FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL EXPERIMENT 2 RESISTORS IN SERIES AND PARALLEL 1.0 INTRODUCTION An electric circuit is a complete path from the positive terminal to the negative terminal of a power source. If the elements of the circuit are arranged in such a way that only one path exists for current flow (i.e. the current is identical for all elements), then the circuit is a series one. If an identical voltage exists across a number of alternative current paths then the circuit is a parallel one. Most practical circuits involve various combinations of series and parallel components. Of course components can be connected so that they are neither in series or parallel. Answer the following questions in your lab books: 1. If voltages are identical, then how are the components connected? 2. If currents are identical, then how are the components connected? 2.0 SERIES CIRCUITS 2.1 SERIES CIRCUIT THEORY A typical series circuit is shown in Figure 2.1, this circuit having four resistors and a power source R1 Vs R2 It R4 R3 Figure 2.1 The total resistance Rt in the circuit may be calculated by a simple summation of the individual resistors: Rt = R1 + R2 + R3 + R4 This may be extended for n number of resistors. From Ohm’s Law, the total current in the circuit may be calculated. Vs = ItRt or It = Vs/Rt An important requirement of a series circuit is that the current is identical throughout the circuit. This feature will be observed in this experiment. Dr. Daniel Nankoo 1 of 8 FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL 2.2 REQUIREMENTS FOR SERIES CONNECTION TEST Select the resistors 1k, 820 and 680, and use the DMM to measure their values. Record your results in Table 2.1, which is to be drawn in your lab book. Nominal Resistance R1 = R2 = R3 = Rtot = Measured Resistance % Difference Table 2.1 Connect the resistors in series on your breadboard, and measure the total resistance, Rtot (do not connect the DC power supply yet, and do the % calculations outside lab time). 2.3 VOLTAGE TESTS Draw Table 2.2 in your lab book. Quantity Measured value from DMM Theoretical predictions using DMM values for Vs and R % Difference Vs Rtot VR1 VR2 VR3 IA IB IC ID Table 2.2 DMM V/ COM red black A B R1 = 680 R2 = 820 Vs ≈ 15V C D R3 = 1k Figure 2.2 Connect the variable DC power supply and, using the DMM in voltmeter mode, adjust the output to about 15V. Measure and record the actual value Dr. Daniel Nankoo 2 of 8 FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL from the DMM into Table 2.2. It is essential that this voltage remains unchanged at the recorded value for the entire series test. Figure 2.2 shows the meter connections for measuring the voltage across R1. You will need to reconnect the red and black wires to measure the voltages across the other resistors. 2.4 CURRENT TESTS The next part of the experiment is to measure the current at various points in the circuit. Use the DMM set up in ammeter mode to measure milliamps at the four points A, B, C and D. Note that it will be necessary to break your circuit and remake it in order to insert the ammeter. Record your results in the appropriate fields in Table 2.2 in your lab book. 2.5 COMMENTS AND CONCLUSIONS Discuss the reasons for any differences in Table 2.1. Use Ohm’s Law to calculate the current flowing in the circuit It and hence calculate the voltage drop expected across each resistor (e.g. voltage drop across R1 is calculated as VR1 = ItR1, etc). Use the values as indicated in the third column of Table 2.2. Compare these theoretical values with the measured values and express them as percentage differences using the following formula: (Measured value – Theoretical value)/Theoretical value 100 List the possible reasons for any differences. If any difference is greater than 5%, there could be a serious problem with either your calculations or tests, and checks will be needed. Comment on the sum of the three measured resistor voltages. Is this result consistent with expectations? Also comment on your current measurements. 3.0 PARALLEL CIRCUITS 3.1 THEORY FOR PARALLEL CIRCUITS It DMM AMMETER Ia Vs + RA Ib mA COM RB - red black Figure 3.1 Dr. Daniel Nankoo 3 of 8 FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL A typical parallel circuit is shown in Figure 3.1. Parallel circuits have more than one path for current flow and there must be the identical voltage across all parallel paths. Two such paths exist in the example circuit as shown. The identical voltage appears across all the resistors in the circuit and the current through each arm is inversely proportional to the circuit resistance (from Ohm’s Law). The total current in the circuit is given by It = Ia + Ib (from Kirchoff’s current law). Note the ‘break-then-remake’ method in order to measure the current using an ammeter. By Ohm’s Law: Ia = Vs / RA Ib = Vs / RB These can be substituted into Kirchoff’s Current Law equation to give: It = Vs(1/RA + 1/RB) = Vs((RA)-1 + (RB)-1) = Vs(RARB)/[RA + RB]) The term RARB / (RA + RB) expresses the total value of resistance (Rt = Vs / It) in the circuit. In practice the inverse form, (Rt)-1 = (RA)-1 + (RB)-1, is often simpler to work with as a calculator’s inverse button (x-1) can be used thus reducing the amount of resistance data inputting. In addition this inverse form is directly extendable to any number of resistors. 3.2 REQUIREMENTS FOR PARALLEL TESTS The following tables are to be drawn into your lab books. Nominal Resistance R4 = 1.5k R5 = 1.5k R6 = 2.7k Rtoti Rtotii Rtotiii Measured Resistance Calculated Resistance from measured V/I ratio Table 3.1: Parallel Circuit Components Quantity Vs VR4 Ia Ib Measured Value from DMM Calculated Values Table 3.2: Parallel Circuit – 1 Resistor Dr. Daniel Nankoo 4 of 8 FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL Quantity Vs VR4 VR5 Ia Ib Ic Measured Value from DMM Calculated Values Table 3.3: Parallel Circuit -2 Resistors Quantity Vs VR4 VR5 VR6 Ia Ib Ic Id Measured Value from DMM Calculated Values Table 3.4: Parallel Circuit – 3 Resistors Select the resistors R4, R5 and R6 as listed in Table 3.1. Use the DMM to measure their values and record your results in Table 3.1. 