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Unformatted text preview: the DMM. 119 QUANTITATIVE CIRCUIT ANALYSIS (PART B) – 1302Lab4Prob10 120 PROBLEM #11: QUALITATIVE CIRCUIT ANALYSIS You have just become a manager at an engineering firm. The engineers who report to you are constantly describing complex circuits; to pinpoint possible problems with their designs, you have to quickly decide which resistors in the circuits will carry the most current. You have been using a calculator to calculate the current through each resistor, and the process is too slow.. A fellow manager suggests that a purely qualitative analysis could get you reliable results much more quickly. You decide to test the technique on the three circuits below, using identical light bulbs so that the brightness of each bulb indicates which parts of the circuit carry more or less current. You will also do some practice calculations to see if you can get faster. You decide to double-check your work by actually building the circuits. Instructions: Before lab, read the laboratory in its entirety as well as the required reading in the textbook. In your lab notebook, respond to the warm up questions and derive a specific prediction for the outcome of the lab. During lab, compare your warm up responses and prediction in your group. Then, work through the exploration, measurement, analysis, and conclusion sections in sequence, keeping a record of your findings in your lab notebook. It is often useful to use Excel to perform data analysis, rather than doing it by hand. Read Tipler & Mosca Section 25.4 EQUIPMENT You will have batteries, wires, and five identical bulbs that you can connect to make the three circuits shown. Circuit XIV Circuit XV Circuit XVI Note: Check to make sure the light bulbs are all of the same type. To find identical bulbs look for markings on the base and check to see that the color of the bead separating the filament wires is the same. Read the section The Digital Multimeter (DMM) in the Equipment appendix. If equipment is missing or broken, submit a problem report by sending an email to [email protected] Include the room number and brief description of the problem. 121 QUALITATIVE CIRCUIT ANALYSIS – 1302Lab4Prob11 PREDICTIONS You will need to use both qualitative rules and formulas from your text book to make predictions about the brightness of the light bulbs in the circuits under study. The following rules are nothing but consequences of conservation of charge, conservation of energy, and Ohm's law in electric circuits. 1. a) Resistors in series all have the same current flowing through them. b) Resistances in series add. c) The current through a path across a fixed potential difference decreases as the total resistance of the path increases. 2. a) Current divides at a junction. b) The current through each path across the same potential difference depends on the resistance of the path – the larger the resistance, the smaller the current. c) Paths of equal resistance will have the same current. 3. a) Resistors in parallel offer less total resistance than the smallest resistance in the configuration. b) Parallel branches connected directly across a battery are independent – each set of parallel branches has the same potential difference as if it were the only connection to the battery. The above rules will help you predict how the bulbs within each circuit should compare in brightness. Include in each prediction, which rule(s) you used answering the question. Circuit XIV How will the brightness of bulb A compare with the brightness of bulb B? How will the brightness of bulb B compare with the brightness of bulb D? How will the brightness of bulb C compare with the brightness of bulb D? Circuit XV How will the brightness of bulb A compare with the brightness of bulb B? How will the brightness of bulb B compare with the brightness of bulb C? How will the brightness of bulb B compare with the brightness of bulb D? Circuit XVI How will the brightness of bulb A compare with the brightness of bulb B? How will the brightness of bulb B compare with the brightness of bulb C? How will the brightness of bulb B compare with the brightness of bulb D? 122 QUALITATIVE CIRCUIT ANALYSIS – 1302Lab4Prob11 Now, try to rank the circuits by the brightness of bulb A. First decide which quantity the brightness of a bulb depends on. Then construct an equation for this quantity in terms of two variables – the resistance of each bulb, say R, (remember that all the bulbs are identical) and the voltage of each battery, say V (same in each of the three circuits). Begin by finding equivalent resistances of certain parts of the circuits. Gradually simplify each circuit applying appropriate equations to pairs of bulbs in series or in parallel up to the point when you can use qualitative considerations to rank the circuits by the current through bulb A or by the potential difference across this bulb. EXPLORATION Set up each circuit and observe the brightness of the bulbs. How can you test whether minor differences you observe are due to manufacturing irregularities in “identical” bulbs? MEASUREMENT Coordinate w...
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This document was uploaded on 02/23/2014 for the course MANAGMENT 2201 at University of Michigan.

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