Pre-LAB 5 Assignment

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1 Name: Lab Partners: Date: Pre-LA 5 Assignment Fundamentals of Circuits III: Voltage & Ohm s Law (Due at the beginning of lab) Directions: Read over the Lab Fundamentals of Circuits III: Voltages :w & Ohm s Law and then answer the following questions prior to doing the lab. 1. Analyze the components in the circuits shown in Fig. 1(a) and Fig. 1(c). What is your prediction for how the brightness of the light bulbs in Fig. 1(a) and Fig. 1(c) compare? 2. WhatdoyoupredictforhowthebrightnessoflightbulbsinFig.2andFig.1(a)compare? Note: assume that all batteries and bulbs used are identical. 3. What device would you use to measure the voltages between points 1 and 2 in the three circuits shown in Fig. 3? Where would you place the device? 4. What do you predict will happen to the voltage you read across the light bulb A in Fig. 7 (a) when you close the switch? 5. What is the function of the power supply in Fig. 9 and Fig. 10? 6. How would you determine the relationship between the voltage across a resistor (the light bulb, in our case) and the current through the resistor? What devices would you use? Describe how would you place them in relation to the resistor? PHYS-204: Physics II Laboratory i

2 Name: Lab Partners: Date: Objectives LA 5 Fundamentals of Circuits III: Voltage & Ohm s Law To further our understanding of the concept of potential difference(voltage) and to explain the role of a power supply in a circuit. To understand how potential difference (voltage) varies across the components in a circuit involving resistors that are connected in series. To understand how potential difference (voltage) varies across the components in a circuit involving resistors that are connected in parallel. To understand the quantitative relationship between the potential difference across a resistor and current through the resistor, and to understand the difference between components that obey Ohm s Law (Ohmic) and the components that do not obey Ohm s Law (non-ohmic). This lab has been adapted from the Real Time Physics Active Learning Laboratories [?]. The goals, guiding principles and procedures of this labs parallel the implementation found in the work of those authors [?,?,?]. Overview In previous lab activities you examined currents through different elements in series and parallel circuits. You saw that in a series circuit, the current is the same through all elements, and that in a parallel circuit, the current is distributed among the branches in such a way that the total current through the battery equals the sum of the currents in each branch. You also saw that in circuits with two or more parallel branches connected directly across a battery, making a change in one branch does not affect the current in the other branch or branches, while in series circuits, making a change in one part of the circuit changes the current in all parts of that series circuit. You also saw that connecting multiple light bulbs in series results in a larger net resistance to current and therefore a smaller current results in the circuit, while adding multiple light bulbs in parallel results in a smaller net resistance in the circuit and consequently a larger current. You have also learned about electric potential difference, or Voltage, and its relationship to work. In this lab, you will establish that a battery produces an electric potential difference, and that this potential difference can cause a current in a circuit. You will then compare the potential differences (voltages) across different parts of series and parallel circuits. In the last part of this lab you will explore the quantitative relationship between the current through a resistor and the potential difference (voltage) across the resistor and arrive at a mathematical relationship between current, voltage and resistance. When this relationship is a linear one, it is known as Ohm s law. PHYS-204: Physics II Laboratory 1

3 Investigation 1: atteries and Voltages in Series Circuits In previous labs on the fundamentals of circuits, you developed a current model and utilized the concept of resistance to explain the relative brightness of bulbs in simple circuits. Your model says that when a battery is connected to a circuit that provides a closed path, there is a current in the circuit. For a given battery, the magnitude of the current depends on the total resistance of the circuit. In this lab you will investigate how adding batteries in series and in parallel changes the potential differences (voltages) between various points in circuits. In order to do this you will need the following items: Computer with Logger-Pro software Lab Pro interface two voltage probes Two 1.5 V D cell battery with holder connecting wires alligator clips Two #14 bulbs in sockets contact switch In a previous lab you saw what happens to the brightness of a bulb in the circuit shown in Fig. 1(a) if you add another bulb in series as shown in circuit 1(b). Neither of the two bulbs is as bright as the original bulb. Adding another bulb (resistor) to the first one in series increased the overall resistance in the circuit has increased, resulting in less current through the bulbs. S S S A C C (a) (b) (c) Figure 1: Series circuits with (a) one battery and one bulb, (b) one battery and two bulbs and (c) two batteries and two bulbs. (All batteries and all bulbs are identical.) Prediction 1.1 What do you predict would happen to the brightness of the two bulbs if you added a second battery in series with the first at the same time that you added the second bulb as in Fig. 1 (c)? How would the brightness of bulb A in circuit 1 (a) compare to bulb in circuit 1(c) and to to bulb C? PHYS-204: Physics II Laboratory 2

