23SeriesandParallelCirc

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23Series and Parallel CircuitsComponents in an electrical circuit are in series when they are connected one after the other, so that the same current flows through both of them. Components are in parallel when they are in alternate branches of a circuit. Series and parallel circuits function differently. You may have noticed the differences in electrical circuits you use. When using some decorative holiday light circuits, if one lamp burns out, the whole string of lamps goes off. These lamps are in series. When a light bulb burns out in your house, the other lights stay on. Household wiring is normally in parallel.You can monitor these circuits using a Current Probe and a Voltage Probe and see how they operate. One goal of this experiment is to study circuits made up of two resistors in series or parallel. You can then use Ohm’s law to determine the equivalent resistance of the two resistors.objectivesTo study current flow in series and parallel circuits. Hypothesis 1: If we create a series circuit, then the current will be the same through each resistor because of Ohm’s Law. If we create a parallel circuit then the current will not be the same at each resistor because some current will flow along each parallel branch and re-combining when the branches meet again. To study voltages in series and parallel circuits. Hypothesis 2: If we create either a series circuit or a parallel circuit, then by Ohm’s Law, voltage will equal current times total resistanceUse Ohm’s law to calculate equivalent resistance of series and parallel circuits. Hypothesis 3: If we create a series circuit, then by Ohm’s Law, the total resistance can be found by adding up the resistance values of the individual resistors. If we create a parallel circuit, then by Ohm’s Law, the resistance can be found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total.

Series R esistors

Para lle l R esistors

MATERIALScomputer Vernier Circuit Board, orVernier computer interface two 10 resistorsLogger Pro two 51 resistorstwo Vernier Current Probes and two 68 resistors one Vernier Differential Voltage Probe momentary-contact switchlow-voltage DC power supply connecting wires

PRELIMINARY QUESTIONS1. Using what you know about electricity, predict how series resistors would affect current flow. The current is the same through each resistor. What would you expect the effective resistance of two equal resistors in series to be, compared to the resistance of a single resistor? The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors.

Physics with Vernier 23 - 1

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2. Using what you know about electricity, predict how parallel resistors would affect current flow. The current in a parallel circuit breaks up depending on resistance, with some flowing along each parallel branch and re-combining when the branches meet again. What would you expect the effective resistance of two equal resistors in parallel to be, compared to the resistance of one alone? The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total.3. For each of the three resistor values you are using, note the tolerance rating. Tolerance is a percent rating, showing how much the actual resistance could vary from the labeled value. This value is labeled on the resistor or indicated with a color code. Calculate the range of resistance values that fall in this tolerance range.

Labeled resistor value

Tolerance Minimum resistance

Maximum resistance

() (%) () ()

10 5 9.5 10.5

51 5 48.45 53.55

68 5 64.6 71.4

PROCEDUREPart I Series Circuits1. Connect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel 2 of the interface. 2. Open the file “23a Series Parallel Circ” in the Physics with Vernier folder. Current and voltage readings will be displayed in a meter.3. Connect together the two voltage leads (red and black) of the Voltage Probe. Click

, then click to zero both sensors. This sets the zero for both probes with no current flowing and with no voltage applied.4. Connect the series circuit shown in Figure 2 using the 10 resistors for resistor 1 and resistor 2. Notice the Voltage Probe is used to measure the voltage applied to both resistors. The red terminal of the Current Probe should be toward the + terminal of the power supply.

5. For this part of the experiment, you do not even have to click on the button. You can take readings from the meter at any time. To test your circuit, briefly press on the switch to

23 - 2 Physics with Vernier

Figure 2

Series and Parallel Circuits

complete the circuit. Both current and voltage readings should increase. If they do not, recheck your circuit. 6. Press on the switch to complete the circuit again and read the current (I) and total voltage (VTOT). Record the values in the data table.7. Connect the leads of the Voltage Probe across resistor 1. Press on the switch to complete the circuit and read this voltage (V1). Record this value in the data table.8. Connect the leads of the Voltage Probe across resistor 2. Press on the switch to complete the circuit and read this voltage (V2). Record this value in the data table.9. Repeat Steps 5–8 with a 51 resistor substituted for resistor 2.

10. Repeat Steps 5–8 with a 51 resistor used for both resistor 1 and resistor 2.Part II Parallel circuits

11. Connect the parallel circuit shown below using 51 resistors for both resistor 1 and resistor 2. As in the previous circuit, the Voltage Probe is used to measure the voltage applied to both resistors. The red terminal of the Current Probe should be toward the + terminal of the power supply. The Current Probe is used to measure the total current in the circuit.

