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23 Series and Parallel Circuits Components in an electrical circuit are in series in series when they are connected one after the other, so that the same current flows through through both of them. Components are in parallel in parallel when 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 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 a nd 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. objectives To 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 resistance Use 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 resistor resistors. s. If we create a parallel circuit, then by Ohm’s Law, the resistance can be found by adding a dding up the reciprocals of the resistance values, and then taking the reciprocal of the total. total .
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MATERIALS computer Vernier Circuit Board, or Vernier computer interface two 10 Ωresistors Logger Pro Pro two 51 Ωresistors two Vernier Current Probes and two 68 Ωresistors one one Vern Vernie ierr Diff Diffeerent rentia iall Volt Voltag agee Prob Probee mome moment ntar aryy-co cont ntac actt swit switch ch low-voltage DC power supply connecting wires PRELIMINARY QUESTIONS 1. Using Using what what you you know know about about elect electric ricit ity, y, pred predict ict how serie seriess resis resistor torss woul would d affec affectt curre current nt flow. The current is the same through each resistor . What would you expect the effective effective resistance of two equal resistors resistors in series to be, compared to the resistance of a single resistor? resistor? The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors resistors.. 2. Using Using what what you you know know about about elect electric ricit ity, y, pred predict ict how parall parallel el resis resistor torss woul would d affe affect ct curr current ent flow. The current in a parallel circuit breaks up depending on resistance, with some flowing along Physics with Vernier
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each parallel branch and re-combining when the branches meet again. What would you expect the effective 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 For eac each h of the the thr three ee resi resist stor or val value uess you you are are usin using g, not notee the thetolerance 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 Tolerance Minimum Maximum value resistance resistance (Ω) (%) (Ω) (Ω) 10
5
9.5
10.5
51
5
48.45
53.55
68
5
64.6
71.4
PROCEDURE Part I Series Circuits 1. Conn Connec ectt the the Curr Curren entt Prob Probee to Chan Channe nell 1 and and the Diff Differ eren enti tial al Vol Volta tage ge Pro Probe be to to Chan Channe nell 2 of the interface. 2. Open pen the the fil file “23 “23aa Se Series ies Par Paral alle lell Ci Circ” in the Physics he Physics with Vernier folder. Vernier folder. Current and voltage readings will be displayed in a meter. 3. Conn Connec ectt toge togeth ther er the the two two vol voltag tagee lead leadss (red (red and and blac black) k) of of the the Vol Volta tage ge Pro Probe be.. Clic Click k , then click to zero both sensors. This sets the zero for both probes with no current flowing and with no voltage applied.
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4. Conn Connec ectt the the ser serie iess cir circu cuit it sho shown wn in Figu Figure re 2 usi using ng the the 10 10 Ωresistors resistors for resistor 1 and resistor 2. Notice 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. supply. 5. For For this this part part of the the expe experi rime ment nt,, you you do not not even even have have to clic click k on the the butt button on.. You 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. 6. Pres Presss on on the the swi switc tch h to to com compl plet etee the the cir circu cuit it aga again in and and rea read d the the cur curre rent nt I ( ) and total voltage (V TOT TOT). Record the values in the data table. 7. Connec Connectt the the leads leads of of the the Vol Voltag tagee Probe Probe across across resis resistor tor 1. Pres Presss on on the the swi switch tch to comp complet letee the circuit and read this voltage (V (V 1). Record Record this value in the data table. 8. Connec Connectt the the leads leads of of the the Vol Voltag tagee Probe Probe across across resis resistor tor 2. Pres Presss on on the the swi switch tch to comp complet letee the circuit and read this voltage (V (V 2). Record Record this value in the data table. 9. Repeat St Steps 5–8 with a 51 Ωresistor substituted substituted for resistor 2. 10. Repeat St Steps 5–8 with a 51 Ωresistor used for both resistor 1 and resistor 2. Part II Parallel circuits 11. 11. Conne Connect ct the the par paral alle lell cir circu cuit it show shown n bel below ow using g 51 Ωresistors for both resistor 1 Figure 2 usin and resistor 2. As in the previous circuit, the Voltage Probe is used to measure the voltage applied to both resistors. The The red terminal of the Current Probe should be toward the + terminal of the power supply. supply. The Current Probe is used to measure the total current in the circuit.
