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Name___________________ ID number_________________________

Date____________________ Lab partner_________________________

Lab CRN ________________ Lab instructor_______________________

Physics 2306

Experiment 6: Direct Current (DC) circuits, Part 2

Objective

• To learn to apply the concept of potential difference to explain the action of batteries in a circuit and to understand how potential difference is distributed in different parts of series and parallel circuits.

• To understand what distinguishes an ohmic device from a non-ohmic device. Required background reading

Young and Freedman, sections 25.2, 25.3, 26.1

Introduction

In the last lab, you explored currents at different points in series and parallel circuits. You saw that in a series circuit, the current is the same through all elements. You also saw that in a parallel circuit, the current divides among the branches so that the total current through the battery equals the sum of the currents in each branch. You have also observed that when two or more parallel branches are connected directly across a battery, making a change in one branch does not affect the current in the other branch(es), while changing one part of a series circuit changes the current in all parts of that series circuit. You have seen that connecting light bulbs in series results in a larger resistance to current flow and therefore a smaller current, while a parallel connection results in a smaller resistance and larger current (for a given battery voltage).

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In this lab, you will first examine the role of the battery in causing a current in a circuit. You will then compare the potential differences (voltages) across different parts of series and parallel circuits. Based on your previous observations, you probably associate a larger resistance connected to a battery with a smaller current, and a smaller resistance with a larger current. You will explore the quantitative relationship between the current through a resistor and the potential difference (voltage) across the resistor. When the conditions are such that this ratio is constant over a range of V and I, this relationship is known as Ohm’s law. You will also look at some circuit devices that do not obey Ohm’s law (called non-ohmic devices).

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Name___________________ ID number_________________________

Lab CRN ________________ Lab instructor_______________________

Ph 2306 Experiment 6

Pre-lab assignment (complete and turn in at the beginning of your lab session)

1. A resistor has four colored stripes in the following order: orange, orange, brown and silver. What is the resistance of the resistor and its tolerance?

2. Resistance is defined asIVR = . The resistance in general varies with the type of

material and other factors such as temperature. When the conditions are such that the resistance R is constant over a range of V and I values we say that the device is “ohmic”; that is it obeys Ohm’s law.

a. Give an example of an ohmic device.

b. Give an example of a non-ohmic device. Explain (in simple terms) why it is non-ohmic.

3. How does a diode behave in a circuit? (Your answer should focus on how its behavior is different for positive and negative voltages.)

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4. In the circuit above, all the batteries and light bulbs are identical. Rank the relative brightness of all five bulbs using >, <, and = signs.

+ _ A +

_

B

C

+ _ D

E _ +

5

Equipment

You will use the following equipment: • Pasco EM-8656 AC/DC Electronics Laboratory • 2 D cell (1.5 V) batteries • Seven 10 cm long wires (in Ziploc bag) • Six 25 cm long wires (in Ziploc bag) • One each of the following resistors: 330 Ω, 560 Ω, 1 kΩ (in Ziploc bag) • One red LED (in Ziploc bag) • One Pasco CI-6556 current sensor (plugged into channel A of the Science Workshop

750 Interface) • Two Pasco voltage sensors (plugged into channels B and C of the Science Workshop

interface) • Two red and two black banana plug – banana plug cables • Four red and three black banana plug to alligator clip adapters (some of these may

already be connected to the cables attached to the current and voltage sensors) • BK Precision 1670A Adjustable Power Supply • Manual Range Digital Multimeter (DMM) Since this lab involves many components, you should take a minute to see if everything in the above list is present at your station. If you are missing something, consult with your TA. Also, make sure that the Pasco sensors are plugged into the correct channels of the Science Workshop interface. One other warning – please do not adjust the CURRENT knob on your BK Precision 1670A Adjustable Power Supply. It has been preset by us (at the 9 o’clock position) to limit the amount of current the supply can put out. If you ever see the “Current Limited” light on the front of the supply come on when you are using it, immediately turn off the supply and consult with your TA. Recall that springs that are connected by a white line on your Pasco circuit board are connected together electrically (see red circled area in the picture below).

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So, for example, you should not connect a circuit element between two such springs, because the two springs are forced to be at the same electric potential by the wire that connects them (underneath the circuit board). Finally, when you detach alligator clips from the springs, please fully open the alligator’s “jaws” before removing the connector. Don’t yank on the connector without opening it; it loosens the solder connections to the spring and eventually they pop out.