4 Activity 1.1: attery Action Step 1: Set up the circuit as shown in Fig. 1(a), and examine how bright the bulb is. Step 2: Now set up the circuit as shown in Fig. 1 (c). (Make sure that the batteries are connected in series this means that the positive terminal of one battery must be connected to the negative terminal of the other.) Question 1.1 Compare the brightness of the bulbs in circuit of Fig. 1 (c) with that of the bulb in Fig. 1(a). Question 1.2 What do you deduce about the quantitative relationship between the current in the two-bulb, two-battery circuit as compared with that in the single-bulb, single-battery circuit? Explain. Question 1.3 What happens to the overall resistance of the circuit as more bulbs are added in series? What do you need to do if you want to keep the current the same? Prediction 1.2 How in your opinion would the the brightness of bulb D in Fig. 2 compare with the brightness of bulb A in Fig. 1(a)? Explain your reasoning. S D Figure 2: Series circuit with two batteries and one bulb PHYS-204: Physics II Laboratory 3

5 Step 3: Connect the circuit in Fig. 2. Close the switch only for a moment to observe the brightness of the bulb to avoid burning out the bulb. Question 1.4 Compare the brightness of bulb D to bulb A in the single bulb circuit with only one battery [Fig. 1(a)]. Question 1.5 How does connecting more than one battery in series affect the current in a series circuit? The voltage marked on a new battery is actually a measure of the electromotive force (emf) or electric potential difference between its terminals. The term voltage is often used in everyday usage but the precise term and one you should try to use in a physics lab is emf or potential difference. In the following exercise, we explore the potential differences obtained by connecting batteries and bulbs in series and parallel circuits. We will try to come up with rules for them through exercises analogous to what we did in earlier exercises for currents. We will investigate what is the resulting potential difference of two batteries when the batteries are connected (i) in series (ii) in parallel. Figs. 3(a), (b) and (c) illustrate these cases and show a single battery, two identical batteries connected in series, and two identical batteries connected in parallel. (a) 1 (b) 1 (c) Figure 3: Identical batteries (a) single, (b) two connected in series and (c) two connected in parallel. Prediction 1.3 Given the potential difference between points 1 and 2 in Fig. 3 (a), predict what the potential difference between points 1 and 2 would be in Fig. 3 (b) (series connection) and in 3 (c) (parallel connection). Explain your prediction. PHYS-204: Physics II Laboratory 4

6 Activity 1.2: atteries in Series and Parallel The predictions you make can be tested by measuring potential differences with the voltage probes connected across the two points you want to measure the potential difference between as shown in Fig. 4. VP1 (a) A VP2 (b) VP1 A VP2 VP1 (c) A VP2 Figure 4: Voltage probes connected to measure the potential difference across (a) single batteries, (b) a single battery and two batteries connected in series, and (c) a single battery and two batteries connected in parallel. Step 1: Open the experiment file L4A1-2 (atteries). Step 2: Zero the probes. Make sure that they are not connected to anything. Step 3: Connect voltage probe l across a single battery (as in Fig. 4 (a) and voltage probe 2 across the other battery. Step 4: Record the potential difference measured for each battery below. Potential difference of battery A: Potential difference of battery : Question 1.6 How do your measured values agree with those marked on the batteries? Step 5: Next, connect the batteries in series as in Fig. 4 (b). Now connect probe 1 so it measures the potential difference across battery A and connect probe 2 so it measures the potential difference across the series combination of the two batteries. Record your measurements below. Voltage of battery A: Voltage of A and in series: PHYS-204: Physics II Laboratory 5