Figure 3 12. 12. As in in Part Part I, you you can take take read reading ingss from from the the mete meterr at any time. time. To tes testt your your cir circui cuit, t, briefly press press on the switch to complete the circuit. Both current an d voltage readings should increase. If they do not, recheck your circuit. 13. 13. Press Press the switc switch h to to compl complete ete the the circu circuit it agai again n and read read the the tota totall curre current nt I (I ) and total voltage (V (V TOT TOT). Record the values in the data table. 14. 14. Connec Connectt the leads leads of of the the Volt Voltage age Prob Probee across across resis resistor tor 1. 1. Pre Press ss on on the swit switch ch to to complete the circuit and read the voltage (V (V 1) across resistor 1. Record Record this value in the data d ata table. 15. 15. Connec Connectt the leads leads of of the the Volt Voltage age Prob Probee across across resis resistor tor 2. 2. Pre Press ss on on the swit switch ch to to complete the circuit and read the voltage (V (V 2) across resistor 2. Record Record this value in the data table. 16. Repeat St Steps 13 13–15 –15 with a 68 Ωresistor substituted for resistor 2. 17. Repeat St Steps 13 13–15 –15 with a 68 Ωresistor used for both resistor 1 and resistor 2. Part III Currents in Series and Parallel circuits 18. 18. For Part Part III III of of the the exper experime iment, nt, you you wil willl use use two two Curre Current nt Probe Probes. s. Ope Open n the experiment file “23b Series Parallel Circ.” Two graphs of current vs. time are displayed.
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19. 19. Disco Disconne nnect ct the the Volt Voltage age Probe Probe and, and, into into the same same chann channel el,, conne connect ct a secon second d Current Probe. 20. 20. With With nothin nothing g connec connected ted to eithe eitherr probe probe,, click click , then then click click to zero zero both sensors. This adjusts the current reading to zero with no current flowing. flowing. 21. 21. Conn Connec ectt the the seri series es cir circu cuit it sho shown wn in Fig Figur uree 4 usi using ng the the 10 10 Ωresistor and the 51 Ω resistor. 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 4 22. 22. For this this part part of of the the exper experime iment, nt, you you wil willl make make a grap graph h of the the curre current nt measu measured red by 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 Click on the button button,, wait wait a second second or two, two, then then press press on the swit switch ch to complete the circuit. Release the switch switch just before the graph is completed. 24. Select Select the reg region ion of of the the graph graph wher wheree the swit switch ch was was on on by draggi dragging ng the the curso cursorr over over it. Click on the Statistics button, , and record the average current current in the data table. table. Determine Determine the average current in the second graph following the same procedure. 25. 25. Conn Connec ectt the the para parall llel el cir circui cuitt as sho shown wn in Fig Figur uree 5 usi using ng the the 51 51 Ωresistor and the 68 Ωresistor. 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. 26. Before Before you you make make any measur measureme ements nts,, sket sketch ch your your predi predicti ction on of of the the curre current nt vs. time graphs for each Current Probe in this configuration. Assume that you start with the switch open as
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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 Click and wait wait a secon second d or two. two. Then Then press press on the swit switch ch to comple complete te the circuit. Release the switch just before the graph is completed. 28. Selec Selectt the reg region ion of of the the graph graph wher wheree the swi switch tch was was on on by dragg dragging ing the the curs cursor or over over it. it. Click the Statistics Statistics button, , and record the average average current current in the data table. Determine Determine the the average current in the second graph following following the same procedure. DATA TABLE Part I Series Circuits Part I: Series circuits R 1 (Ω)
R 2 (Ω)
I (A)
V1 (V)
V2 (V)
R eq eq (Ω)
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 R 1 (Ω)
R 2 (Ω)
I (A)
V1 (V)
V2 (V)
R eq eq (Ω)
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 R 1 (Ω)
R 2 (Ω)
I1 (A)
I2 (A)
1
10
51
.0758
.0764
2
51
68
1.231
0.070
ANALYSIS 1. Examin Examinee the the res result ultss of of Part Part I. What What is is the the rela relation tionshi ship p bet betwe ween en the the thre threee volt voltage age reading readings: s: V 1, V 2, and V TOT TOT? V1 and V2 add up to Vtot. 2. Usin Using g the the mea measu sure reme ment ntss you you have have mad madee abov abovee and and your your kno knowl wled edge ge of of Ohm Ohm’s ’s law law,, calculate the equivalent resistance ( R Req) of the circuit for each of the three series circuits you tested. 3. Study Study the equiva equivale lent nt resis resistan tance ce read reading ingss for for the serie seriess circ circuit uits. s. Can you come come up with with a rule for the equivalent resistance ( R Req) of a series circuit with two resistors? resistors? Req = R1 + R2 4. For each each of the three three ser series ies circuit circuits, s, compar comparee the the expe experim riment ental al resul results ts with with the resis resistan tance ce 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 minimum and maximum values in your calculations. The results are consistent with the tolerance of each resistance.