3.3 ONE RESISTOR IN PARALLEL WITH VOLTAGE SOURCE b Vs ≈ 10V + R4 a Figure 3.2i Connect the circuit as shown in Figure 3.2i with only R4 in the circuit. Use the DMM’s voltmeter in order to ensure that the DC power supply is set to about 10V. It is essential that this voltage remains unchanged at the recorded value for the entire parallel test. Disconnect the DMM and reset it as an ammeter. Use the ‘break-then-make’ method (Figure 3.1) to measure and record the currents flowing at points a and b. Then use the DMM to measure and record the voltage across R4. Enter your results in your lab book in Table 3.2. Dr. Daniel Nankoo 5 of 8 FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL 3.4 TWO RESISTORS IN PARALLEL Add resistor R5 to your circuit, so that it is in parallel with R4, as shown in Figure 3.2ii. Measure the resistance of the (R4R5) combination, remembering that when the DMM measures resistances, power to your circuit must be off. Measure the currents through points a, b and c, and the voltages across R4 and R5. Record all your results in Table 3.3. b + Vs ≈ 10V c R4 R5 a Figure 3.2ii 3.5 TESTS ON THREE RESISTORS IN PARALLEL b Vs ≈ 10V + R4 d c R5 R6 a Figure 3.2iii Add R6 to the circuit as shown in Figure 3.2iii. Use the DMM to measure the total resistance, Rtotiii and record it in Table 3.1. Then, using the DMM connected in the correct configuration, measure and record all the currents and voltages associated with this circuit, recording your results in your lab books in Table 3.4. 3.6 COMMENTS AND CONCLUSIONS This is to be done outside lab time. Carry out the calculations to complete Tables 3.1 to 3.4. Check your results in the event of any serious discrepancy between theory and practice. Comment on the relation between your measured V and I results and the voltage and current principles of the parallel connection. Dr. Daniel Nankoo 6 of 8 FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL 4.0 SERIES – PARALLEL CIRCUITS 4.1 THEORY FOR SERIES-PARALLEL CIRCUITS Many circuits consist of resistor networks, in which series and parallel connections appear. Such a circuit is shown in Figure 4.1. The theory required derives directly from that for the series and parallel tests. R8 I8 I7 R7 I9 Vs ≈ 10V R9 + IA A Figure 4.1 The total resistance in this case is a combination of series and parallel principles. 4.2 REQUIREMENTS FOR TESTS Draw the following tables into your lab books. Nominal Resistance R7 = 820 R8 = 680 R9 = 680 Rtot Resistance DMM Measured by Resistance calculated from V/I ratio Table 4.1 Quantity Vs V7 V8 V9 IA I7 I8 I9 DMM Measurement Calculated Values % Difference Table 4.2 Select the resistors R7, R8 and R9 listed in Table 4.1 and use the DMM to measure their values, recording your results. Now connect the three resistors in the series-parallel configuration shown in Figure 4.1 on your breadboard. Measure their total value Rtot, and record this result (do not connect the DC power supply yet). Dr. Daniel Nankoo 7 of 8 FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL 4.3 TESTS FOR SERIES-PARALLEL CIRCUIT Connect the power supply and using the DMM in voltmeter mode, adjust the output so that Vs is about 10V. Record the DMM reading. As before, it is essential that this voltage remains unchanged at the recorded value for the entire test. Change the DMM connections and thus measure and record the voltage drops across each of the three resistors. Reconfigure the DMM in order to measure current and reconnect it as an ammeter at point A, noting the ammeter wiring principle indicated in Figure 3.1. Then, still using the ‘break-then-make’ principle, reconnect it to measure the currents through the three resistors. Record all your results in Table 4.2. Based on your observations, why do you think that an ammeter must always be connected in series with a resistor and never in parallel? You should consider that the DMM has an internal resistance when thinking of an answer to this question. 4.4 COMMENTS AND CONCLUSIONS This is to be done outside of the lab time. Carry out the necessary calculations to complete Tables 4.1 and 4.2. Check your results in the event of any serious discrepancy between theory and practice. Comment on the relation between your measured results and the voltage and current principles of the series and parallel connections. 5.0 GENERAL POINTS Before leaving the lab, ensure that your work has been signed by a member of staff. When handing in your work, this signature must be present in order to get a mark. Your write up should contain three aspects: i) An outline of what you did in the lab (its aim, theory, method, equipment and results using data tables and graphs) ii) Theoretical calculations. Make sure your methods are clear by providing a single, typical example worked out with detailed steps for each method. Just give the end results of other calculations that use the same method. iii) Conclusions, comments, calculations on what principles are demonstrated by the data obtained and any comparisons between theory and practice. The first part is relatively straight forward, but it is the second and third parts that are important as they help to develop your engineering competence. Some suggestions have been made above, but you should extend these making reference to series, parallel, Ohm’s Law and Kirchhoff’s Laws where appropriate. Dr. Daniel Nankoo 8 of 8

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# Experiment 2: Resistors in Series and Parallel