Activity 1: Batteries and Voltages in Series Circuits

So far you have developed a model of electric current and 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 complete circuit, there is a current. For a given battery, the magnitude of the current depends on the total resistance of the circuit. In this investigation you will explore batteries and the potential differences (voltages) between various points in circuits. You have already seen what happens to the brightness of the bulb in the circuit shown in Figure 1a when you add a second bulb in series as shown in Figure 1b. The two bulbs are not as bright as the original bulb. We concluded that the resistance of the circuit is larger, resulting in less current through the bulbs.

(a) (b) (c)

Figure 1: Series circuit with (a) one battery and one bulb, (b) one battery and two bulbs, and (c) two batteries and two bulbs. (All batteries and bulbs are identical.)

Prediction 1-1: What do you predict would happen to the brightness of the bulbs if you connected a second identical battery in series with the first at the same time you added the second bulb as in Figure 1c? How would the brightness of bulb A in circuit figure 1a compare to bulb B in circuit figure 1c? To bulb C?

+ _ A +

_

B

C

+ _ B

C_ +

7

Part 1: Battery Action

1. Connect the circuit in Figure 1a, and observe the brightness of the bulb. Use the push button switch on the breadboard for the switch.

2. Now connect the circuit shown in Figure 1c. Be sure that the two D cell batteries on the board are connected in series – the positive terminal of one must be connected to the negative terminal of the other.

Question 1-2: Compare the brightness of each of the bulbs to the single-bulb circuit.

Question 1-3: What do you conclude about the current in the two-bulb, two-battery circuit as compared to the single-bulb, single-battery circuit? Explain.

Question 1-4: What happens to the resistance of a circuit as more bulbs are added in series? What must you do to keep the current from decreasing?

Prediction 1-5: What do you predict about the brightness of bulb D in Figure 2 compared to bulb A in Figure 1a? Explain your prediction.

Figure 2: Series circuit with two batteries and one bulb.

+ _

D _ +

8

3. Connect the circuit shown in Figure 2. Close the switch for only a moment to observe the brightness of the bulb; if you leave the switch closed for too long it may burn out the bulb.

Question 1-6: Compare the brightness of bulb D to the single-bulb circuit with only one battery (bulb A in Figure 1a).

Question 1-7: How does increasing the number of batteries connected in series affect the current in a series circuit?

When a battery is fresh, the voltage marked on it is actually a measure of the emf (electromotive force) or electric potential difference between its terminals. Voltage is an informal term for emf or potential difference. In the next activities, you will explore the potential differences of batteries in series and parallel circuits to see if you can come up with rules for them as you did in the last lab for currents.

How do the potential differences of batteries add when the batteries are connected in series or parallel? Figure 3 shows a single battery, two batteries identical to it connected in series, and two batteries identical to it connected in parallel.

(a) (b) (c)

Figure 3: Identical batteries: (a) single, (b) two connected in series, and (c) two connected in parallel.

Prediction 1-8: If the potential difference between points 1 and 2 in Figure 3a is known to be V, then predict the potential difference between points 1 and 2 in Figure 3b (series connection) and in Figure 3c (parallel connection).

+ _

_ +

1

2

+ _

1

2

+ _ _

+

1

2

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Part 2: Batteries in Series and Parallel

You can measure potential differences with voltage probes connected as shown in Figure 4. (a) (b) (c)

Figure 4: Voltage probes connected to measure the potential difference across (a) two single batteries, (b) a single battery and two batteries connected in series, and (c) a single battery and two batteries connected in parallel.

1. Open the DataStudio file Batteries from the ClassNotes folder on the Desktop.

2. Connect voltage probe 1 across a single battery (as in Figure 4a) and voltage probe 2 across the other identical battery.

3. Record the voltage measured for each battery below:

Voltage of battery A:_______________ Voltage of battery B: _________________

Question 1-9: How do your measured values agree with those marked on the batteries? 4. Now connect the batteries in series as in Figure 4b, and connect probe 1 to measure the potential difference across battery A and probe 2 to measure the potential difference across the series combination of two batteries. Record your measured values below.

