resistance of the unknown resistor. Enter this value on Table 10. Temporarily remove the unknown resistor, R4, and measure its resistance using a DMM set to measure “resistance”. Enter this DMM resistance measurement on Table 10. Calculate the percent error and record on Table 10. Replace R1 and R3 with 2 k  resistors having 0.1% tolerance. Reinsert the unknown resistor, R4. If necessary, readjust the Decade Box until the current is zero ( V BC = 0). Enter the Decade Box resistance on Table 11. Enter the previously recorded DMM measurement for R4 on Table 11. Lastly, calculate the percent error and record on Table 11.

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 8 Lab 2 Rev 2.0 09/16/2022 In your report, compare the values measured for the unknown resistor, R4, when using the 5% tolerance resistors and the 0.1% tolerance resistors in the bridge. Discuss the errors between the two measurements and any observations that you may have. Table 10 Measurement of Unknown Resistor, R4, using Bridge with 5% tolerance resistors Decade Box R4 DMM Measured 𝑅 ସ % 𝐸𝑟𝑟𝑜𝑟 ൌ ሺ𝐷𝑀𝑀 െ 𝐵𝑟𝑖𝑑𝑔𝑒ሻ 𝐷𝑀𝑀 𝑥100 Table 11 Measurement of Unknown Resistor, R4, using Bridge with 0.1% tolerance resistors Decade Box R4 DMM Measured 𝑅 ସ (from Table 8) % 𝐸𝑟𝑟𝑜𝑟 ൌ ሺ𝐷𝑀𝑀 െ 𝐵𝑟𝑖𝑑𝑔𝑒ሻ 𝐷𝑀𝑀 𝑥100 For your lab report, calculate the theoretical value of the total resistance across Node A and Node D in the balanced state. For this theoretical calculation, use the measured values for R2 and R4 (using the measurements when your bridge had 0.1% tolerance parts). Record this value in your lab report. Repeat the calculation when R2 is 10% less than the value you measured – this would be an unbalanced state as 𝑅2 ് 𝑅4 . For this unbalanced state, calculate V BD , V CD , V BC , and all the currents in R1 through R5. In your report, include a schematic showing all voltages, including polarities, and all currents, including directions.

ECE 2004 Lab 2 Power Measurements and Bridge Circuits Rev 2_0

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