phys 2 lab 5

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Simple Resistor Circuit Aaron Besa Lab Due: June 21, 2023 Prof. Shylnov Physics 221-L01 TA: Alireza Alipour Introduction To understand the principles of this lab we must first understand Ohm’s law which is described in the formula below: V=IR Where V is the voltage, I is the current, and R is the resistance of the circuit. The differences in voltage drops depends on which type of resistor is used. If the resistors are in series and share one node, that means that the total voltage drop can be calculated as the sum of every resistor voltage added together as seen below. When in series, the current is held constant. V = V 1 + V 2 + … V n This Ohm’s law also applies to current, but in the opposite effect. When resistors are in series as explained above, the current is the same; however, when the resistors are in parallel, the total current can be calculated as a sum of each current from each resistor. I = I 1 + I 2 + … I n Lastly, we can calculate the total resistance of resistors in series by adding them together similarly to finding the voltage differences. R = R 1 + R 2 + … R n After understanding the fundamental principles of Ohm’s Law we can now talk about the experiment approach we did to test and prove Ohm’s Law. Experiment Methods This experiment had three parts to it, with the first being putting a set of three resistors in series, the second part putting them in parallel, and the third part combining both. First before starting the actual parts of the experiment, we measured the resistance of each of the 4 resistors and recorded the color codes of each to calculate their theoretical resistance.

For part 1a of the experiment, we measured the values and the voltages of 3 resistors. This was done by placing an ammeter parallel to the resistors that were all placed in series. This shows that the resistors have the same current, but different voltage values since they are in parallel. For part 1b, we put the 4 resistors in parallel. This makes it so the voltage drop can be calculated by adding all the voltage drops of each resistor together to get V total. Then we measured the current through each resistor while voltage is constant. For part 2, we put resistor 1 in series with a combination of resistor 2 and 3 in parallel. Here we measured the voltage and the current of every resistor and matched our measurements using the equations above making sure that the total voltage and total current is the same when you add the individual resistors’ voltage and current together. Results and Discussion Part 1a: 1. Resistor Color Theoretical Resistance (Ohms) Exp Resistance (Ohms) percent error (%) voltage (V) amperage (A) R1 Red Violet Brown Gold 270 +/- 5% 268 0.740740740 7 1.41 0.005 R2 Green Blue Brown Gold 560 +/- 5% 550 1.785714286 2.88 0.005 R3 Brown Brown Red Gold 1100 +/- 5% 1106 0.545454545 5 5.72 0.005 R4 orange orange red silver 3300 +/- 10% 3600 9.090909091 - - 2. 𝐼𝑅 = 𝐼 1 𝑅 1+ 𝐼 2 𝑅 2+ 𝐼 3 𝑅 3 𝑅 = 𝐼 1 𝑅 1+ 𝐼 2 𝑅 2+ 𝐼 3 𝑅 3 𝐼 I = I1 = I2 = I3, so R = I(R1+R2+R3)/I The Is cancels, and Rtot = 268 +550 +1106= 1924 Ω for the 3 resistors. 3. As seen in the percent error calculations, the error is below the expected error in our theoretical calculations using Ohm’s law. This shows that even though there are experimental errors such as breadboard issues, slight differences in recording voltage or ohms due to equipment, there is still a consistency with our data and it isn’t to the point where our data is inaccurate since it falls below the percentage error.

4. We did not use resistor 4 because the equipment cannot reach the low value to measure the very small current value. With all the 4 resistors, the current would be so small that it would not be read by the ammeter with the scale of .005. This is proven below: 𝐼 = 10 270 + 560 + 1100 + 3300 = . 0019𝐴 Part 1b: 1. resistor voltage (v) amperage(A) theoretical resistance experimental resistance from eq 1 percent error (%) R1 10.06 0.036 270 +/- 5% 279.4444444 3.497942387 R2 10.06 0.017 560 +/- 5% 591.7647059 5.672268908 R3 10.06 0.008 1100 +/- 5% 1257.5 14.31818182 R4 10.06 0.003 3300 +/- 10% 3353.333333 1.616161616 2. 𝐼𝑡𝑜𝑡𝑎𝑙 = 𝐼 1+ 𝐼 2+ 𝐼 3+ 𝐼 4= .036 + .017 + .008 + .003 = .064 A Vtotal = 10.06V Reffective = V/Itot = 10.06/.064 = 157 𝛺 3. 1/ 𝑅𝑒𝑞 = 1 280 + 1 592 + 1 1258 + 1 3353 = . 006353 = . 006353 −1 = 157. 4𝛺 The percent error between half of the resistor measured values are below the required percentage meaning the results are accurate, but for resistor 2 and 3, the percent error was over. This shows that our data may be inaccurate. This is probably due to many experimental errors such as our voltage being higher than 10 volts or even equipment malfunctioning in measuring. We found that we had to replace our DMM and some of the measuring instruments because the values that we read were too inaccurate. Part 2: 1. Resistor Volatage (V) Amperage (A) R1 4.25 0.015 R2 5.78 0.01 R3 5.78 0.005 total 10.05 0.015

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