PHYS182B_196L_LAB4_Ohms_Law(1)(1)

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PHYS182B/196L LAB 4 – Ohm’s Law Page 1 of 10 Lab 4: Ohm's Law San Diego State University Department of Physics Physics 182B/196L Name: Partner(s): Introduction: The purpose of this experiment is to verify Ohm’s Law. The equivalent resistance of series/parallel circuits is also examined. This lab builds upon the previous in which we analyzed the resistance of different metals as a function of the amount of material present (varying the length). We will analyze electric circuits with components that have a fixed resistance placed in various combinations and determine how those combinations effect the voltage and current measurements. Theory: As a recap, we previously saw that in metals (this is also true for other materials, especially commercially manufactured resistors), one finds experimentally that the voltage drop, V, across the metal is directly proportional to the current, I, through the material (provided the temperature remains relatively constant): V I . ∝ This is referred to as Ohm’s Law. It is convenient to define a proportionality constant called the resistance (unit: Ohm [Ω] = V/A) such that V = IR. (1) A resistor generally refers to a device that obeys Ohm’s Law (many devices do not) and has a resistance R. Two (or more) resistors can be connected in series (as in Figure 1), or in parallel (as in Figure 2). Resistors could also be connected in a series/parallel combination circuit like Figure 3. Resistors connected in series can be thought of as connected head-to-tail, whereas parallel Written by Chuck Hunt, modified by Alex Bates

PHYS182B/196L LAB 4 – Ohm’s Law Page 2 of 10 connections are head-to-head and separately tail to tail. An equivalent resistor is a single resistor (generally a theoretical construct) that could replace a more complex circuit and produce the same total current when the same total voltage is applied. For a series circuit, the resistances are additive: R eq = R 1 + R 2 (2) where R eq is the equivalent resistance. For a parallel circuit, the resistances add as reciprocals 1 R eq = 1 R 1 + 1 R 2 (3) A more complex circuit like Figure 3 can be handled by noting that R 1 and R 2 are in parallel and can be reduced to an equivalent resistance using Equation 3. That equivalent resistance is then in series with R 3 and can be treated using Equation 2 to find the equivalent resistance of the entire series/parallel circuit. Figure 1: Series Figure 2: Parallel Figure 3: Series/Parallel Written by Chuck Hunt, modified by Alex Bates

PHYS182B/196L LAB 4 – Ohm’s Law Page 3 of 10 Ohm’s Law Setup/Procedure: 1. Press the power button on the 850 Universal Interface to turn it on. Open PASCO Capstone. Click on “File” and “Save Experiment As…” as shown below. Give your experiment a name then save it. Save your data frequently throughout the course of the experiment in case the software crashes 2. Set up the circuit shown in Figure 4 using the 3.3 kΩ resistor. 3. Click on “Hardware Setup”, then click on the yellow circle around “Output 1” and select the Output Voltage Current Sensor. Set the sample rate of all the sensors to 100 Hz. Set the Common Sample Rate to 100 Hz. See below for some screenshots describing how to do this step. Written by Chuck Hunt, modified by Alex Bates Figure 4: Ohm’s Law Setup

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PHYS182B/196L LAB 4 – Ohm’s Law Page 4 of 10 The image on the top left shows how to connect the Output Voltage- Current Sensor. The image on the bottom left shows where to change the sample rate. 4. Click open the Signal Generator at the left of the screen. Set Output 1 for a DC Waveform with a DC Voltage of 1 V. Click On. 5. Create a table with four columns: Create user-entered data sets called “Voltage” with units of V, “Zero Current” with units of mA, and “Measured Current” with units of mA. Leave the fourth column blank for now. 6. Open the Calculator and create the following calculations: Written by Chuck Hunt, modified by Alex Bates

PHYS182B/196L LAB 4 – Ohm’s Law Page 5 of 10 Iavg = avg([Output Current])*1000 Units of mA True Current = [Measured Current]-[Zero Current] Units of mA 7. In the fourth column of your table, select the “True Current” calculation you created in step 6. 8. Create two digits displays and select Output Voltage and the Iavg . 9. The 850 Universal Interface can read currents with a resolution of about 0.01 mA. However, this is a small current and the instantaneous value fluctuates quite a bit. Fortunately, by taking an average over several seconds, we get a value with a precision of 0.01-0.02 mA. The noise can produce a systematic error up to about 5 mA with a variation across the range of almost 1 mA, so we must calibrate the system to get accurate values (±0.1 mA due to variation in zero noise). 10. Calibration Run: Unplug the red cable from the 850 Universal Interface. The current should now be zero for all voltage, but as you will see in a moment, it is not. Click RECORD. Wait a few seconds until the Iavg reading stops drifting. Record the Iavg value in the Zero Current column of Table I and record the Output Voltage value in the Voltage column of Table 1. Click STOP. 11. Change the Signal Generator to 3V and record Iavg and Output Voltage. Repeat again for voltages of 6 V, 9 V, 12 V, & 15 V. 12. Set the Signal Generator back to 1 V. 13. Experiment Run: Plug the red lead back into the 850 Output 1 jack. Repeat data collection for 1 V, 3 V, 6 V, 9 V, 12 V, and 15 V except record the values for Iavg in the Measured Current column. The True Current is the difference between the Measured Current and the Zero Current. This column should populate automatically. 14. Turn off the Signal Generator and save your data. Written by Chuck Hunt, modified by Alex Bates

