Experiment 16: Series and Parallel Circuits Figure 16.1: Series Circuit Figure 16.2: Parallel Circuit 85
86 Experiment 16: Series and Parallel Circuits Figure 16.3: Combination Circuit EQUIPMENT Universal Circuit Board (2) 100- Resistors (2) 200- Resistors (2) 300- Resistors (2) Digital Multi-Meters Power Supply (5) Jumpers (6) Wire Leads
Experiment 16: Series and Parallel Circuits 87 Advance Reading Text: Resistors in series, parallel, combination. Lab Manual: Appendix B Appendix C -DMM Objective The objective of this lab is to study circuits with resistors connected in series, parallel, and combination and to determine the internal resistance of an ammeter. resistor value. The current has more than one path available and takes all available paths. For a parallel circuit, the total equivalent resistance, R eq,is: 1 = 1 + 1 + 1 + + 1 = R eq R 1 R 2 R 3 R N (Resistors in Parallel) NX i=1 1 R i (16.2) Theory In the previous experiment, you constructed 4 circuits, each circuit built with one resistive element. In this experiment, you will construct circuits using multiple resistors. The first type of circuit you will construct is a series circuit (Fig. 16.1 and Fig. 16.4). In a series circuit, the resistors are connected end-to-end such that the current is the same through each resistor: The current has only one path available. The voltage drop across each resistor depends on the resistor value. For a series circuit, the total equivalent resistance, R eq is: R eq = R 1 + R 2 + R 3 + + R N = (Resistors in Series) NX R i (16.1) i=1 Figure 16.5: Parallel Circuit Schematic The third type of circuit you will construct is a combination circuit (Fig. 16.3 and Fig. 16.6). Resistive elements are not connected in series or parallel. To calculate the total equivalent resistance of a combination circuit, it should first be simplified (reduced to an equivalent resistor, R eq ). This is done by choosing resistors that are connected in either series or parallel, one step at a time, adding those elements by use of Eq. 16.1 or Eq. 16.2, then proceeding to the next set of elements. Figure 16.4: Series Circuit Schematic The second type of circuit you will construct is a parallel circuit (Fig. 16.2 and Fig. 16.5). Resistors are said to be in parallel when they are connected to each other at each end. In this way, the potential di erence applied across the combination is the same as the potential di erence applied across an individual resistor. The current through each resistor depends on the Figure 16.6: Combination Circuit Schematic Note that it is not correct to, for example, calculate the resistance of the 3 resistors across the top of the circuit using Eq. 16.1, and then calculate the resistance of R 4, R 5, and R 6 using Eq. 16.2. You must identify which resistors are either in parallel or in series, then apply the appropriate equation one step at a time.
88 Prelab 16: Series and Parallel Circuits Name: 1. What is a series circuit? (10 pts) 2. What is a parallel circuit? (10 pts) 3. Is the equivalent resistance, R eq, of a series circuit greater than or less than any individual resistor? (10 pts) 4. Is the equivalent resistance, R eq, of a parallel circuit greater than or less than any individual resistor? (10 pts) 5. Calculate R eq for each of the first three circuits shown in Fig. 16.4 - Fig. 16.6 using the stated nominal values for resistance. (Show all work on back of this sheet.) (25 pts) 6. You will plot Ivs.V for each of the three circuits on one graph. What value should each slope have (use the stated values for resistance)? (25 pts) 7. Create Data Tables in your lab notebook for all parts of this experiment. Sketch the column headings on the back of this sheet. (10 pts)
Experiment 16: Series and Parallel Circuits 89 PROCEDURE PART 1: Series Circuit Record all data in table format. Recall that (i = 1, 2,..., n) 1. Measure R i, then construct a series circuit (Fig. 16.4) with 100-, 200-, and 300- resistors and ammeter (200 ma DCA); do not connect the power supply yet. 2. Draw the schematic using measured R i s. 3. Calculate R eq. 4. Measure R eq. 5. Connect the unplugged power supply and the voltmeter (DCV) to your circuit. Get instructor approval of your circuit 6. Always be sure the power supply is turned o before you plug it into an outlet. Plug in the power supply, and set the voltage to 1.00 V. Measure the current and voltage. 7. Record the current (A) and the voltage (V) as you increase the voltage in 1.0 V increments up to 4.0 V. 8. Leave the voltage at 4.0 V; disconnect the voltmeter from the power supply. Maintaining the same orientation of the leads (if clockwise, black follows red), measure V i. 9. Add these potential di erences ( P i=1 V i). 10. Does P i=1 V i equal 4.0 V? If not, ask your TA for guidance. PART 2: Internal Resistance of an Ammeter 11. Turn o, then unplug and disconnect the power supply and the ammeter from the circuit. (Note that you will need to insert a jumper when the ammeter is disconnected in order to complete the circuit.) 12. Measure R eq of the circuit. 13. Insert the ammeter (scale: 200 µa DCA) in the circuit. 14. Measure R eq. 15. As you change the scale of the ammeter, measure R eq for each of the ammeter scales (e.g., 2 ma, 20 ma). You will have a total of 8 R eq s. PART 3: Parallel Circuit 16. Repeat Part 1, Step 1 - Step 8, for the parallel circuit (Fig. 16.5). 17. Does V 2 = V 1 + V A, or does V 2 = V 1 = V 3? Are each of these values negative or positive?! Yes, it matters! 18. Does V = V 1 + V A? PART 4: Combination Circuit 19. Repeat Part 1, Step 1 - Step 8, for the combination circuit (Fig. 16.6). PART 5: Graphing 20. Graph Ivs.V for each of the first three circuits on one graph (Part 1, Part 3, and Part 4). 21. Part 5 of this experiment may also be on an exam. Be certain you know how to produce a complete graph. Ask for help if needed. QUESTIONS 1. Why should the voltage drops (electric potential differences) across the resistors connected in parallel be the same? Were your values equal? 2. Calculate the equivalent resistance of each of the first three circuits you constructed for this experiment using your measured values. Show each step in this process (math and schematic). Remember to include R A in your calculations. 3. Consider your data from Part 2. Create a table similar to the one shown below. Why does R eq change when you change the scale of the ammeter? Ammeter Scale R eq R A No Ammeter 20 µa 200 µa 2 ma 20 ma 200 ma 2A 20 A