Fall2023 Simple Electrical Circuits Lab Online

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Apr 3, 2024

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Simple Electrical Circuits Lab Online Purpose The purpose of this activity is to examine how Ohm’s Law can be applied to simple resistors arranged in simple electrical circuits. Theory Ohm’s Law tells us that resistance of an object is proportional to the voltage applied to it, and inversely proportional to the induced current passing through it. R = ∆V i When multiple resistors are arranged in series and a steady stream direct current is flowing through them we have three rules related to the current, the voltage, and the resistance of all of those resistors together. Those three rules are as follows: 1. For resistors in series the current passing through each of them is the same. i = i j = i 1 ,i 2 ,i 3 … 2. For resistors in series the voltage being applied to all of them is the sum of the voltage passing over all of them ∆V = ∑ j n ∆V j = ∆V 1 + ∆V 2 + ∆V 3 + … 3. For resistors in series the equivalent resistance of all of them together is just the sum of all of their resistance. R eq = ∑ j n R j = R 1 + R 2 + R 3 + … 1

When multiple resistors are arranged in parallel and a steady stream direct current is flowing through them we have three rules related to the current, the voltage, and the resistance of all of those resistors together. Those three rules are as follows: 1. For resistors in parallel the total current passing through all of them is the sum of the current passing through each of them. i = ∑ j n i j = i 1 + i 2 + i 3 + … 2. For resistors in parallel the voltage passing over each of them is the same. ∆V = ∆V j = ∆V 1 ,∆V 2 ,∆V 3 ,… 3. For resistors in parallel the inverse of the equivalent resistance of all of them is the sum of the inverses of all of them. 1 R eq = ∑ j n 1 R j = 1 R 1 + 1 R 2 + 1 R 3 + … When using these two sets of equations it can be best to draw simple circuit diagrams to help determine which circuit components are in series with each other, and which are parallel to each other. Let us start by examining two basic circuit component symbols. 1. A Potential Difference Source - Power supply, battery, fuel cell, or anything that will induce a potential difference to exist in the circuit. The circuit diagram symbol for such a device is two uneven parallel lines. The longer line represents the positive side of the Voltage Source, and the shorter line its negative side. The lines pointing out of both sides represent the wires that will connect the Voltage Source to the rest of the circuit. 2. Resistors – A component that hinders the flow of current through the circuit. Resistors are represented by few sharp jagged lines right in row. 2

This is drawn with the connecting wires coming out of both ends. Setup Part 1: Resistors in Series 1. Go to the following website: https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab 2. You should now see the following: 3. Click the down arrow to download the software. Once finished, you should see the following: 4. Near the bottom left of the screen, click on the Potential Difference symbol. 3

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5. On the right side of the screen just below the Voltmeter & Ammeter, click the Green/White Plus symbol next to Advanced. 6. In the drop-down menu for Advanced, make sure that Wire Resistivity and Battery Resistance are both set to ‘tiny’, then click the Red/Minus to close the drop-down menu. 7. In the White Box at the top right of your screen make sure “Show Current” is checked, select “Conventional”, make sure “Labels” is checked, and make sure that “Values” is checked. Procedure Part 1 1. On the Left side of your screen you will see a white box with the symbols of various basic circuit components. You will ‘Click and Drag” the various components to build simple circuit boards. 2. On the right side of your screen, and about a third of the way from the top you will see a white box with a voltmeter and an ammeter. You will ‘insert’ these instruments into the circuit you build in order to measure the voltage and the current. 3. Build the following circuit of three resistors in series with each other: (You can use the plus and minus at the bottom of the left side of your screen to give yourself more room to work with if you need it.) 4. Click on the Potential Difference source (Battery) and set it to 100 V. 5. Click on each of the resistors to set its resistance. Set R 1 = 10.0 Ohms, R 2 = 50.0 Ohms, and R 3 = 100.0 Ohms. 6. Read off the currents for each ammeter in front of each resistor and record the currents for each resistor in Table 1. 7. Using the voltage meter, measure the voltage for each resistor and record those voltages in Table 1. a. Remember that the voltmeter probes have to go on opposite ends of the resistor to get a reading. 4