Figure 312. As in Part I, you can take readings from the meter at any time. To test your

circuit, briefly press on the switch to complete the circuit. Both current and voltage readings should increase. If they do not, recheck your circuit.

13. Press the switch to complete the circuit again and read the total current (I) and total voltage (VTOT). Record the values in the data table.

14. Connect the leads of the Voltage Probe across resistor 1. Press on the switch to complete the circuit and read the voltage (V1) across resistor 1. Record this value in the data table.

15. Connect the leads of the Voltage Probe across resistor 2. Press on the switch to complete the circuit and read the voltage (V2) across resistor 2. Record this value in the data table.

16. Repeat Steps 13–15 with a 68 resistor substituted for resistor 2.17. Repeat Steps 13–15 with a 68 resistor used for both resistor 1 and resistor 2.

Part III Currents in Series and Parallel circuits18. For Part III of the experiment, you will use two Current Probes. Open the

experiment file “23b Series Parallel Circ.” Two graphs of current vs. time are displayed.


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19. Disconnect the Voltage Probe and, into the same channel, connect a second Current Probe.

20. With nothing connected to either probe, click , then click to zero both sensors. This adjusts the current reading to zero with no current flowing.

21. Connect the series circuit shown in Figure 4 using the 10 resistor and the 51 resistor. The Current Probes will measure the current flowing into and out of the two resistors. The red terminal of each Current Probe should be toward the + terminal of the power supply.

Figure 422. For this part of the experiment, you will make a graph of the current measured by

each probe as a function of time. You will start the graphs with the switch open, close the switch for a few seconds, and then release the switch. Before you make any measurements, think about what you would expect the two graphs to look like. Sketch these graphs showing your prediction. Note that the two resistors are not equal. (See prediction in graph #8)

23. Click on the button, wait a second or two, then press on the switch to complete the circuit. Release the switch just before the graph is completed.

24. Select the region of the graph where the switch was on by dragging the cursor over it. Click on the Statistics button, , and record the average current in the data table. Determine the average current in the second graph following the same procedure.

25. Connect the parallel circuit as shown in Figure 5 using the 51 resistor and the 68 resistor. The two Current Probes will measure the current through each resistor individually. The red terminal of each Current Probe should be toward the + terminal of the power supply.

Figure 5



26. Before you make any measurements, sketch your prediction of the current vs. time graphs for each Current Probe in this configuration. Assume that you start with the switch open as before, close it for several seconds, and then open it. Note that the two resistors are not identical in this parallel circuit. (See prediction in graph #16)

27. Click and wait a second or two. Then press on the switch to complete the circuit. Release the switch just before the graph is completed.28. Select the region of the graph where the switch was on by dragging the cursor over it. Click the Statistics button, , and record the average current in the data table. Determine the average current in the second graph following the same procedure.DATA TABLEPart I Series Circuits

Part I: Series circuits

R1

()R2

()I(A)

V1

(V)V2

(V)Req

() VTOT

(V)1 10 10 .0397 .397 .401 20.23 .798

2 10 51 .0276 0.276 1.408 60.74 1.694

3 51 51 .0265 1.351 1.421 101.63 2.712

Part II: Parallel circuits

R1

()R2

()I(A)

V1

(V)V2

(V)Req

() VTOT

(V)1 51 51 .0212 .5423 .5412 25.50 .5405

2 51 68 .0643 1.900 1.869 29.14 1.875

3 68 68 .0465 1.594 1.587 34 1.590

Part III: Currents

R1 ()

R2 ()

I1 (A)

I2 (A)

1 10 51 .0758 .0764

2 51 68 1.231 0.070

ANALYSIS1. Examine the results of Part I. What is the relationship between the three voltage readings: V1, V2, and VTOT? V1 and V2 add up to Vtot.2. Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (Req) of the circuit for each of the three series circuits you tested.3. Study the equivalent resistance readings for the series circuits. Can you come up with a rule for the equivalent resistance (Req) of a series circuit with two resistors? Req = R1 + R24. For each of the three series circuits, compare the experimental results with the resistance calculated using your rule. Percentage errors for pairings 1, 2, and 3 respectively are 3.5%, 2.7%, and 5.1%. In evaluating your results, consider the tolerance of each resistor by using the