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5. Usin Using g the the mea measu sure reme ment ntss you you have have mad madee abov abovee and and your your kno knowl wled edge ge of of Ohm Ohm’s ’s law law,, calculate the equivalent resistance ( R Req) of the circuit for each of the three parallel para llel circuits you tested. 6. Study Study the equiva equivale lent nt resis resistan tance ce read reading ingss for for the parall parallel el circ circuit uits. s. Devis Devisee a rule rule for for the the equivalent resistance of a parallel circuit of two resistors. 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. Exam Examine ine the the res resul ults ts of of Par Partt II. II. What What do do you you noti notice ce abo about ut the the rel relat atio ions nshi hip p betw betwee een n the three voltage readings V 1, V 2, and V TOT TOT in parallel circuits? They’re all about the same. 8. What What did did you you dis disco cove verr abou aboutt the the curr curren entt flow flow in a ser serie iess circ circui uitt in Par Partt III? III?The The current is the same through each resistor . 9. What What did did you you dis disco cove verr abou aboutt the the curr curren entt flow flow in a para parall llel el cir circu cuit it in in Part Part III 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. 10. If the the two two measu measured red curre currents nts in in your your parall parallel el circui circuitt were were not not the same same,, which 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 of 0.070 A and the resistor with the lower resistance of 51 ohms has a higher current of 1.231 A. A. This is because both must have the same voltage, and V=IR V=IR.. EXTENSIONS 1. Try Try thi thiss exp exper erim imen entt usin using g thr three ee res resis isto tors rs in in ser serie iess and and in para parall llel el.. (See graph #11 and #15, respectively) 2. Try Try Part Part III III of this this expe experim riment ent usin using g smal smalll lamps lamps inst instead ead of of res resist istors ors.. Can Can you you expla explain in the 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 resistance increases as temperature increases. LO conclusion: 1) Our hypotheses answer the lab questions. 2) Hypothesis Hypothesis 1 was correct. In the Part III: Currents Currents chart, the first trial represents a series circuit. The currents of resistor 1 and resistor 2, respectively, respectively, are 0.0758 and 0.076 0.0764. 4. Since these are so extremely close (only a .0006 difference), 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, respectively, are 1.231 and 0.070. Since these are so much farther apart than the series circuit (a differe difference nce of 1.161), it is safe to assume that current is not consistent throughout a parallel circuit. Hypothesis 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 (20.23Ω) by current (.0397A), we get 0.803ΩA. This is only 0.6% off from from the actual total voltage (.798V). (.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. (25.50 50Ω) by current (.0212A), we get .5406ΩA. This is less than .01% off from the total voltage (.5405V). (.5405V). Thus, we can safely conclude that V=IR in a parallel circuit. Hypothesis Hypothesis 3 was correct. Looking at the Part I: Series Series Circuits chart, the first trial represents a series circuit. When we add the resistance values of resistor 1 (10Ω) and resistance 2 (10Ω), we get 20Ω. This is only 1.1% off from the total resistance (20.23Ω). 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 (51Ω) and resistance 2 (51Ω), we get (2/51Ω). The reciprocal of this is 25.50Ω. This is 0% off from the measured total resistance (20.50Ω). 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.
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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 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 This could be alleviated by using a circuit board with bigger resistor resistor pins. Another possible source of error is that the Vernier readings jumped around every few milliseconds. milliseconds. As a result, we didn’t know which reading to record. This would have skewed skewe d our calculations for total voltage and total resistance. This could be alleviated by calling the Vernier phone number and asking costumer costumer service what to do in this situation. A final source of error could be that for the parallel circuit of Part III, we we needed to use over ten wires. This got very confusing, confusing, and it would have been b een 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 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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