Green River Community College Ohm Law Analysis & Conclusions Sheet

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Ohm's Law Introduction: The purpose of this experiment is to verify Ohm’s Law. The equivalent resistance of series/parallel circuits is also examined. This may be performed as a single lab or two short stand-alone labs. Theory: In metals and some other materials (in particular, commercially manufactured resistors), one finds experimentally that the voltage drop, V, across the material is directly proportional to the current, I, through the material (provided the temperature remains relatively constant): Vα I which 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 Eq. (1) A resistor generally means 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 circuit like Figure 3. An equivalent resistor is a single resistor 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: Req = R1 + R2 Eq. (2) where Req is the equivalent resistance. For a parallel circuit, the resistances add as reciprocals 1/Req = 1/R1 + 1/R2 Eq. (3) A more complex circuit like Figure 3 can be handled by noting that R1 and R2 are in parallel and can be reduced to an equivalent resistance using Equation 3. That equivalent resistance is then in series with R3 and can be treated using Equation 2 to find the equivalent resistance of the entire series/parallel circuit I I I R1 = 3.3 kΩ R1 = 3.3 kΩ R1 = 3.3 kΩ R2 R2 = 1.0 kΩ R2 = 1.0 kΩ = 1.0 kΩ R3 = 1.0 kΩ Figure 1: Series Figure 2: Parallel Figure 3: Series/Parallel Figure 4: Ohm’s Law Setup Setup: 1. Take the 850-UI out of the box and set it up like you have for previous procedures. 2. Plug a red banana plug wire into the red port at the end of the 850-UI where it says “OUTPUTS” and plug a black banana plug wire into the black port next to it. 3. Plug the black banana plug wire into the left side of the 3.3kΩ resistor and the red banana plug wire into the right side of the 3.3kΩ resistor. 4. Turn on the 850-UI and start the Capstone software. 5. Click the Signal Generator in the left column of Capstone to open it. a. If the button for signal generator is not there find it by clicking on the small eye icon under the word “Tools” on the same side of the screen. 6. Under Output 1: a. Set waveform to DC b. Set DC voltage to 1V c. Set Voltage Limit to 15V d. Set the Current Limit to 1.5A e. Press the AUTO button 7. Create a table with Output Voltage (V) and Output Current (mA) values and a graph of Output Current (mA) vs Time with the mean value displaying. Make sure you are in Keep Mode. Important: The 850 Universal Interface (850-UI) 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. However, 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). Procedure: Calibration Run: 1. Unplug the red lead from the 850 Universal Interface. NOTE: The current should be zero for any voltage in an open circuit, but because of the interface we are using it will not display as zero and we must instead measure all of our values relative to this base “zero” value. 2. Click RECORD and wait about a minute until the mean Current reading stops drifting. 3. Record the mean Current value from capstone in the “Zero” Current row of your table. Record the Output Voltage on your table in the Measured Voltage row. 4. Click STOP. 5. Change the Signal Generator to 3V and repeat steps two through four. Repeat again for voltages of 6 V, 9 V, 12 V, & 15 V. 6. Set the Signal Generator back to 1 V. Experiment Run: 1. Plug the red lead back into the 850 Output 1 jack. 2. Repeat the Calibration Run section except record the values for mean Current in the Measured Current column. The True Current is the difference between the mean Current and the “Zero” Current. 3. Turn the Signal Generator OFF. Ohm's Law Voltage Setting Measured Voltage (V) “Zero” Current Value (mA) Measured Current Value (mA) True Current (mA) Calculate d Resistanc e (Ω)(RC) Actual Resistanc e (Ω)3.3kΩ+/1% (RA) % Accuracy 1 V 3 V 6 V 9 V 12 V 15 V 1.003 2.999 5.998 8.989 11.987 14.978 0.045 0.137 0.224 0.305 0.411 0.478 0.427 1.101 2.153 3.167 4.187 5.207 0.382 0.964 1.929 2.862 3.776 0.473 2.625 3.111 3.110 3.141 3.175 31.666 3.3KΩ 3.3KΩ 3.3KΩ -0.205 -0.057 -0.058 3.3KΩ 0.048 3.3KΩ 0.144 3.3KΩ 8.596 Ohm's Law – Analysis & Conclusions Sheet Analysis: Ohm’s Law Use the data from your table to create a Voltage vs Current graph in capstone 1. Click on the black triangle by the Curve Fit icon on the graph toolbar and select Linear. 