LU6_Resistors

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Name ______________________ Class Section ________ Date _____________ PHY 202 – Laboratory LABORATORY 6: RESISTORS Objectives:  Explain the difference between resistance and resistivity.  Predict how geometry and resistivity affect the resistance of a resistor.  Verify Ohm’s Law. Materials Required:  Computer Computer with Excel and access to Resistance in a Wire and Battery Resistor Circuit simulations: https://phet.colorado.edu/sims/html/resistance-in-a-wire/ latest/resistance-in-a-wire_en.html http://phet.colorado.edu/en/simulation/battery-resistor-circuit Software Requirements: Windows Macintosh Linux Microsoft Windows XP/Vista/7/8.1/10, latest version of Java OS X 10.9.5 or later, latest version of Java Latest version of Java Introduction: The resistor is an electrical component to create resistance in the flow of electric current. Resistors are found in almost all electrical networks and electronic circuits. If the resistance is constant over a considerable range of voltage, the behavior of the resistor is dictated by the relationship specified by Ohm's law: V = I R Ohm's law states that the voltage ( V ) across a resistor is proportional to the current ( I ), where the constant of proportionality is the resistance ( R ). The ohm (symbol: Ω) is the SI unit of electrical resistance. An ohm is equivalent to a volt per ampere. The electrical resistance of a wire is greater for a longer wire, less for a wire of larger cross-sectional area, and depends upon the material out of which the wire is made. 1

Experimentally, the dependence upon these properties is expressed as: R = ρ l A The factor in the resistance which takes into account the nature of the material is the resistivity, and it is it is temperature dependent. The electrical resistivity ρ of a particular conductor material is a measure of how strongly the material opposes the flow of electric current through it. Over sizable ranges of temperature, its temperature dependence can be predicted from a temperature coefficient of resistance. Activity 1: Resistance of a Wire 1. Start the Resistance in a Wire PhET simulation and explore it. You will verify the equation R = ρ l A using the PhET simulation. 2. Increase the resistivity ρ of the resistor while keeping L and A constant, to investigate how the resistance of the resistor changes. Record your data in Table 1 below. L = 10 cm A = 7.5 cm 2 Table 1: ρ ( Ω m ) R ( Ω ) 0.20 0.267 0.40 0.533 0.60 0.800 0.80 1.07 1.00 1.33 3. Use Excel to plot a graph of R vs . ρ (see LU0_Excel file for help). Make sure that your graph is a scatter plot . Customize the graph - graph title and label the axes (using the Chart Tools menu). Add the best-fit line passing through your data points (use the Trendline menu), and check the Display Equation on Chart option near the bottom. Insert a copy (screenshot) of your graph in the space below 2

. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 f(x) = 1.33 x + 0 R vs p p (Ω m) R (Ω) 4. Does a linear fit describe your data? Compare the slope of the graph to the ratio L A . The linear fit does describe the data. When comparing the slope to the ratio L/A they both the same or close enough making the data accurate. 5. Increase the length of the resistor while keeping the resistivity ρ and A constant. Record your data in Table 2 below. ρ = 0.50 Ω cm A = 7.50 cm 2 Table 2: L ( m ) R ( Ω ) 4.03 0.269 8.08 0.539 12.13 0.809 16.08 1.07 20.00 1.33 6. Use Excel to plot a graph of Rvs .L . Add the best-fit line passing through your data points (use the Trendline menu), and check the Display Equation on Chart option near the bottom. Insert a copy (screenshot) of your graph in the space below. 3

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2 4 6 8 10 12 14 16 18 20 22 0 0.2 0.4 0.6 0.8 1 1.2 1.4 f(x) = 0.07 x + 0 R vs L L (m) R (Ω) 7. Does a linear fit describe your data? Compare the slope of the graph to the ratio ρ A . Yes the linear fit describe the data from the table. Compare to the slope of the graph and the ration p/A they both are equal to 0.066 making the comparison accurate. 8. Increase the area of the resistor while keeping the resistivity ρ and L constant. Record the your data in Table 3 below. ρ = 0.5 Ωcm L = 10 cm Table 3: A ( m ) A − 1 ( m − 1 ) R ( Ω ) 3.00 0.333 1.67 6.05 0.165 0.826 9.03 0.110 0.544 12.01 0.083 0.416 15 0.066 0.333 9. Use Excel to plot a graph of R vs . A − 1 . Add the best-fit line passing through your data points (use the Trendline menu), and check the Display Equation on Chart option near the bottom. Insert a copy (screenshot) of your graph in the space below. 4