7 Question 1.7 Do your measured values agree with your predictions? How do you explain any differences? Step 6: Next, connect the batteries in parallel as in Fig. 4(c). Connect probe 1 so it measures the potential difference across battery A and connect probe 2 so it measures the potential difference across the parallel combination of the two batteries. Record your measurements below. Voltage of battery A: Voltage of A and in parallel: Question 1.8 Do your measured values agree with your predictions? How do you explain any differences? Question 1.9 Now, based on your observations, deduce a rule for the combined potential difference (voltage) of a number of identical batteries connected in series. Question 1.10 Next, also based on your observations, deduce a rule for the combined potential difference (voltage) of a number of identical batteries connected in parallel. Activity 1.3: Voltages in Series Circuits Now let s learn about the potential difference across different parts of a simple series circuit. We begin with the circuit with two bulbs in series with a battery, which you looked at in a Lab 4, Activities 1-1 and 1-2. It is shown in Fig. 5(a). Prediction 1.4 If you have two identical bulbs A and, predict how the potential difference (voltage) across bulb A in Fig. 5 (b) will compare to the potential difference across the battery. Do the same for bulb. How does the potential difference across the series combination of bulbs A and compare with the potential difference across the battery? Test your prediction. PHYS-204: Physics II Laboratory 6

8 A C VP1 VP2 (a) (b) Figure 5: (a) A series circuit with one battery and two bulbs, and (b) the same circuit with voltage probe 1 connected to measure the potential difference across the battery and probe 2 connected to measure the potential difference across the series combination of bulbs A and. Step 1: Use the same experiment file L4A1-2 (atteries) that you used in the previous activity. Step 2: Zero both probes with nothing connected to them. Step 3: Connect the circuit shown in Fig. 5(b). Comment: Always zero current and voltage probes without connecting them to anything before you start taking measurements. Step 4: Measure the potential differences and record your readings below. Potential difference across the battery: Potential difference across bulbs A and in series: Question 1.11 How do the two potential differences compare? How did your observations compare with what you predicted? Step 5: Connect the voltage probes as in Fig. 6 to measure the potential difference across bulb A and across bulb. Record your measurements below. Potential difference across bulb A: Potential difference across bulb : Question 1.12 Did your measurements agree with your predictions? PHYS-204: Physics II Laboratory 7

9 A VP1 VP2 Figure 6: Connection of voltage probes to measure the potential difference across bulb A and across bulb. Question 1.13 Now, based on your observations, deduce a rule for how the potential difference across individual bulbs connected in series relate to the total potential difference across the combination of the bulbs. How is this related to the potential difference supplied by the battery? Investigation 2: Voltage in Parallel Circuits We will also need to learn about the potential differences across different parts of a simple parallel circuit. Let s begin with the circuit with two bulbs in parallel with a battery. You looked at this circuit in a previous lab. It is shown in Fig. 7(a). S S A VP1 A VP2 (a) (b) Figure 7: (a) Parallel circuit with two bulbs and a battery, and (1)) same circuit with voltage probe 1 connected to measure the potential difference across the battery and probe 2 connected to measure the potential difference across bulb A. Prediction 2.1 What do you predict will happen to the potential difference across the battery when you close the switch in Fig. 7(a)? Will it increase, decrease or remain essentially the same? Explain. Prediction 2.2 With the switch in Fig. 7(a) closed, how will the potential difference across bulb A compare to the potential difference of the battery? How will the potential difference across bulb compare to the potential difference of the battery? PHYS-204: Physics II Laboratory 8

10 To test your predictions you will need: Computer with Logger-Pro software Lab Pro interface Two voltage probes 1.5 V D cell battery with holder connecting wires alligator clips Two #14 bulbs in sockets contact switch Activity 2.1: Voltages in a parallel Circuit Step 1: The experiment file L4A1-2 (atteries) should still be open, and the axes that follow should be on the screen. Voltage 2 (V) Voltage 1(V) Time (s) Step 2: Zero both probes with nothing connected to them. Step 3: Connect the circuit shown in Fig. 7(b). Step 4: egin graphing, and then close and open the switch as you have done before. Step 5: Sketch the graphs on the axes above. Step 6: Read the voltages using the analysis feature of the software. Switch open: Voltage across battery: Voltage across bulb A: Switch closed: Voltage across battery: Voltage across bulb A: PHYS-204: Physics II Laboratory 9