2. The horizontal error bars represent the +/- 0.1 mA uncertainty in the True Current which was achieved by calibrating the system (see previous page). The uncertainty in the Voltage is much too small to show. 3. The uncertainties in the slope and intercept arise from the spread of the data points but do not include the uncertainty in the True Current. This means that the quoted uncertainties are too small. You can get a good approximation to the actual uncertainties in slope and intercept (without elaborate math) by holding a transparent ruler up to the screen (or printing off the graph) and seeing how much you can vary the slope and intercept with a straight line that still fits the data (including error bars) reasonably well. Conclusions: Ohm’s Law 1. How well does your data support Ohm’s Law? Explain fully! 2. What is the physical meaning of the slope of the Linear Fit to the data on the Ohm’s Law graph. Hint: what are the units of the slope? Circuits in Series and Parallel Equivalent Circuits Diagrams: I I I R1 = 3.3 kΩ R1 = 3.3 kΩ R1 = 3.3 kΩ R2 R2 = 1.0 kΩ R2 = 1.0 kΩ = 1.0 kΩ R3 = 1.0 kΩ Figure 1: Series Figure 5: Series Figure 2: Parallel Figure 6: Parallel Figure 3: Series/Parallel Figure 7: Series/Parallel Equivalent Resistance: Resistor Check: The resistors on the UI-5210 circuit board are accurate to within +/- 5%. This can be improved substantially if a multi-meter is available. These will generally measure resistance +/- 1%. 1. Disconnect all the wires from the circuit board. 2. Use a multi-meter to measure the resistance of resistors R2, R3, & R4 on the circuit board. Enter the values in the Resistor Check Values table, replacing the nominal values in column 2. Theory Resistance: Using Equivalent Circuits (see Theory section above) and the values for the resistors from the Resistance Check Values table, calculate the equivalent resistance for each of the three circuits shown on the previous page. Enter the values in the Theory Resistance column of the Equivalent Circuits table below. 1 2 3 Resistor Resistance (Ω) R2 3270 R3 970 R4 970 Resistor Check Values Table Circuit Theory Resistance (kΩ) 1 Series 4.3 2 Parallel 0.767 3 Series/Parallel 1.767 Equivalent Resistance Table Procedure (with setup): Equivalent Circuits 1. Click open the Signal Generator. 2. Under Output 1: a. Set waveform to DC b. Set DC voltage to 15 V c. Set Voltage Limit to 15 V and the Current Limit to 1.5 A d. Press the ON button and close the panel Calibration Check: With nothing attached to Output 1 of the 850 Universal Interface, click RECORD and record until the mean Current stops changing (about a minute). Record the value of the mean Current in the Zero Current column of the Equivalent Circuits table. Enter the same value in each of the three rows. Record the Output Voltage on your table in all 3 rows. 3. Set up the circuit shown in Figures 1 & 5 on the previous page. 4. Click Preview and wait until the Average Current stops changing. Record the value of the mean Current in the Avg. Current column of the Equivalent Circuits table. “True Cur” = “Avg. Current” – “Zero Current”. 5. Using the “True Current” values and Equation 1 from Theory, calculate the total resistance (experimental) of the circuit. Enter the value in the Experimental Resistance column of the table. 6. Set up the circuit shown in Figures 2 & 6 on the previous page. Repeat steps 4 & 5. 7. Set up the circuit shown in Figures 3 & 7 on the previous page. Repeat steps 4 & 5. Clean Up: 1. Turn off the 850-UI and unplug all wires and cords. Put the 850-UI back in the box according to the labeled picture inside the box lid. Separate the two parts of the power cord. **Do not wrap the cord around the power supply** 2. Put the banana plug wires back in the bag they came out of. **Do not put anything other than the banana plug wires in the bag** 3. Put the multi-meter and probes back into the box. **Do not put banana plug wires in the box. 4. Put the LRC board back in the appropriately labeled bag that it came out of. 5. Neatly place all equipment near the center of the row. Circuits in Series and Parallel – Data and Questions Sheet Output Voltage (should be ~15 V) (V) Zero Current (mA) Avg. Current (mA) True Current (mA) Experimental Resistance (kΩ) 14.979 0.555 4.197 3.642 4.113 14.979 0.555 21.104 20.549 0.728 14.979 0.555 9.443 8.999 1.685 Conclusions: Equivalent Circuits 1. How well does the method of equivalent circuits work? QUESTIONS PART B: Ohm’s Law 1. How could this experiment be performed with an ammeter and batteries instead of the 850 Interface? 2. Make a diagram of the circuit. Include the direction of charge flow. Represent positive charges with a “+.” Represent negative charges with a “-.” 3. What is the physical meaning of the slope for the Voltage vs. Current graphs? 4. What is the physical meaning of the vertical intercept for the Voltage vs. Current graphs? 5. Starting with y = mx + b, write an equation that represents the relationship between Voltage vs. Current for the resistors. Don't forget to include units on all numbers. 6. Why is the voltage-current relationship different for a light bulb vs. a resistor?
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