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minimum and maximum values in your calculations. The results are consistent with the tolerance of each resistance.5. Using the measurements you have made above and your knowledge of Ohm’s law, calculate the equivalent resistance (Req) of the circuit for each of the three parallel circuits you tested. 6. Study the equivalent resistance readings for the parallel circuits. Devise a rule for the equivalent resistance of a parallel circuit of two resistors. The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total.7. Examine the results of Part II. What do you notice about the relationship between the three voltage readings V1, V2, and VTOT in parallel circuits? They’re all about the same.8. What did you discover about the current flow in a series circuit in Part III? The current is the same through each resistor.9. What did you discover about the current flow in a parallel circuit in Part III? The current in a parallel circuit breaks up depending on resistance, with some flowing along each parallel branch and re-combining when the branches meet again.

10. If the two measured currents in your parallel circuit were not the same, which resistor had the larger current going through it? Why? The resistor with the higher resistance of 68 ohms has a lower current of 0.070 A and the resistor with the lower resistance of 51 ohms has a higher current of 1.231 A. This is because both must have the same voltage, and V=IR.EXTENSIONS1. Try this experiment using three resistors in series and in parallel. (See graph #11 and #15, respectively)2. Try Part III of this experiment using small lamps instead of resistors. Can you explain the change in the shape of the current vs. time graphs? (See graphs #6 and #14) The graphs aren’t linear because light bulbs do not follow Ohm’s law: resistance increases as temperature increases. LO conclusion:1) Our hypotheses answer the lab questions.2) Hypothesis 1 was correct. In the Part III: Currents chart, the first trial represents a series circuit. The currents of resistor 1 and resistor 2, respectively, are 0.0758 and 0.0764. Since these are so extremely close (only a .0006 difference), it is safe to conclude that the current is consistent throughout an entire series circuit. On the other hand, trial 2 represents a parallel circuit. The currents of resistor 1 and 2, respectively, are 1.231 and 0.070. Since these are so much farther apart than the series circuit (a difference of 1.161), it is safe to assume that current is not consistent throughout a parallel circuit. Hypothesis 2 was also correct. Looking at the Part I: Series Circuits chart, the first trial represents a series circuit. When we multiply total resistance (20.23) by current (.0397A), we get 0.803 A. This is only 0.6% off from the actual total voltage (.798V). Thus, we can safely conclude that V=IR in a series circuit. On the other hand, looking at the Part II: Parallel Circuits chart, the first trial represents a parallel circuit. When we multiply total resistance (25.50) by current (.0212A), we get .5406 A. This is less than .01% off from the total voltage (.5405V). Thus, we can safely conclude that V=IR in a parallel circuit. Hypothesis 3 was correct. Looking at the Part I: Series Circuits chart, the first trial represents a series circuit. When we add the resistance values of resistor 1 (10) and resistance 2 (10), we get 20 . This is only 1.1% off from the total resistance (20.23). Thus, we can safely conclude that total resistance in a series circuit is the sum of the resistance values of each resistor. On the other hand, looking at the Part II: Parallel Circuits chart, the first trial



represents a parallel circuit. When we add the reciprocals of the resistance values of resistor 1 (51) and resistance 2 (51), we get (2/51). The reciprocal of this is 25.50. This is 0% off from the measured total resistance (20.50). Thus, we can safely conclude that total resistance in a parallel circuit can be found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total.3) There are three possible sources of error in this lab. For one, the parallel circuit of Part III required three alligator clips on one resistor pin. There really wasn’t enough room for all three, so sometimes the clips didn’t get a solid connection to the resistor pin. As a result, the current and voltage readings would have been skewed. This could be alleviated by using a circuit board with bigger resistor pins. Another possible source of error is that the Vernier readings jumped around every few milliseconds. As a result, we didn’t know which reading to record. This would have skewed our calculations for total voltage and total resistance. This could be alleviated by calling the Vernier phone number and asking costumer service what to do in this situation. A final source of error could be that for the parallel circuit of Part III, we needed to use over ten wires. This got very confusing, and it would have been easy to misconnect a wire. This would have skewed our calculations for total voltage and total resistance. A way to alleviate this is to have numerous people check the circuit setup numerous times. 4. I use a simple series circuit in my everyday life. It’s called a space-heater. Electricity runs from an outlet through a wire and into the unit. Inside is a resistor, which converts some of the electric energy into heat. The rest continues along another wire that runs back into the outlet. In the end, I am comfortably warm on a cold day.


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23SeriesandParallelCirc