Voltage of battery A:_____________ Voltage of A and B in series: _________________

+ _

_ +

VP1 VP2

A

B

+ _ _

+ VP1 VP2 A B +

_ _ +

VP1 VP2 A B

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Question 1-10: Do your measured values agree with your predictions? Can you explain any differences? 5. Now connect the batteries in parallel as in Figure 4c, and connect probe 1 to measure the potential difference across battery A and probe 2 to measure the potential difference across the parallel combination of the two batteries. Record your measured values below.

Voltage of battery A:____ Voltage of A and B in parallel: _________________

Question 1-11: Do your measured values agree with your predictions? Can you explain any differences? Question 1-12: Based on your observations make up a rule for finding the combined voltage of a number of batteries connected in series. Question 1-13: Based on your observations make up a rule for finding the combined voltage of a number of identical batteries connected in parallel.

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You can now explore the potential difference across different parts of a simple series circuit. You will start with two bulbs in series with a battery as shown in Figure 5a. (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 B.

Prediction 1-14: If bulbs A and B are identical, predict how the potential difference (voltage) across bulb A in Figure 5a will compare to the potential difference across the battery. How about bulb B? How about the potential difference across the series combination of bulbs A and B – how will this compare to the voltage across the battery?

Part 3: Voltages in Series Circuits

1. Open the DataStudio file Batteries, if it is not already open. 2. Connect the circuit shown in Figure 5b. 3. Measure the voltages, and record your readings below. Potential difference across the battery (VP1): ________________________ Potential difference across bulbs A and B in series (VP2): _____________________

+ _

A

B

+ _

A

B VP1 VP2

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Question 1-15: How do the two potential differences compare? Did your observations agree with your predictions?

Figure 6: Connection of the voltage probes to measure the potential difference across bulb A and across bulb B.

4. Connect the voltage probes as in Figure 6 to measure the potential difference across bulb A and across bulb B. Record your measurements below. Potential difference across bulb A: ___________________________ Potential difference across bulb B: ___________________________ Question 1-16: Did your measurements agree with your predictions? Question 1-17: Formulate a rule for how potential differences across individual bulbs in a series connection combine to give the total potential difference across the series combination of bulbs. How is this related to the potential difference of the battery?

+ _

A

B

VP1

VP2

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Activity 2: Voltages in Parallel Circuits

You can also explore the potential differences across different parts of a simple parallel circuit. You’ll investigate this with the circuit shown in Figure 7.

Figure 7: Voltage probes connected to measure the potential differences across bulbs A and B.

1. Open the DataStudio file Batteries, if it is not already open. 2. Connect the circuit shown in Figure 7. Use the push button switch for S1. 3. Record the voltage measurements with S1 both open and closed: Switch S1 open Voltage across bulb A: __________________ Voltage across bulb B: ______________ Switch S1 closed Voltage across bulb A: __________________ Voltage across bulb B: ______________ When you are done with your observations, please disconnect the battery immediately so the bulb does not remain lit. Question 2-1: Did closing and opening switch S1 significantly affect the voltage across bulb A (by more than several %)?

+ _

S1

A B VP1 VP2

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Question 2-2: Did closing and opening switch S1 significantly affect the voltage across bulb B (by more than several %)? Question 2-3: Based on your observations, formulate a rule for the potential differences across the different branches of a parallel circuit. How are these related to the voltage across the battery? You have now observed several times in these activities that the voltage across an ideal battery doesn’t change no matter what is connected to the battery (ie. no matter how much current flows in the circuit). No battery is truly ideal (this is especially true for a less than fresh battery), so the voltage usually drops somewhat when the load on the battery is increased.

