 # Series and Parallel Resistive Circuits Given two resistors: R1 = ...

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Series and Parallel Resistive Circuits Given two resistors: R1 = 120 W and R1 = 500 W Series Combination: theoretically the total resistance RTotal = R1 + R2 = 120 + 500 W = 620 W Parallel Combination: theoretically the total resistance ! "#\$%&' = ! "* + ! ", → �/0123 = "*×", "*5 ", = !678×9778 !67859778 = 97Ω Experimentally, we can measure the resistance by using Ohm’s Law �=>? = @ A Ohm’s Law Where V is voltage in volts (V), and I current in Ampere (A). 1 @ B = 1 W. Below is a table for experimental measured current and voltage data in a series and parallel cases. Use Ohm’s Law to calculate the experimental resistance. Series Case: For this experiment the two resistors are: R1 = 390.0 W and R2 = 250.0 W RTotal = R1 + R2 = ________[_____] V[v] I[A] * R[W ] = @ A 3.06 5.00 x 10-3 612.0 3.17 5.00 x 10-3 6.75 10.0 x 10-3 10.06 15.0 x 10-3 13.45 25.0 x 10-3 16.61 25.0 x 10-3 19.67 30.0 x 10-3 22.68 35.0 x 10-3 Rexp = Ravrg *throw out largest and smallest outliers to calculate average, standard deviation, uncertainty, and percent variability (i.e., Use only five R values for your average, standard deviation, etc.) 1. Rexp = Ravrg = _______________[_____] 2. Standard deviation of Rexp (SD)= ___________[_____] 3. % Variability of Rexp = CD "&EFG × 100 = ________[_____] 4. % difference = J"#\$%&'K "&EFGJ "#\$%&' × 100 = _________[_____] Parallel Case: For this experiment the two resistors are: R1 = 510.0 W and R2 = 390.0 W RTotal = �/0123 = "*×", "*5 ", = ________[_____] V[v] I[A] * R[W ] = @ A 1.00 5.0 x 10-3 200.0 1.04 5.0 x 10-3 2.22 10.0 x 10-3 3.37 15.0 x 10-3 4.49 20.0 x 10-3 5.62 25.0 x 10-3 6.63 30.0 x 10-3 7.76 35.0 x 10-3 Rexp = Ravrg *throw out largest and smallest outliers to calculate average, standard deviation, uncertainty, and percent variability (i.e., Use only five R values for your average, standard deviation, etc.) 1. Rexp = Ravrg = _______________[_____] 2. Standard deviation of Rexp (SD)= ___________[_____] 3. % Variability of Rexp = CD "&EFG × 100 = ________[_____] 4. % difference = J"%\$%&'K "&EFGJ "#\$%&' × 100 = _________[_____] Questions/Conclusions: 1. Can you say anything about how accurate your values for the total resistance for the Series and Parallel cases? If so, discuss how accurate they are using the appropriate values from the data. If not, discuss why not. 2. Can you say anything about how precise your values for the total resistance for the Series and Parallel cases? If so, discuss how precise they are using the appropriate values from the data. If not, discuss why not. 3. For the series and parallel cases, does your experiment support the theory for how resistors combine? Explain why you think so use ininformation/numbers from the data. 4. For the Series and Parallel, is the theoretical value of the total resistance equal to the experimental total resistance within experimental uncertainty? Show work indicating if they do, or do not, overlap for each case.

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