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 f(x) = 5.02 x − 0 R vs ^-1 𝐴 A^-1 (m^-1) R (Ω) 10. Does a linear fit describe your data? Compare the slope of the graph to the product ρL . Yes the linear fit describe the data. Compare to the slope of the graph to the product pL which equals to 5 they have the same making the slope accurate. 11. Does your data prove that R = ρ l A ? Yes my data does prove that the equation is true since each p or l or A have an affect on R causing R to change when either one is change. As well the slope of the graph show the truth in the relation between each component. 12. Based on your data, what must happen for the wire’s resistance to be at its greatest? Base on the data the longest L is as well as the highest p is and having the smallest A would cause to have a greatest resistance. Activity 2: Ohm’s Law 13. Start the Battery Resistor Circuit PhET simulation and explore it. Make sure that the show core box is checked. The simulation allows you to change either the potential difference (voltage) of this circuit or the resistance. Play around with these variables to see what happens when you increase and decrease each one. 14. How does increasing the resistance affect the current passing through the circuit? Increasing the resistance it affect the current by slowing it down. 5

15. What must happen to the voltage and resistance for the circuit to get hot? To make the circuit to get hot the voltage has to be at its maximum and resistance to be the least possible. 16. What happens to the current in this scenario? In this scenario the current is travelling through the circuit at a fast pace making the circuit to get hot. 17. What must happen to the voltage and resistance for the circuit to get cold? To make the circuit get cold the resistance has to be the maximum and the voltage has to be right at zero or close to it. 18. What happens to the current in this scenario? In this scenario the current is going slow since there is a high resistance slowing it down making the circuit cold. 19. Set the voltage to 7.20 V and do not change it. For the resistance values listed in Table 4 below, read the current in the circuit on the ammeter dial in the lower left-hand corner. Table 4: R ( Ω ) I ( A ) I − 1 ( A − 1 ) .20 39 0.025 .40 19 0.052 .60 12 0.083 .80 9 0.111 .93 8 0.125 20. Use Excel to plot a graph of R vs .I − 1 . Add the best-fit line passing through your data points (use the Trendline menu), and check the Display Equation on Chart option near the bottom. Insert a copy (screenshot) of your graph in the space below. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f(x) = 7.15 x + 0.02 R vs I^-1 I^-1 (Amps) R (Ω) 6

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21. Does a linear fit describe your data? Compare the slope of the graph to the voltage recorded above, by calculating the % diff. % diff = | 7.1453 − 7.2 7.2 | × 100 = 0.76 % The linear fit does describe the data having not much different from the actual voltage. 22. Set the resistance in this circuit to 0.60  and do not change it. Start at 9.0 V and incrementally decrease the voltage for the 6 trials listed in Table 5 below. Read the current in the circuit on the ammeter dial in the lower left-hand corner. Table 5: V ( V ) I ( A ) 9.12 14 6.00 9 3.12 4 -3.12 -4 -6.00 -9 -9.12 -14 23. Use Excel to plot a graph of V vs .I . Add the best-fit line passing through your data points, and check the Display Equation on Chart option near the bottom. Insert a copy (screenshot) of your graph in the space below. -20 -15 -10 -5 0 5 10 15 20 -15 -10 -5 0 5 10 15 f(x) = 0.66 x − 0 R vs I I (Amps) R (Ω) 7

24. Does a linear fit describe your data? Compare the slope of the graph to the resistance recorded above, by calculating the % diff. % diff = | 0.6627 − 0.6 − .6 | × 100 = 10.45% is the difference making it be really close to the actual resistance. Making the linear fit describe the data. 25. Does your data verify Ohm’s Law V = I R ? My data does verify Ohm’s Law V = IR since calculating the change in R and V have an affect on I making all the variables linked together. References: CC-BY license, PhET Interactive Simulations, University of Colorado Boulder, http://phet.colorado.edu https://phet.colorado.edu/sims/html/resistance-in-a-wire/latest/resistance-in-a-wire_en.html http://phet.colorado.edu/en/simulation/battery-resistor-circuit 8

LU6_Resistors

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