Activity 3: Making Measurements with a Digital Multimeter

A multimeter is a versatile device that is essential in making measurements in DC circuits. They are a common piece of apparatus in any laboratory. Find the digital multimeter (DMM) on your lab tabletop. This device can be used to make a variety of measurements. The circular dial is used to select the type of measurement and the sensitivity of that measurement. It can measure voltage: the V_ symbol stands for DC voltage while the V~ symbol stands for AC voltage. It can measure current: the A_ symbol stands for DC current while the A~ symbol stands for AC current. It can be used to measure resistance: the Ω symbol. It can also be used to measure other things like capacitance, temperature and frequency, but we won’t be concerned with those here. Note the connectors at the bottom. The black cable should always be plugged into the connector labeled COM. When you need to measure current you use either the 10 A or mA inputs (for currents up to 200 mA). For all other measurements (voltage and resistance) you should plug the red cable into the connector labeled VΩHz. Check that your black cable is connected to COM and your red cable is connected to VΩHz. You will practice using the DMM by measuring the resistance of some resistors. To make the design and analysis of circuits as simple as possible, it is desirable to have circuit elements with resistances that do not change. For that reason, resistors are used in electric circuits. The resistance of a well-designed resistor doesn’t vary with the amount of current passing through it (or with temperature), and they are inexpensive to manufacture. One type of resistor is a carbon resistor, and it uses graphite suspended in a hard glue binder. It is usually surrounded by a plastic case with a color code painted on it. You should find three of these with different colors in your Ziploc bag. The resistance of each resistor can be determined using the color code on it. Figure 8 explains the color code.

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Figure 8: The resistor color code. The first two stripes indicate the first two digits of the resistance value. The third stripe indicates the power of 10 multiplier, and the fourth strip tells the tolerance. For example, a resistor with the colors yellow – violet – orange – silver in order would mean: 47 x 103 = 47 kΩ with a tolerance of ±10%.

Turn the circular knob on the DMM to the resistance (Ω) region. Always select the most sensitive scale you can for a given reading. If the resistance is too large for a given scale, then the DMM will just read “1” with no decimals. You should then click up to the next higher scale. Also, be careful in recording the value read from the screen. For example, if you are on the 2 k scale, and you read .560, that would imply a value of .560 kΩ for the resistance. For each of the three resistors, determine the resistance and tolerance from the color code and then measure the actual resistance with your DMM. Resistor 1: colors on band: _________________________________________________ R from code = __________________ Tolerance from code = ____________ Measured resistance with DMM = ____________________________________________ Resistor 2: colors on band: _________________________________________________ R from code = __________________ Tolerance from code = ____________ Measured resistance with DMM = ____________________________________________ Resistor 3: colors on band:_________________________________________________ R from code = __________________ Tolerance from code = ____________ Measured resistance with DMM = ____________________________________________

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Activity 4: Ohm’s Law

What is the relationship between current and potential difference? You have already seen on several occasions that there is only a potential difference across a bulb or resistor when there is a current through the circuit element. The next question is how are the potential difference and current across a circuit element related? In the next set of activities you will measure the current through a device for various potential differences across the device. You will measure this relationship for two different devices – a resistor and a light emitting diode (LED).

Figure 9: Circuit with a variable power supply to explore the relationship between current and potential difference for a resistor.

Examine the circuit shown in Figure 9. A variable DC power supply is like a variable battery. When you turn the dial, you change the voltage (potential difference) between its terminals. Therefore, this circuit allows you to measure the current through the resistor when different voltages are applied across it. Prediction 4-1: In Figure 9, what will happen to the current through the resistor as your turn the dial on the power supply and increase the applied voltage from zero? Prediction 4-2: In Figure 9, what will happen to the potential difference across the resistor as the current through it increases from zero? Prediction 4-3: What will be the mathematical relationship between the current through the resistor and the voltage across the resistor?

+

CP1 +

_

DC power supply VP1

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Part 1: Current and Potential Difference for a Resistor

1. Open the DataStudio file Ohms_law_1. Remove any wires, cables, and connectors left over on your circuit board from prior parts of the lab. 2. Set up the circuit shown in Figure 9. For the resistor, use the 330 ohm resistor in your Ziploc bag. You can set up the circuit using the springs on the lower right hand corner of your circuit board (REMEMBER that two springs connected by a white line are connected together – reread the discussion at the bottom of page 5). You can plug the power supply leads directly into the female banana plug connectors on the lower right hand corner of the board. 3. After you have the circuit connected up, make sure the voltage knob on the power supply is turned all the way down (fully counter-clockwise) and then turn the power supply on. Leave the current knob untouched. It was preset to limit the amount of current (it should be at the 9 o’clock position). When you are using the power supply, consult with your TA if you ever see the “Current Limited” light come on. 4. Start data-taking. Your screen should show a current versus voltage plot. A data point will be recorded automatically every 2 seconds. Slowly turn up the power supply voltage so that you get a data point roughly in 1 volt steps. Don’t exceed 10 volts on the power supply voltage. When you have done with that, turn the voltage knob back to zero and turn the supply off. We now want to take data with the opposite polarity of applied voltage. To do that, you should simply reverse the leads coming out of the power supply. Then turn the power supply back on and slowly increase the voltage to fill in your graph for negative voltage. At the end you should have roughly 20 data points that cover the range from -10 V to + 10 V. 5. We are interested in the mathematical form of the current versus voltage data that you have just obtained. To see if it is linear, click on the FIT button in the graph window and select linear. You should print out a copy of this graph for both you and your lab partner and include it after this sheet. You should put your name on the plot using the “A” icon in the panel of buttons at the top of the graph window. Question 4-4: From your plot, what do you conclude about the mathematical relationship between current and potential difference for a resistor? Explain based on your graph. Question 4-5: Assuming that we define resistance through the relation I = V/R, what does the measured slope from the linear fit imply about the resistance? Show your

