Lab3_Worksheet_Resistive

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BMEN 3220 – Electrical and Electronic Circuits in Biomedical Engineering Lab Lab 3: Resistive Circuits See the Report Guideline at the end the file for details on what to include in your Lab Report. Submit a single docx or pdf file in eLearning. Contents Introduction .............................................................................................................................................. 1 Exercise 1. Using the Multimeter .............................................................................................................. 2 1.1 Measuring resistance ...................................................................................................................... 2 1.2 Measuring voltage and current ....................................................................................................... 2 1.3 Kirchoff’s voltage law ...................................................................................................................... 3 Things to remember .............................................................................................................................. 3 Exercise 2. Power and equivalent resistance ............................................................................................ 4 2.1 Voltage sources .............................................................................................................................. 4 2.2 Series and parallel resistors ............................................................................................................ 5 Exercise 3. Analyzing a complex circuit ..................................................................................................... 6 3.1 Building the circuit .......................................................................................................................... 6 3.2 Finding all voltages ......................................................................................................................... 6 3.3 Finding all currents (without using Ohm’s law) ............................................................................... 7 3.4 Power consumption ........................................................................................................................ 7 3.5 Simulation ....................................................................................................................................... 8 Report Guideline ....................................................................................................................................... 9 Introduction In Lab-2, you have learned how to build simple resistive circuits and take basic measurements using Tinkercad. In this lab, you will physically build circuits and take measurements using actual circuit elements (you will use Tinkercad only in Exercise 3.5). As voltage sources, you can use benchtop power supplies (Agilent E3631A or Keysight E36312A available in the ML1 labs) and/or batteries (for example, use a 9 V battery for circuits with 9 V voltage sources; however, the actual voltage will likely be different; measure the actual battery voltage and use that value in your calculations instead of 9 V). Use color codes to identify resistors; you should use a multimeter to find their exact values. When directed, take a clear picture of the circuit for your report. BMEN 3220 – Resistive Circuits Page 1

Exercise 1. Using the Multimeter 1.1 Measuring resistance a) Pick resistors that have nominal values (NV) of 1 kΩ and 3 kΩ based on the color code. b) Use a multimeter to measure their actual resistances (MV) and fill in Table 1. c) Calculate the percentage error as, | NV − MV | NV × 100% Resistor Nominal Value (NV) Using Multimeter Measured Value (MV) Percentage Error R 1 1.0 k Ω 0.98320 1.68% R 2 3.0 k Ω 2.98470 0.52% Table 1 In your report, include a picture of the multimeter displaying the resistance of the resistor with nominal value of 1 kΩ. 1.2 Measuring voltage and current Connect a 1.5 V source across the 1 kΩ resistor. Measure the voltage across the resistor and the current passing through the resistor using your multimeter. In your report, include a picture of the multimeter displaying the voltage, and another displaying the current. BMEN 3220 – Resistive Circuits Page 2

1.3 Kirchoff’s voltage law Build the circuit shown in Figure 1 using a 9 V source, an LED and two resistors. The top resistor is 3 kΩ and the bottom one is 1 kΩ. Figure 1 Demonstrate Kirchoff’s voltage law (KVL) in this circuit upon taking the measurements you think are necessary. Describe what tasks you have performed; if and how you were able to demonstrate KVL; include relevant results and pictures. Things to remember  When you pick a resistor for building a circuit, do not just rely on the color codes (which give you the nominal values). Measure them using a multimeter to ensure you have the right value.  For all your calculations, use the measured resistor and supply voltage values for more accurate estimations rather than the nominal values as you have seen there is almost always an error.  Remember that a voltage between any two nodes of a circuit can be measured simply by touching the two probes of the voltmeter to these nodes. But when measuring current, you have to break the circuit and allow the current to pass through the ammeter. BMEN 3220 – Resistive Circuits Page 3