11 Question 2.1 Did your measurements agree with your predictions? Did closing and opening the switch significantly affect the potential difference across the battery (by more than several %? Did it significantly affect the potential difference across bulb A? Step 7: Connect the voltage probes as shown in Fig. 8. Measure and graph the individual potential differences across bulb A and bulb. Again close and open the switch while graphing. S VP1 A VP2 Figure 8: Voltage probes connected to measure the potential differences across bulbs A and. Step 8: Sketch your graphs on the axes below. Voltage 2 (V) Voltage 1(V) Time (s) Step 9: Record your measurements using the analysis feature of the software. Switch open: Voltage across bulb A: Voltage across bulb : Switch closed: Voltage across bulb A: Voltage across bulb : PHYS-204: Physics II Laboratory 10

12 Question 2.2 Did your measurements agree with your predictions? Did closing and opening the switch significantly affect the potential difference across bulb A (by more than several %? Question 2.3 Did closing and opening the switch significantly affect the potential difference across bulb by more than several %? Under what circumstances is there a potential difference across a bulb? Question 2.4 ased on your observations, deduce a rule for the potential differences across different branches of a parallel circuit. How do these relate to the potential difference across the battery? Question 2.5 In analyzing your observations, would you deduce that the battery is a constant current source which delivers essentially a fixed amount of current regardless of the components connected to it or would you deduce that it is a constant voltage source which essentially applies a fixed potential difference regardless of the circuit connected to it or do you think that neither deductions necessarily follow from your observations? Explain, based on your observations in this and the previous lab. Question 2.6 What is the potential difference between two points on a short length of wire when there is no bulb, battery or resistor between the points? You may assume that the wire has negligible resistance. Investigation 3: Ohm s Law What is the relationship between current and potential difference? You have observed in previous investigations that there is a potential difference across a bulb or resistor only when there is a current through that circuit element. So how does the potential difference depend on the current? In order to examine this, you will need the following: Computer with Logger-Pro software Lab Pro interface voltage probe current probe variable DC power supply 10 Ohm resistor PHYS-204: Physics II Laboratory 11

13 connecting wires alligator clips The circuit shown below contains a power supply. A power supply has the same purpose as a battery. oth raise the potential energy of the electric charges that flow through them; the battery uses chemical energy to do this, while the power supply uses electrical energy. A variable DC power supply lets you adjust the potential difference. When you turn the dial, you change the voltage between its terminals. Therefore, this circuit allows you to measure how the current through the resistor varies as you change the potential difference across it. CP2 DC Power Supply VP1 Figure 9: Circuit with a variable power supply to explore the relationship between current and potential difference for a resistor. Prediction 3.1 What will happen to the current through the resistor as you increase the applied voltage from zero? Prediction 3.2 What will happen to the potential difference across the resistor as the current through it increases from zero? Prediction 3.3 What do you predict for the mathematical relationship between the potential difference across the resistor and the current through the resistor? Activity 3.1: Current and Potential Difference for a Resistor Step 1: Open the experiment file called L4A3-1 (Ohm s Law). Step 2: Zero both probes with nothing connected to them. Step 3: e sure the power supply is turned off. Also, check to see that the voltage control (the knob on the left) is turned down all the way (counter clockwise). Connect the circuit in Fig. 9. Note that the current probe is connected to measure the current through the resistor, and the voltage probe is connected to measure the potential difference across the resistor. Step 4: Turn on the power supply. egin graphing current and voltage starting with the power supply set to zero voltage, and graph as you turn the voltage control up slowly to about 3 volts. Warning: Do not exceed 3 volts! PHYS-204: Physics II Laboratory 12

14 Question 3.1 What happened to the current in the circuit as the power supply voltage was increased? How did this compare with your prediction? Question 3.2 How did the potential difference across the resistor change as the current through the resistor changed? How did this compare with your prediction? Step 5: You can display axes for voltage vs. current on the top graph. Click on the word time below the horizontal axis, then select current in the dialog box that comes up. Close the dialog box. You will also need to change the maximum value on the horizontal axis. 0.5 A would be an appropriate value. The axes should now appear as shown below. Voltage 1(V) Current 2 (A) Current 2 (A) Time (s) Reminder: We are interested in the mathematical relationship between the voltage across the resistor and the current through the resistor. This can be determined from the graph by drawing a smooth curve that fits the plotted data points. Some definitions of possible mathematical relationships are shown below. In these examples, y might be the voltage reading and x the current. PHYS-204: Physics II Laboratory 13