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calculation. How does the resistance determined from the slope compare to the resistance you directly measured with the DMM?

Part 2: Current and Potential Difference for a Light Emitting Diode (LED)

1. Open the DataStudio file Ohms_law_3.

Figure 10: Circuit with a variable power supply to explore the relationship between current and potential difference for a light emitting diode (LED).

2. Set up the circuit shown in Figure 10. The new circuit symbol stands for a diode; for that element you should insert the red LED from your Ziploc bag. Note particularly the 1 kohm resistor; if you do not include it you will burn out the red LED. 3. After you have the circuit connected up, make sure the voltage knob on the power supply is turned all the way down (fully counter-clockwise) and then turn the power supply on. Start data-taking. For this plot, YOU SHOULD NOT EXCEED 10 VOLTS ON THE POWER SUPPLY. A data point will be recorded automatically every 2 seconds. Slowly turn up the power supply voltage so that you get a reasonable number of data points. You will have to watch your curve that you are mapping out to determine what reasonable is. Don’t exceed 10 volts on the power supply voltage. When you have done with that, turn the voltage knob back to zero and turn the supply off. We now want to take data with the opposite polarity of applied voltage. To do that, you should simply reverse the leads coming out of the power supply. Then turn the power supply back on and slowly increase the voltage to fill in your graph for negative voltage. At the end you should have roughly 20 data points that cover the range from the voltage range, but not exceeding 10 volts for either sign of applied voltage.

+

CP1 +

_

DC power supply

VP1

1 kΩ

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5. Print out a copy of the plot for both you and your partner and include it after this sheet. Question 4-6: From your plot, do you conclude that the LED is an ohmic or nonohmic device? Explain why it is or is not. Question 4-7: For one direction of applied voltage, you should have observed almost zero current and the red LED should not have turned on. For the other direction of applied voltage, you should observe a place in your graph where the diode clearly turned on. From the slope of your curve after the LED has “turned on”, what is your conclusion about the resistance of the LED after it has turned on (i.e. is it very large or very small)? What is your conclusion about the resistance of the LED when it is “off”? When you are done with the lab (or if there are only 10 minutes left in the period) answer the two postlab questions on the following page. Also, please put your components and wires back in their plastic bags and tidy things up for the next group of students. Disconnect any voltage probes or current probes that are connected to your electronics board. Disconnect any leads to the power supply. Your TAs can take points off of your lab if you don’t leave your area neat after the lab.

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Post Lab Question 1: Rank the absolute value of the difference in potential (voltage) between each of the pair of points in the circuit below. If the difference in potential is the same for two or more points, place them in the same rank space. Some of the rank spaces may be blank. (Note: all of the resistors have the same resistance.)

B

C + _

_ +

A

D

E

6 V

6 V

A. BA − B. CA − C. CB − D. DC −

E. ED − F. AE − G. CE − Largest 1.______ 2.______ 3.______ 4._______ 5._______ 6.______ 7.______ Smallest Or all have the same difference in potential ______________

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Post Lab Question 2: Rank the absolute value of the difference in potential (voltage) between each of the pair of points in the circuit below. If the difference in potential is the same for two or more points, place them in the same rank space. Some of the rank spaces may be blank. (Note: all of the resistors have the same resistance.)

+ _ D

EA

B

C

F

G

H

6 V

A. BA − B. CB − C. EB − D. HB −

E. ED − F. AC − G. GF − Largest 1.______ 2.______ 3.______ 4._______ 5._______ 6.______ 7.______ Smallest Or all have the same difference in potential ______________