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Exercise 2. Power and equivalent resistance 2.1 Voltage sources Figure 2 (a) Figure 2 (b) As shown in Figure 2(a), build a circuit with V S 1 = 1.5 V and R = 1 kΩ. Measure V R and I R . In your report, include a picture of the circuit with the ammeter displaying I R . Calculate the powers absorbed or delivered by the resistor and the source. Fill in the third column of Table 2. Next modify the circuit as Figure 2(b) with V S 2 = 9 V and repeat the above (fill in the last column of Table 2). For Figure 2 (a) For Figure 2 (b) Measurements Resistance, R 0.98926 kOhms Voltage, V R 1.5006 V Current, I R 1.5098 mA For Resistor Does it absorb power or deliver ? absorb What is the amount of this power? 0.002266 W For the source, V S 1 Does it absorb power or deliver ? deliver What is the magnitude of this power? 0.0022509 Does current leave the V S 1 terminal or enter ? leave Table 2 BMEN 3220 – Resistive Circuits Page 4

2.2 Series and parallel resistors Figure 3 (a) Build the circuit shown in Figure 3 using three arbitrary resistors (pick three different values in the 500 Ω to 3 kΩ range). Calculate R bc , the equivalent resistance between nodes b and c from R 1 , R 2 and R 3 . Then measure R bc directly using the Ohmmeter and see if it matches the calculated value. Repeat this for R ac . Fill in Table 3 with your results. In your report, include a picture of the circuit with the Ohmmeter displaying R ac . Resistor Values (measured) R 1 = ¿ R 2 = ¿ R 3 = ¿ Equivalent Resistance Calculated (show your calculation) Measured R bc = ¿ R ac = ¿ Table 3 (b) Connect a 1.5 V power supply across the circuit such that V ac =+ 1.5 V. Demonstrate Kirchoff’s current law (KCL) at node b upon taking the measurements you think are necessary. Describe what tasks you have performed; if and how you were able to demonstrate KCL; include relevant results and pictures. (c) When building a circuit, you will often need a specific resistor value that may not be available. In such cases, you can use multiple resistors in series and parallel combinations to obtain an equivalent resistance that is equal or very close to your desired resistance value. For example, if you require a 1.5 kΩ resistor but do not have one, you can place one 1.2 kΩ and three 110 Ω resistors in series to obtain an equivalent resistance of 1.53 kΩ. Alternately, if you use 110 Ω, 5.1 kΩ and 2 kΩ as R 1 , R 2 and R 3 , respectively, in Figure 3, you can obtain an equivalent resistance of 1.49 kΩ. Using any number of resistors from your lab kit, create a resistive network with an equivalent resistance of 1.88 kΩ (within ± 2% ). Take a picture of your circuit with the Ohmmeter displaying the equivalent resistance of the network. State which resistor values you used and in what fashion. BMEN 3220 – Resistive Circuits Page 5

Exercise 3. Analyzing a complex circuit You will physically build the circuit and take measurements for Exercises 3.1 to 3.4. Use Tinkercad for Exercise 3.5. 3.1 Building the circuit Build the circuit shown in Figure 4 using resistors: R 1 = 5.1 kΩ, R 2 = 2 kΩ, R 3 = 110 Ω, R 4 = 3 kΩ and R 5 = 1 kΩ (measure their actual resistances and write them in the first column of Table 6 in page 8). Here, V s1 = 9 V and V s2 = 1.5 V. Figure 4 Take a picture of the circuit for your report. 3.2 Finding all voltages Remember that the voltage across multiple components in series is simply the sum of the voltages across the individual components. If you apply this principle to a closed loop in the circuit, and keep in mind that a node can have one and only one voltage, you get Kirchoff’s voltage law (KVL) . It states that the sum of all voltages around a loop of circuit elements is zero. Now your goal is to find out all the voltages, V s1 , V s2 ,V 1 , V 2 , V 3 … V 5 , using the minimum number of voltmeter measurements . Some of these voltages may be equal. Find out how many different voltages there are in the circuit. If there are x different voltages, you don’t necessarily need to take x BMEN 3220 – Resistive Circuits Page 6

