PHYS204L Physics Lab Ohm’s Law & RC Time Constant

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Name:_______________________ Section:_________ Graphing and Excel Homework These exercises contain examples of data you will encounter during Phys204L/206L. If some terms are unfamiliar right now, that’s fine. The purpose of this homework is to practice using doing linear fits with Microsoft Excel (or Google Sheets) and to gain experience with interpreting best-fit equations. You may use Microsoft Excel or Google Sheets to do the fit. NOTE: If you need help creating a scatter plot and inserting a linear trendline, use google to find a tutorial, ask a peer or help, or feel free to see me during my office hours. Instructions: Complete exercises 1 and 2. Follow all steps for each exercise. Record answers where instructed to. Staple all graphs to this assignment. Exercise 1: Ohm’s Law In this exercise you will practice plotting data, adding a linear trendline and interpreting the data. According to Ohm’s Law, the potential difference ΔV is related to the current I by the equation Δ𝑉 = 𝐼𝑅 (Eq 1) where R stands for resistance. Potential difference is measured in the unit volts, current in amperes (or amps) and resistance in ohms (using the Greek symbol omega: Ω). Part A: Making a Scatter Plot 1. Using your favorite spreadsheet program, make a scatter plot of the following dataset: Use current as the independent (x) variable and potential difference as the dependent (y) variable. Current, I (A) Potential Difference, V (V) 0.12 1.3 0.25 2.8 0.30 3.4 0.45 4.9 0.52 5.7 2. Give your graph the title “Ohm’s Law.” 3. Label the x and y axes with the appropriate data labels. Part B: Linear Regression 1. Fit a linear trendline to the data. 2. Display the equation on your graph. 3. Write the equation from the linear trendline in the space below: 4. Save and print your graph with the scatterplot, trendline, and equation. Attach it to this homework. Part C: Interpretation 1. Reference the equation for Ohm’s Law (Eq 1). Which of the variables represents the slope of the graph of Current vs Potential Difference? Explain your reasoning. 2. Use the equation of the linear trendline to determine the experimental value of the resistance. 3. Your instructor informs you that the actual (theoretical) value of the resistance in this lab setup was 11 Ω. Calculate the percent error of the experimental value in the space below. Exercise 2: The RC Time Constant Most physics phenomena do not follow a linear equation. In these cases, there are two options: you can fit a more complicated equation to the data or you can “linearize” the data and then fit a linear trendline as previously. In this exercise you will gain experience in fitting a linear trendline to data that is (initially) not linear. This semester you will encounter a special circuit called and “RC Circuit.” Here the potential difference across a circuit element called a capacitor changed with time. The theoretical equation that relates the voltage across the capacitor in this circuit to time is 𝑉 = 𝑉0 𝑒 −𝑡/τ (Eq. 2) V is the potential difference at time t. V0 is the potential difference across the capacitor at t=0 and τ is a characteristic of the circuit called the time constant. Part A: Scatter Plot and Linear Trendline Below is a data table of the measured potential difference (V) across the capacitor as a function of time. Time (s) 5 15 30 40 60 75 90 Potential Linearized Potential Difference Difference (V) ln(V) 1.5 0.92 0.39 0.24 0.083 0.037 0.02 1. Create a scatter plot displaying time (x axis) vs potential difference (y axis). 2. Do the data appear to follow a linear pattern? 3. Now calculate the natural log of the potential difference for each time period to fill in the righthand column in chart above. 4. Create a scatter plot of time (x axis) vs ln(V) (y axis). 5. Do the data appear to follow a linear pattern? 6. Generate a linear trendline for your new scatter plot of time vs ln(V). 7. Insert the equation of the trendline, add an appropriate title and axes labels. 8. Save and print the graph with the trendline and attach to this assignment. Part B: Interpretation The goal in this section is to use the linear equation generated by experimental data to calculate an experimental value for the time constant τ. Follow the steps below and show all work in the space to the left of the steps. 1. Begin with the theoretical equation (Eq. 2). 2. Take the natural log of both sides and simplify the result (hint: remember ln(𝐴𝐵) = ln 𝐴 + ln 𝐵). 3. Arrange the result of the previous step so your equation resembles a linear equation in the form 𝑦 = 𝑚𝑥 + 𝑏. 4. Use this new theoretical equation (that you have linearized in steps 1-3) to interpret the slope and y intercept of your experimental equation (found using Excel). Write your answer below. 5. Use the results of step 4 to calculate 𝑉0 and τ. 6. Your instructor informs you that the theoretical value for τ=19 s. Calculate the percent error of the experimental value in the space below.

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