Lab 2 Resistance and Ohms Law

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Dec 6, 2023

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Name: Lab: 2 Lab 2: Resistance and Ohm’s Law Objectives: Upon completion of this lab, you should be able to: • Determine the nominal value of a resistor using its color code. • Measure resistance using a Digital Multimeter (DMM) • Determine the tolerance of a resistor using its color code. • Calculate the percent of variation between a nominal value and a measured value. Materials: 1 x Elvis Unit with: Variable Power Supply Digital Multi-Meter Prototyping board 1 x Digital Multimeter Fluke 78 or equivalent 10 x Assorted Resistors. Located in bins labeled “EET 221 LAB #2” Discussion: Resistors are common electronic components that provide direct opposition to the flow of current . They come in a variety of shapes and sizes that reflect their application. While it may seem contradictory, the size of a resistor itself is independent of its resistance. This is because the rated or nominal resistance is a result of the type of material used in its construction, rather than how much material is used. Because of this, a resistor with a particular resistance rating can come in many sizes. Why then would an individual use one sized resistor as compared to another? As it turns out, the physical size of a resistor is an extremely important consideration in electronics. While it is independent of the component’s resistance rating, it is characteristic of its power rating. This power rating determines how much heat the device can dissipate without being damaged or destroyed. As a general rule, larger components are often able to dissipate more heat than smaller devices as a result of the additional material used in construction and the resulting additional surface area. Because of variability in the manufacturing process, resistors have not only nominal values assigned to them, but tolerances as well. These tolerances specify the maximum allowable variation from the nominal value. As an example, if a 1 kΩ resistor was rated at 10% tolerance, its measured value could range from 900 Ω to 1,100 Ω. If its measured value fell outside of this range, then it would be said to be out of tolerance.

Georg Ohm discovered in 1827 that there is a direct relation between the voltage and current in a circuit. Ohm’s Law, named in his honor, states that the current through a conductor is directly proportional to the potential difference applied across the conductor. Georg Ohm originally stated in 1827 that the conductivity of the conductor represented the proportionality constant relating the voltage across and current through it. As a result, Ohm’s Law was originally expressed as 𝐼𝐼 = 𝜎𝜎𝜎𝜎 , where σ represents the conductance of the material. Later, when resistance was defined as the reciprocal of the conductance, Ohm’s Law was restated in its current form: 𝜎𝜎 = 𝐼𝐼𝐼𝐼 This Lab is intended to introduce the resistor color code and to demonstrate Ohm’s Law and its application in analyzing single element circuits. Procedure: Part 1: Resistor Color Code 1. Use the resistor color code to determine the nominal value and tolerance of one of the resistors provided in the lab. Record these values along with the resistor’s color code in the corresponding columns of Table 1. Table 1: Measured and Calculator Resistor Values Color Band Nominal Tolerance Value Range Measured Variation EX: Red/Purple/Orange/Gold 27 kΩ ±5% 25.7k Ω –28.4 kΩ 26.2 kΩ 2.9 % 2. Using the nominal value and tolerance, calculate the expected minimum and maximum values expected and record in the corresponding column of the table. 3. Use the Digital Multimeter to measure each resistor and record the measured value in the corresponding column of the table. Refer to the diagram to the right or the User Manual to properly measure resistance. Tip: It is advisable to use the prototyping region of the Elvis unit to hold the resistor so that human contact does not influence the measurement. 4. Determine the percent of variation (error) between the nominal value and the measured value using the formula on the following page.

% 𝜎𝜎𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉 = | 𝑁𝑁𝑉𝑉𝑁𝑁𝑉𝑉𝑉𝑉𝑉𝑉𝑁𝑁 𝜎𝜎𝑉𝑉𝑁𝑁𝑉𝑉𝑉𝑉 − 𝑀𝑀𝑉𝑉𝑉𝑉𝑀𝑀𝑉𝑉𝑉𝑉𝑉𝑉𝑀𝑀 𝜎𝜎𝑉𝑉𝑁𝑁𝑉𝑉𝑉𝑉 | 𝑁𝑁𝑉𝑉𝑁𝑁𝑉𝑉𝑉𝑉𝑉𝑉𝑁𝑁 𝜎𝜎𝑉𝑉𝑁𝑁𝑉𝑉𝑉𝑉 𝑥𝑥 100% Record the percent variation in Table 2 . 1 . 5. Repeat Steps 1 through 4 for the remaining 9 resistors included in the kit. This will complete Table 1. 6. Use the DMM to measure the resistance of the 1 𝑀𝑀Ω resistor using the same method described in Step 3 above. Record the measurement in the space provided. Measurement : 7. Repeat this measurement, however this time; touch both ends of the resistor while performing the measurement. Measurement : 8. Select a resistor with a red multiply band and use the DMM to measure its resistance using the method described in Step 6 above. Measurement : 9. Repeat this measurement as described in Step 7 above. Measurement : Part 2: Ohm’s Law 10. Using Ohm’s Law, calculate the nominal current through the circuit illustrated below using the nominal voltage and resistance values, then repeat this procedure for the other three resistors. Record your calculated current in the first column of Table 2. 11. Change 𝜎𝜎 𝑠𝑠 to 5 V and repeat Step 10. Table 2 Nominal Voltage Nominal Resistance Nominal Current Measured Voltage Measured Resistance Measured Current Current Variation (%) 15 V 1 kΩ 15 V 2 kΩ 15 V 5.6 kΩ 15 V 22 kΩ 5 V 1 kΩ 5 V 2 kΩ 5 V 5.6 kΩ 5 V 22 kΩ

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12. Locate a 1 𝑘𝑘Ω Resistor from the kit used in part 1 above. Use it to construct the circuit shown above. Use the supply voltages provided on pins 51 and 54 for the +15 V and +5 V and pin 53 as ground reference for the circuit. Verify that the DC power supply is off before connecting the circuit to the source. 13. Measure the voltage applied to the circuit and record it in the second column of Table 2. 14. Measure the current in the circuit as illustrated in the diagram to the right. To measure current, place the ammeter in series with the circuit. Refer to the Fluke 78 User Manual for operation of the digital multi-meter as an ammeter. Record the current in Table 2. 15. Determine the percent variation between the measured and calculated current and record in the final column of Table 2. 16. Repeat Steps 12 through 15 for the remaining resistor and voltage combinations illustrated in Table 2.

Questions: Part 1 1. Assume that a 47 𝑘𝑘Ω resistor and a 22 𝑘𝑘Ω resistor each vary by 0.5% from their nominal values. Which of these resistors will vary by the largest actual value? Why? 2. Assume that a 330 𝑘𝑘Ω resistor has a measured value of 338 𝑘𝑘Ω while a 1.1 𝑘𝑘Ω has a measured value of 1.066 𝑘𝑘Ω . Which component has the greatest variation between its rated and measured values? 3. How much did your measurement vary between steps 6 and 7? Which measurement was more accurate? Explain your answer. 4. Determine the percent variation between the measured values in steps 6 and 7 and the percent variation between steps 8 and 9. In which case was the percent variation the greatest? Why? Part 2 5. Based on the results of Table 2, explain what happens when voltage is fixed and circuit resistance increases. 6. Explain why measured component values are preferred to nominal values when performing circuit calculations. 7. Assume that you do not have a volt meter but do have a functioning ammeter. Explain how you could use Ohm’s Law to estimate the value of the voltage in the circuit. 8. In Table 2, you determined the percent variation between your measured and calculated values. Explain the source of the variations and provide a method to minimize the difference.