b. If you get a negative voltage just record the absolute value. [This just means you put the positive probe (red) at the negative end of the resistor, and the negative probe (black) at the positive end of the resistor.] Setup Part 2: Resistors in Parallel 1. Use the orange button in the bottom right of your screen to reset the simulator. a. Your screen should now look like the following: 2. Near the bottom left of the screen, click on the Potential Difference symbol. 3. On the right side of the screen just below the Voltmeter & Ammeter, click the Green/Plus symbol next to Advanced. 4. In the drop-down menu for Advanced, make sure that Wire Resistivity and Battery Resistance are both set to ‘tiny’, then click the Red/Minus to close the drop-down menu. 5. In the White Box at the top right of your screen make sure “Show Current” is checked, select “Conventional”, make sure “Labels” is checked, and make sure that “Values” is checked. Procedure Part 2: Resistors in parallel 1. Build the following circuit of three resistors in parallel with each other: (You can use the plus and minus at the bottom of the left side of your screen to give yourself more room to work with if you need it.) 5

2. Set the Potential Difference (Battery) to 50.0 V, and the resistors as follows, R 1 = 10 Ohms, R 2 = 50.0 Ohms, and R 3 = 100.0 Ohms. 3. Record the currents for each resistor in Table 2. Using the voltmeter, measure the voltage for each resistor, and then record your measurements in Table 2. Setup Part 3: Resistors in a mix of series and parallel 1. Use the orange button in the bottom right of your screen to rest the simulator. a. Your screen should now look like the following: 2. Near the bottom left of the screen, click on the Potential Difference symbol. 6

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3. On the right side of the screen just below the Voltmeter & Ammeter, click the Green/Plus symbol next to Advanced. 4. In the drop-down menu for Advanced, make sure that Wire Resistivity and Battery Resistance are both set to ‘tiny’, then click the Red/Minus to close the drop-down menu. 5. In the White Box at the top right of your screen make sure “Show Current” is checked, select “Conventional”, make sure “Labels” is checked, and make sure that “Values” is checked. Procedure Part 3: Resistors in a Mix of Series and Parallel 6. Build the following circuit: (You can use the plus and minus at the bottom of the left side of your screen to give yourself more room to work with if you need it.) 7. Set the Potential Difference (Battery) to 50.0 V, and the resistors as follows, R 1 = 10 Ohms, R 2 = 25.0 Ohms, R 3 = 40.0 Ohms, and R 4 = 100.0 Ohms. 8. Record the currents for each resistor in Table 3. Using the voltmeter, measure the voltage for each resistor, and then record your measurements in Table 3. Analysis of Simple Electrical Circuits Lab Online Name: Hoang Tran 7

Course/Section: Phy-1631-011 Instructor: Joaquin Ray Duran For each of the three simple circuit boards you will need to calculate the total resistance, R eq , for the entire circuit board by using the measured resistances of each of the resistors, and the equations given to you in the theory section. Use the applied voltage for each setup as the theoretical voltage, V th , for the entire circuit board, to calculate the theoretical current, i th , for the entire circuit board. Table 1(Resistors in Series) R(Ω) i ex (A) V ex (V) i th (A) V th (V) % Error i % Error V R eq 160 0.62 100 0.625 100 0.8% 10Ω 10 0.62 6.25 0.625 6.25 0.8% 0% 50Ω 50 0.62 31.25 0.625 31.25 0.8% 0% 100Ω 100 0.62 62.50 0.625 62.50 0.8% 0% 1. Using the equations for resistors in series calculate the theoretical voltages, and currents for each of the resistors, and the entire circuit. Use the measured values of the resistance in your calculations. Then calculate the % errors. Show work. (20 points) 𝑅 𝑒𝑞 = 𝑅 1 + 𝑅 2 + 𝑅 3 = 10 + 50 + 100 = 160 Ω 𝐼 h 𝑡 = 𝐼 1 , 𝐼 2 , 𝐼 3 = 0.625 𝐴 ∆ 𝑉 𝑗 = ∆ 𝑉 1 + ∆ 𝑉 2 + ∆ 𝑉 3 = 6.25 + 31.25 + 62.50 = 100 𝑉 𝑉 1 = 𝐼 1 𝑅 1 = ( 0.625 ) ( 10 ) = 6.25 𝑉 𝑉 2 = 𝐼 2 𝑅 2 = ( 0.625 ) ( 50 ) = 31.25 𝑉 𝑉 3 = 𝐼 3 𝑅 3 = ( 0.625 ) ( 100 ) = 62.5 𝑉 % 𝐸𝑟𝑟𝑜𝑟 ( 𝐼 ) = | 0.62 − 0.625 | 0.625 ⋅ 100 = 0.8% % 𝐸𝑟𝑟𝑜𝑟 ( 𝑉 1 ) = | 6.25 − 6.25 | 6.25 ⋅ 100 = 0% % 𝐸𝑟𝑟𝑜𝑟 ( 𝑉 2 ) = | 31.25 − 31.25 | 31.25 ⋅ 100 = 0% % 𝐸𝑟𝑟𝑜𝑟 ( 𝑉 3 ) = | 62.5 − 62.5 | 62.5 ⋅ 100 = 0 % 2. According to our equations, what should be the relationship between the total current and the currents passing through each resistor? Does your data show this relationship? (5 points) 8

