Student Name Title of Experiment: Ohm?s Law Section # Day and time of lab Physics 261 Lab Partner list of names Date of Report (date turned into instructor) Instructor?s Name Abstract: Experimental data was collected for Voltage and Current in a single loop resistive circuit to demonstrate the validity of Ohm?s Law. Voltage was varied manualy and recorded as wel as the asociated change in current. Resistance was calculated using Ohm?s Law and compared to the known resistance of the simple circuit. The calculated resistance values matched within wel within the nominal resistance range provided by the manufacturer and the fited graphical value of resistance. Introduction: Ohm?s Law is an empirical formula that relates the voltage drop across a resistor to the current through the resistor. Specificaly, if I (the current), and V (the voltage drop across the resistor) V ? I The proportionality constant is caled the resistance, R, so Ohm?s Law is writen as V = I R. Experiment: The validity of the equation above was studied by making measurements of V and I for a simple loop circuit. The circuit consisted of a voltage source (with a digital voltmeter atached across its inputs), a resistor, and a digital ameter as shown in Figure 1. These voltage and current values were plotted V vs. I. A linear trendline was used to determine the experimental value of the resistance, specificaly the slope of a linear fit. This value was compared to the nominal value of the resistance. Also, resistance was calculated for each data point with asociated uncertainty and compared to the nominal value of resistance. The y-intercept of the linear fit was also examined as it should be equal to zero. This is clearly sen in the rewriting of Ohm?s law as V = IR + 0. Figure 1: Circuit Diagram Insert circuit diagram here Data and Analysis: The following are uncertainties for the resistor and multimeters used. ? The resistor used was 10,000 ohms. It had a gold acuracy band that indicates a tolerance or uncertainty of ± 5%. ? The manufacturer?s provided value for the uncertainty of the voltmeter was given as ? ± 1% for the dial range 2-20Volts. ? The manufacturer?s provided value for the uncertainty of the ameter was given as ? ± 2% for the dial range 20-200mA. Data recorded by experimenters is shown in table 1. The voltage was changed manualy and the resulting change in the current was recorded. Table 1: Table of Curent and Voltage data I (A) sigma I (A) V (V) sigma V (V) 1.62E-04 3.24E-06 1.69 1.69E-02 2.4E-04 4.8E-06 2.54 2.54E-02 2.98E-04 5.96E-06 3.10 3.10E-02 3.95E-04 7.90E-06 4.1 4.1E-02 4.79E-04 9.58E-06 4.98 4.98E-02 5.9E-04 1.20E-05 6.23 6.23E-02 6.85E-04 1.37E-05 7.13 7.13E-02 7.75E-04 1.5E-05 8.06 8.06E-02 8.89E-04 1.78E-05 9.25 9.25E-02 1.08E-03 2.16E-05 1.26 1.13E-01 1.27E-03 2.54E-05 13.24 1.32E-01 1.4E-03 2.8E-05 15.0 1.50E-01 1.58E-03 3.16E-05 16.42 1.64E-01 1.76E-03 3.52E-05 18.28 1.83E-01 1.86E-03 3.72E-05 19.30 1.93E-01 The nominal value of the resistor is R = 10,000 ± 500 ohms Thus, the resistor value by manufacturer?s tolerance is from 9,500 ohms to 10,500 ohms. The equation R = V/I was used to solve for resistance values. Uncertainty was propagated using the equation: sigma R = sqrt(1/I)^2*sigmaV^2 + (-V/I^2)^2*sigmaI^2) in Excel, the results are in the second column of table 2. Table 2: Calculated values of Resistance with associated uncertainty R (Ohms) sigma R (ohms) 10432 23 10410 23 10403 23 10405 23 10397 232 10401 23 10409 23 R (Ohms) sigma R (ohms) 1040 23 10405 23 10426 23 10425 23 10417 23 10392 232 10386 232 10376 232 A graph was made in Excel and using the trendline fit, a slope was obtained. It is noted that the graph is linear verifying the proportionality of voltage and current in a simple resistive circuit. Graph 1: Voltage vs. Curent Results: Note: The graph theoreticaly should have had a zero intercept. Notice that although the intercept is not zero, it is relatively smal (les than 1%) when compared to the values of voltage that range from 1.69 to 19.30 volts. Here it should be noted that the trendline linear fit routine in Excel does not take into acount the uncertainty in voltage or current. Resistance values: Note: The calculated resistance was obtained by taking the average and average uncertainty of the calculated resistance values. Here the average value is simply the sum of the values divided by the number of measurements. The uncertainty value is determined by asuming the uncertainty values of the resistance are equal even though the values fluctuated betwen 233 and 232 ohms. The value of 232.5 ohms was used as a constant uncertainty value for each measurement of resistance. Since the value of uncertainty is taken to be equal for each measurement, determining the uncertainty of the average of the resistance values is simply ! " avg = " R N as shown in the introductory homework for physics 261. Table 3: Review of Resistance Values from Experiment Nominal Resistance (Ohms) Graph Resistance (Ohms) Calculated Resistance (Ohms) 10,000 ± 500 10,389 10,406 ± 62 The graphical resistance value is within the uncertainty of both the nominal and calculated values of the resistances. Therefore, al values of resistances agre. It is worth noting again that the graphical uncertainty omited any uncertainty in either the voltage or current and therefore did not supply a zero y-intercept value. If the uncertainty of the ameter values are ignored, one may use the least square fit algorithm supplied under Resources on the Physics 261 website. This wil calculate the slope (the resistance) with asociated uncertainty taking the uncertainty of the voltage values into acount, se Sample Calculations for details. Using this algorithm the following values were obtained Slope = Resistance = 10398 ± 1774 ohms y-intercept = 0.000413 ± 0.00304 volts The above additional analysis indicates that even without taking the uncertainty of the current into consideration that the y-intercept value with asociated uncertainty easily encompases the predicted zero value. Discusion: The validity of Ohm?s Law as demonstrated. Predictions matched nominal values as shown in Table 3, the graph of voltage vs. current, and subsequent fiting analysis presented above. Al resistance values obtained were within the nominal value?s uncertainty range. Improvement could be sen in analysis with the addition of current uncertainties in the determination of the slope and y-intercept of the least squares fit analysis. References: Physics 261 Laboratory online manual: Ohm?s Law Giancoli Physics text used in Physics 260 lecture Atached to this report would be an Appendix with hand-writen sample calculations mary ewell Microsoft Word - sample_ohms.doc
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