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measurements. You can deduce some of the voltages from others using KVL. Fill in Table 4. Enter the voltages across each of the elements in the second column of Table 6. What is x , the number of different voltages in this circuit? What are these voltages? [do not assume that the supply voltages are exactly the same as their nominal values; measure or calculate them] What is the minimum number of voltmeter measurements that you need to deduce all x voltage values? Which values did you measure using the voltmeter and how did you calculate the rest? Table 4 3.3 Finding all currents (without using Ohm’s law) Keep in mind that all currents flowing into a node must sum to zero . In other words, the sum of all currents entering a node equals the sum of all currents leaving the node . This is known as Kirchoff’s current law (KCL). Your next goal is to find all the currents using the minimum number of ammeter measurements (you WILL NOT use Ohm’s law to calculate them from the resistances and voltages; you will rely only on ammeter readings and KCL). Some of these currents are the same. Find out how many different currents there are in the circuit. If there are y different currents, you don’t necessarily need to take y ammeter measurements. As before, you can deduce some of the currents from others. Fill in Table 5. Enter the values of all currents in the third column of Table 6. What is y , the number of different currents in this circuit? What are these currents? What is the minimum number of ammeter measurements that you need to deduce all y current values? Which values did you measure using the ammeter and how did you calculate the rest? Table 5 3.4 Power consumption The power absorbed by an element is equal to the product of the voltage across it and the current passing through it (in the direction from high to low potential), i.e. P = V ×I . For a resistor, this value is always positive (implying that the resistor “absorbs” power). The value will be negative if an element “delivers” power (which is usually but not always the case for a voltage source). In the fourth column of Table 6, calculate (with proper sign) the power absorbed or delivered by each of the seven components of the circuit. Then see if the “total power dissipated” is equal to the “total power generated” in the circuit (as it should according to the law of conservation of energy ). BMEN 3220 – Resistive Circuits Page 7

Element Voltage (V) Current (A) Power (W) R 1 = V 1 = I 1 = P 1 = R 2 = V 2 = I 2 = P 2 = R 3 = V 3 = I 3 = P 3 = R 4 = V 4 = I 4 = P 4 = R 5 = V 5 = I 5 = P 5 = 9 V source V S1 = I S1 = P S1 = 1.5 V source V S2 = I S2 = P S2 = Total power dissipated in the circuit (sum of all positive quantities) = Total power generated in the circuit (sum of all negative quantities) = Table 6 Briefly comment on these results. 3.5 Simulation Construct the circuit from Exercise 3.1 (Figure 4) in Tinkercad. Use two ammeters and two voltmeters to measure the four quantities shown in Table 7. Fill in Table 7. Attach a screenshot of your simulation in your report. Compare to the experimental results you obtained in Exercise 3.4 and briefly comment on these results. Quantity Experimental results obtained in Exercise 3.4 (copy from Table 6) Simulated values from Tinkercad V 1 V 3 I 2 I 4 Table 7 . Report Guideline You do not need to write a formal lab report explaining every task you performed. In most cases, you need to present results such as tables, screenshots, pictures, etc. only (screenshots and images must BMEN 3220 – Resistive Circuits Page 8

be legible and cropped appropriately). In some cases, a brief analysis and a description of your experiment is required. Below is a list of items for this lab report along with the rubric. If you work with a partner, include their name at the beginning of the report. If you do some exercises individually and some with a partner, state which exercises you have worked with them. Exercise What to include in report Points Exercise 1.1 Completed Table 1 and one picture 7 Exercise 1.2 Two pictures 8 Exercise 1.3 Discussion with relevant results and pictures Measuring the voltage drops across each indivial resistor and the LED we got 1.79V (1kohm), 1.808V (LED), and 5.399V(3kohm) which sums to 9.009 V. 8 Exercise 2.1 Completed Table 2 and two pictures (ammeter readings for Figures 2(a) and 2(b)) 12 Exercise 2.2(a) Completed Table 3 and one picture 10 Exercise 2.2(b) Discussion with relevant results and pictures 8 Exercise 2.2(c) Circuit description or diagram, and one picture 7 Exercise 3.1 One picture 5 Exercise 3.2 Completed Table 4 6 Exercise 3.3 Completed Table 5 6 Exercise 3.4 Completed Table 6 and Analysis 15 Exercise 3.5 Completed Table 7, Analysis, Screenshot 8 BMEN 3220 – Resistive Circuits Page 9

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