According to our equations for Resistors in Series, the relationship between the total current and the currents passing through each resistor is equal as they are in series. And based on our data, it agrees with the relationship. 3. According to our equations, what should be the relationship between the total voltage and the voltages passing over each resistor? Does your data show this relationship? (5 points) The relationship between the total voltage and the voltage passing over each resistor is that the total voltage should be equal to the sum of the three voltages passing over each resistor. In our data, this is true as (6.25V+31.25V+62.5V) = 100V. With 100V being the total voltage used for the experiment. Table 2(Resistors in Parallel) R(Ω) i ex (A) V ex (V) i th (A) V th (V) % Error i % Error V R eq 0.13 6.5 50 6.5 50 0% 10Ω 10 5.0 50 5.0 50 0% 0% 50Ω 50 1.0 50 1.0 50 0% 0% 100Ω 100 0.5 50 0.5 50 0% 0% 4. Using the equations for resistors in parallel calculate the theoretical voltages, and currents for each of the resistors, and the entire circuit. Use the measured values of the resistance in your calculations. Then calculate the % errors. Show work (20 points) 1 𝑅 𝑒𝑞 = ( 1 𝑅 1 + 1 𝑅 2 + 1 𝑅 3 ) = ( 1 10 + 1 50 + 1 100 ) = 0.13 Ω 𝐼 𝑡𝑜𝑡𝑎𝑙 = 𝐼 1 + 𝐼 2 + 𝐼 3 = 5 + 1 + 0.5 = 6.5 𝐴 ∆ 𝑉 h 𝑡 = ∆ 𝑉 1 + ∆ 𝑉 2 + ∆ 𝑉 3 = 50 𝑉 𝐼 1 h 𝑡 = 𝑉 Ω 1 = 50 10 = 5.0 𝐴 𝐼 2 h 𝑡 = 𝑉 Ω 2 = 50 50 = 1.0 𝐴 𝐼 3 h 𝑡 = 𝑉 Ω 3 = 50 100 = 0.5 𝐴 % 𝐸𝑟𝑟𝑜𝑟 ( 𝑉 ) = | 50 − 50 | 50 ⋅ 100 = 0% % 𝐸𝑟𝑟𝑜𝑟 ( 𝐼 𝑡 ) = | 6.5 − 6.5 | 6.5 ⋅ 100 = 0% % 𝐸𝑟𝑟𝑜𝑟 ( 𝐼 1 ) = | 5 − 5 | 5 ⋅ 100 = 0% 9

