IB Physics Lab - Resistance

paths.  There are two formulas that are used in this lab:  1)  Equivalent resistance in series circuits =In series circuits, the equivalent resistance (total resistance) is determined by simply adding all the resistors in that circuit.      2)  Equivalent resistance in parallel circuits = In parallel circuits, the equivalent resistance is determined by adding the reciprocals of each resistor and then taking the reciprocal of the sum.ObjectiveThe objective of this lab is to determine how the equivalent resistance of a collection of resistors in series or parallel depends on the individual resistors.HypothesisI believe that the theoretical equivalent resistance of a series circuit and a parallel circuit will always be slightly more than the experimental equivalent resistance. I also believe that when more resistors are added in a circuit, either series or parallel, the percent error will increase.   MaterialsResistorsBreadboardMultimeterProcedure1.   First, we obtained several different resistors, a breadboard, and a multimeter.2.  Then we made 5 different series circuits with different combinations of resistors.3.  Then we calculated the theoretical resistance of each of them and measured the actual resistance using the multimeter.  4.  Then we repeated steps 2 and 3 but with parallel circuits.    Data PointsTrialsResistorsTheoreticalExperimentalPercent Error1st1KΩ (x3)3.0KΩ2.96KΩ-1.333%2nd2KΩ (x1)4.0KΩ3.94KΩ-1.5%1KΩ (x2)3rd220Ω (x1)2.22KΩ2.19KΩ-1.351%1KΩ (x2)4th1KΩ (x1)1.69KΩ1.67KΩ-1.183%220Ω (x1)470Ω (x1)5th 220Ω (x1)1.16KΩ1.15KΩ-0.869%470Ω (x2)TrialsResistorsTheoreticalExperimentalPercent Error1st1KΩ (x1)69.7KΩ69.8KΩ0.14%150Ω (x2)2nd1KΩ (x1)94.4KΩ94.0KΩ-0.42%220Ω (x2)2KΩ (x1)3rd220Ω (x2)89.1KΩ88.7KΩ-0.45%470Ω (x1)4th220Ω (x1)72.3KΩ72.0KΩ-0.41%470Ω (x1)150Ω (x1)2kΩ (x1)5th220Ω (x1)62.6KΩ62.5KΩ-0.16%470Ω (x2)150Ω (x2)2kΩ (x1)GraphsAnalysis To calculate the theoretical data we used the series and parallel resistance formulas. TrialsResistorsTheoreticalExperimentalPercent Error1st1KΩ (x3)3.0KΩ2.96KΩ-1.333%Ex. Trial 1 for Series CircuitWe know that the resistance formula for series circuits is Req = R1+R2+R3+…RnIn our case, we can use this formula:  Req = R1+R2+R3 , because there are only three resistors.So Req = 1KΩ + 1KΩ + 1KΩ = 3KΩ Then to find the % error we can use this formula:  ((experimental value – theoretical value) / (theoretical value)) X 100So ((2.96KΩ - 3.0KΩ) / (3.0KΩ)) X 100 = -1.333%Ex. Trial 1 for Parallel Circuit TrialsResistorsTheoreticalExperimentalPercent Error1st1KΩ (x1)150Ω (x2)69.7KΩ69.8KΩ0.14%We know that the resistance formula for parallel circuits isIn our case, we can use this formula:                                                               1/Req = 1/R1 + 1/ R2 + 1/ R3So 1/Req = 1/ 1000Ω + 1/150Ω + 1/150Ω      1/Req  = 0.0143         Req = (0.0143)ˆ-1 = 69.7ΩOnce again, we can use this formula to find the % error:  ((experimental value – theoretical value) / (theoretical value)) X 100So ((69.8KΩ - 67.7KΩ) / (69.7KΩ)) X 100 = 0.14%Error AnalysisIn this type of experiment, human error is unlikely, but still possible.  The only reason that the experimental data wasn’t exactly matched with the theoretical data would be because each resistor has a tolerance.  All the resistors we used had a ±5% tolerance, which seems right because all the different combinations of resistors didn’t have a percent error greater than1.5% or less than -1.351%. There are virtually no anomalies in the series circuit graph, as you can see in the graph that all the pairs are nearly equal.There are also no anomalies in the parallel circuit graph, as you can hardly see the theoretical line (blue) under the experimental line (red).    Conclusion I have learned several things in this lab:That the experimental total resistance of either a series or parallel circuit will always be slightly less than the theoretical total resistance of that circuit, most likely due to the tolerance of the resistor(s).  There was only one group of data that didn’t follow this trend:  Trial 1 of Parallel Circuits, where there was a positive 0.14% error. I also learned that the % error tends to increase when more resistors are added.  This makes sense because each resistor has its own tolerance, so when you add more resistors to a circuit, you also have to take the individual tolerance values into account.    The two formulas that were used in this lab and stated in the introduction proved Ohm’s law effective, as the resistance formulas are based on Ohm’s law.  My initial hypotheses were proven correct as they were that the theoretical equivalent resistance of a series circuit and a parallel circuit will always be slightly more than the experimental equivalent resistance and that when more resistors are added in a circuit, both in series and in parallel, the percent error will increase.  This all can be clearly seen on the data tables.  EvaluationThis is the type of experiment that’s very valid.  This is due to the fact that the properties of electricity are constant and that we used precise measuring equipment.    This experiment virtually doesn’t need any improvements or changes as it achieves it purpose in a quick, efficient way.In my opinion, a good further assignment would be to research certain electronically appliances or devices and figure out the resistance of each of them, and find out why that specific resistance is applied to that appliance/device.