15 y y y x x x y is a function of x, which increases as x increases. y is a linear function of x which increases as x increases according to the mathematical relationship y = mx b, where b is a constant called the y intercept. y is proportional to x. This is a special case of a linear relationship where y = mx, and b, the y intercept, is zero. These graphs show the differences between these three types of mathematical relationship. y can increase as x increases, and the relationship doesn t have to be linear or proportional. Proportionality refers only to the special linear relationship where the y intercept is zero, as shown in the example graph on the right. Step 6: Usethefitroutineinthesoftware toseeiftherelationshipbetweenvoltage andcurrent for a resistor is a proportional one. Step 7: Sketch your graphs on the axes shown previously. Question 3.3 Describe in words, what the mathematical relationship between the potential difference across a resistor and the current through that resistor is. Explain, based on your graphs. When the relationship between potential difference and current for a resistor is linear, it means that current changes proportionally to the change in voltage and the value of this proportionality does not change no matter what the voltage is. When such a linear relationship exists between current and voltage, the mathematical relationship between current and voltage is known as Ohm s law. We now define a quantity known as resistance. Resistance is defined as the slope of the voltage vs. current graph. If potential difference is measured in volts and current is measured in amperes, then the unit of resistance is the Ohm, which is usually represented by the Greek letter omega Ω. Question 3.4 Write a mathematical equation that expresses the relationship between V, I, and R. PHYS-204: Physics II Laboratory 14

16 Question 3.5 ased on your graph, what can you say about the value of R for a resistor is it constant or does it change as the current through the resistor changes? Explain. Question 3.6 From the slope of your graph, what is the experimentally determined value of the resistance of your resistor in ohms? How does this agree with the value written on the resistor? (Remember that your resistance has a tolerance coded on it.) Note: Not all circuit elements obey Ohm s law. The definition for resistance is still the same as the relation you obtained, but the resistance changes as the current changes. Circuit elements that follow Ohm s law like resistors are said to be ohmic, circuit elements that do not are called non-ohmic. In the last activity you explored the relationship between the potential difference across a resistor and the current through the resistor. It is a proportional relationship. In the following extension you will explore the relationship between current and potential difference for a light bulb instead of a resistor. Extension 3-2: Relationship between Current and Potential Difference for a Light ulb Step 1: Connect a light bulb in the place of the resistor, as shown in the circuit in Fig. 10. CP2 DC Power Supply VP1 Figure 10: Circuit with a variable power supply to explore the quantitative relationship between the current and potential difference for a light bulb. Prediction 3.4 What do you predict will happen to the brightness of the bulb as you turn the dial on the power supply and increase the voltage from zero? Explain. Prediction 3.5 What do you predict for the mathematical relationship between the voltage across the bulb and the current through the bulb? PHYS-204: Physics II Laboratory 15

17 Step 2: Prepare to graph current vs. time with current probe 1 and voltage vs. time with voltage probe 2. (Adjust the horizontal axis on the top graph back to time, and adjust the horizontal scale to give a range from 0 to 30 seconds). Step 3: egin graphing with the power supply set to zero voltage, and graph current and voltage as you turn the dial and increase the voltage slowly to about 3 volts. Warning: Do not exceed 3 volts, since this may burn out the bulb! Also, return the voltage of the power supply to zero as soon as you are done with your measurements. Question E3.1 What happened to the brightness of the bulb as the power supply voltage was increased? How did this compare with your prediction? Question E3.2 How is the brightness of the bulb related to the potential difference across the bulb? To the current through the bulb? Step 4: You can again display a graph of potential difference vs. current by changing the variable on the horizontal axis on the bottom graph to current as before. Voltage 1(V) Current 2 (A) Current 2 (A) Time (s) Question E3.3 Compare your graph of voltage vs. current for the bulb to that for the resistor in the previous activity. In what ways are they similar, and in what ways are they different? Step 5: Use the fit routine in the software to determine if the relationship between voltage and current for a light bulb is a proportional one. Step 6: Sketch the graphs, or print and affix them over the axes. PHYS-204: Physics II Laboratory 16

18 Question E3.4 ased on your graph of voltage vs. current for a bulb, what can you say about the value of the resistance R for a bulb is it constant or does it change as the current through the bulb changes? Explain. Question E3.5 Is a light bulb an ohmic device? Explain. This laboratory exercise has been adapted from the references below. PHYS-204: Physics II Laboratory 17

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