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% 𝐸𝑟𝑟𝑜𝑟 ( 𝐼 2 ) = | 1 − 1 | 1 ⋅ 100 = 0% % 𝐸𝑟𝑟𝑜𝑟 ( 𝐼 3 ) = | 0.5 − 0.5 | 0.5 ⋅ 100 = 0% 5. According to our equations what should be the relationship between the total current and the currents passing through each resistor? Does your data show this relationship? (10 points) According to our equations for Resistors in Parallel, the relationship between the total current and the current passing through each resistor should be that the total current should be a summation of all currents passing through each resistor. This is evident in the data, as (5A+1A+0.5A) = 6.5A, with 6.5 being the total current of the experiment. 6. According to our equations what should be the relationship between the total voltage and the voltages passing over each resistor? Does your data show this relationship? (10 points) According to our equations for Resistors in Parallel, the relationship between the total voltage and the voltage passing through each resistor is equal as they are in parallel. And based on our data, it agrees with the relationship. Table 3(Resistors in both Series and Parallel) R(Ω) i ex (A) V ex (V) i th (A) V th (V) % Error i % Error V R eq 63.57 0.79 50 0.79 50 0% 10Ω 10 0.79 7.87 0.79 7.87 0% 0.4% 25Ω 25 0.79 19.66 0.79 19.66 0% 0.5% 40Ω 40 0.56 22.47 0.56 22.4 0% 0.3% 100Ω 100 0.22 22.47 0.22 22.0 0% 2% 7. Using the equations for resistors in series and in parallel, calculate the theoretical voltages and currents for each of the resistors, and the entire circuit. Use the measured values of resistance in your calculations, then calculate the % errors. Show work. (20 points) 𝑅 𝑒𝑞 = 𝑅 1 + 𝑅 2 + 1 𝑅 3 + 1 𝑅 4 = ( 10 + 25 + 1 40 + 1 100 ) 21 = 63.57 Ω 𝐼 h 𝑡 = 𝑉 𝑡𝑜𝑡𝑎𝑙 𝑅 𝑒𝑞 = 50 63.57 = 0.79 𝐴 10

𝐼 1 h 𝑡 = 𝑉 1 𝑅 1 = 7.87 10 = 0.787 𝐴 ≈ 0.79 𝐴 𝐼 2 h 𝑡 = 𝑉 2 𝑅 2 = 19.66 25 = 0.786 𝐴 ≈ 0.79 𝐴 𝐼 3 h 𝑡 = 𝑉 3 𝑅 3 = 22.47 40 = 0.561 𝐴 ≈ 0.56 𝐴 𝐼 4 h 𝑡 = 𝑉 4 𝑅 4 = 22.47 100 = 0.224 𝐴 ≈ 0.22 𝐴 𝑉 1 h 𝑡 = 𝐼 1 𝑅 1 = ( 0.79 ) ( 10 ) = 7.9 𝐴 𝑉 2 h 𝑡 = 𝐼 2 𝑅 2 = ( 0.79 ) ( 25 ) = 19.75 𝐴 𝑉 3 h 𝑡 = 𝐼 3 𝑅 3 = ( 0.56 ) ( 40 ) = 22.4 𝐴 𝑉 4 h 𝑡 = 𝐼 4 𝑅 4 = ( 0.22 ) ( 100 ) = 22 𝐴 % 𝐸𝑟𝑟𝑜𝑟 ( 𝐼 1 + 2 ) = | 0.79 − 0.79 | 0.79 ⋅ 100 = 0 % % 𝐸𝑟𝑟𝑜𝑟 ( 𝐼 3 ) = | 0.56 − 0.56 | 0.56 ⋅ 100 = 0% % 𝐸𝑟𝑟𝑜𝑟 ( 𝐼 4 ) = | 0.22 − 0.22 | 0.22 ⋅ 100 = 0% % 𝐸𝑟𝑟𝑜𝑟 ( 𝑉 1 ) = | 7.87 − 7.9 | 7.87 ⋅ 100 = 0.4 % % 𝐸𝑟𝑟𝑜𝑟 ( 𝑉 2 ) = | 19.66 − 19.75 | 19.66 ⋅ 100 = 0.5% % 𝐸𝑟𝑟𝑜𝑟 ( 𝑉 3 ) = | 22.47 − 22.4 | 22.47 ⋅ 100 = 0.3% % 𝐸𝑟𝑟𝑜𝑟 ( 𝑉 4 ) = | 22.47 − 22 | 22.47 ⋅ 100 = 2% 8. Do the results of the experiment agree with theoretical predictions for resistors in series and parallel? Explain your answer. (10 points) 11

The results of the experiment do agree with the theoretical predictions for resistors in series and parallel as the results between the theoretical and experimental when performing the percent error was close to 0%, with and outlier being 𝑉 4 as the percent error was 2%. Besides that, the formulas used to calculate were very much exactly to the experiment results. 12

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Fall2023 Simple Electrical Circuits Lab Online

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