PHYS182B/196L LAB 4 – Ohm’s Law Page 6 of 10 Analysis: Ohm’s Law 1. Create a graph of Voltage (user-entered data) vs. True Current 2. Select a Linear fit, as shown below. A box should appear on your graph showing you the slope of your line. Ohm’s Law Conclusions 1. Paste an image of your Ohm’s Law graph below. PASTE IMAGE HERE 2. Paste an image of Table I below. PASTE IMAGE HERE 3. Restate Ohm’s Law using your own words. Explain how your data supports Ohm’s Law. Written by Chuck Hunt, modified by Alex Bates

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PHYS182B/196L LAB 4 – Ohm’s Law Page 7 of 10 4. What physical quantity does the slope of your Ohm’s Law graph represent? Compare your slope to the theoretical value of this physical quantity by calculating the percent difference: (|Experimental - Theoretical|/Theoretical)*100% Written by Chuck Hunt, modified by Alex Bates

PHYS182B/196L LAB 4 – Ohm’s Law Page 8 of 10 Equivalent Resistance Setup: Equivalent Circuits Diagrams: Figure 1: Series Figure 2: Parallel Figure 3: Series/Parallel Figure 5: Series Figure 6: Parallel Figure 7: Series/Parallel 1. Open a new page in Capstone. 2. Create the two tables shown below: “Resistor”, “Resistance”, “Circuit”, and “Theory Written by Chuck Hunt, modified by Alex Bates

PHYS182B/196L LAB 4 – Ohm’s Law Page 9 of 10 Resistance” are user-entered data sets. 3. Theory Resistance: Using the rules for Equivalent Circuits discussed in the Theory section and the values for the resistors from Table II, calculate the equivalent resistance for each of the three circuits shown on the previous page. Both you and your lab partner should perform these calculations so you can double-check each other’s work . Enter the values in the Theory Resistance column of Table III. Equivalent Resistance Procedure: 1. Create a new table: Select “Circuit” for the first column. Except for the calculations “True Cur” and “% Diff”, the rest of the columns are all user-entered data sets. Open the calculator and make the calculations: True Cur = [Av. Current]-[Zero Cur.] Units of mA % Diff=100*([Exp. Resist]-[Theory Resistance])/[Theory Resistance] 2. Click open the Signal Generator. Set Output 1 for a DC waveform with a DC Voltage of 15 V. Click On. Close the Signal Generator panel. 3. Calibrate Check : With nothing attached to Output 1 of the 850 Universal Interface, click RECORD and record until the Average Current stops changing (a few seconds). Record the Written by Chuck Hunt, modified by Alex Bates

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PHYS182B/196L LAB 4 – Ohm’s Law Page 10 of 10 value of the Average Current in the Zero Cur. column of the Table IV. Enter the same value in each of the three rows. If the Output 1 Voltage reading is different from 15.00 V, enter the value in column 1, replacing the 15.00 values. 4. Set up the circuit shown in Figures 1 & 5. 5. Click RECORD and record until the Average Current stops changing. Record the value of the Average Current in the Av. Current column of Table IV. “True Cur” = “Av. Current” – “Zero Current”. 6. Using the “True Cur” values and Equation 1 from Theory, calculate the total resistance (experimental) of the circuit. Enter the value in the Exp. Resist. column of the table. 7. Set up the circuit shown in Figures 2 & 6. Repeat steps 5 & 6. 8. Set up the circuit shown in Figures 3 & 7. Repeat steps 5 & 6. Equivalent Circuits Conclusions: 1. Paste images of your data tables below. PASTE IMAGES HERE 2. State the percent differences between your calculated equivalent resistances and your experimentally measured resistances. How closely do your experimental values compare to your calculated values? Discuss any potential sources of error in the experiment. Written by Chuck Hunt, modified by Alex Bates

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