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UA PHYS 241 - Lab: Vulture Iguana Rabbit

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Physics 241 Lab: Vulture Iguana Rabbithttp://bohr.physics.arizona.edu/~leone/ua/ua_spring_2010/phys241lab.htmlName:____________________________Section 1:1.1. The resistance of a circuit is defined to be the amount of voltage applied to the circuit dividedby the total current through the circuit, € Rtotal≡ΔVtotal appliedItotal. When someone speaks of the resistanceof a component of a circuit, they mean the voltage drop across the component divided by the currentflowing through the component, € Rcomponent≡ΔVdrop across componentIthrough component.Express the SI unit of resistance W (ohms) in terms of other SI units. Your answer:If you apply a large voltage difference across a light bulb but only get a trickle of current through thelight bulb, what can you qualitatively say about the light bulb’s resistance? Justify this using thedefinition of resistance. Your answer and justification:Imagine you are in the desert and there is a vulture flying in the sky and a rabbit and iguana on theground. The rabbit sees the vulture flying over the iguana! This is a pneumonic device to rememberthe definition of resistance. What would the iguana see? What would the vulture see? Write two newequations relating V, I and R based upon this pneumonic device. This is merely a way to avoid sillyerrors when trying to rearrange the equation € R =ΔVI. Your two new equations:1.2. There is no reason to suspect a priori that the ratio of € ΔVI should be the same for differentvoltages. Therefore, a particular component may have different resistances for different appliedvoltages. For example, a diode will have a very large resistance until the applied voltage potentialdifference reaches a certain value and then drop to nearly zero for larger voltages. Components thathave a resistance that depends on the voltage applied are called non-Ohmic. For introductory students,we usually work with Ohmic resistors in most (but not all) the labs. For an Ohmic resistor, theequation € Rconstant=ΔVI implies the resistance is the same value no matter what voltage is applied. If a 1.5 Volt battery is discharged through a 2.5 W resistor, what is the current through the resistor?Your work and answer in SI units:1.3. Answer the questions about each of the following graphs.Does this graph describe an Ohmic resistor? What does theslope of this graph represent? Explain your answers.Does this graph describe an Ohmic resistor? Explain youranswer.Does this graph describe an Ohmic resistor? Explain youranswer.1.4. Make a sketch of the small board of resistors provided to you and use your DMM to measurethe resistance of each with as much accuracy as possible. Label the values on your sketch. (There isnever any reason to trust the values written on the resistors or the color codes!)Your sketch and labeled values:Section 2:2.1. Experimentally verify that the “1,000” W resistor on your resistor board is Ohmic at roomtemperature. Do this by gathering (voltage, current) data and making the appropriate graph. Yourgraph of your data should quite nicely show the linear behavior of your Ohmic resistor. The correctchoice of (V vs. I) or (I vs. V) should give your resistance as the slope. WARNING: Do not apply sucha large voltage that the resistor becomes very hot, dangerous and non-Ohmic. Conduct thisexperiment now, collect and appropriately graph your data on graph paper. Determine theexperimentally observed value for resistance from your graph and record it here in SI units. Measure the resistance of your “1,000” W resistor with your DMM (which gives the true value) andcompare this to your experimental value by finding the percent error: € Rexperimental-− RDMMRDMMx100%.Your answers:2.2. When two resistors are put into series, it is often useful to treat them as a single compositeresistor and to find the total resistance. The formula for this is € Rtotal= R1+ R2. You will learn toderive this by answering the following questions. Label the current through each resistor as I1 and I2. How are these two currentsrelated (as a simple equation)? What is the reason for your answer? Youranswers:Label the voltage difference across each resistor as V1 and V2. Write an equationrelating V to V1 and V2. Here you must use the idea that the sum of all voltagedifferences in a circuit must be zero or else one could extract an infinite amount ofenergy from the electrons whirling around the loop.Your work and answer:Now use Ohm’s law in the equation from part b to substitute R1, R2, I1, and I2 for V1 and V2.Your work and answer:At this point, your equation should read € V = I1R1+ I2R2. Now use your answer from part a bysubstituting € I = I1= I2 (there is no reason to differentiate between the current in the two resistors sojust write I). Distribute the I from the addition on the right hand side of the equation to get€ V = I R1+ R2( ). Explain why this tells you that two resistors in series have an effective resistance of€ R1+ R2( ). Your explanation:2.3. Experimentally verify that the 100 W resistor and the 200 W resistor in series produce aneffective resistance of 300 W by taking (voltage, current) data and making the appropriate graph. Yourvoltage data should be gathered from across both resistors simultaneously since you want to treat themas a single resistor. Remember that the current is the same through both resistors. WARNING: Do notapply such a large voltage that the resistor becomes very hot, dangerous and non-Ohmic. Conductthis experiment now, collect and appropriately graph your data. Determine the experimentallyobserved value for series resistance and record it here.Measure the series resistance of both resistors (in a single measurement) with your DMM (which givesthe true value) and compare this to your experimental value by finding the percent error:€ Rexperimentalseries− RDMMseriesRDMMseriesx100%. Your answers:2.4 Now examine two resistors in parallel. We would like to be ableto treat them as a single effective resistor to make examining the totalbehavior of the circuit easier. Here is the derivation withoutexplanations. You will need to provide the derivation with explanationsfor each step in your lab report (so you should work through it now


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UA PHYS 241 - Lab: Vulture Iguana Rabbit

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