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uncertainty see the appendices Significant Figures and Accuracy, Precision and
Uncertainty) Does the equipment contribute any? Do you? Be specific in explaining
how and why. 111 RESISTORS AND LIGHT BULBS – 1302Lab4Prob8 112 PROBLEM #9: QUANTITATIVE CIRCUIT ANALYSIS
(PART A)
As a member of the safety group for the space shuttle scientific program, you have been
asked to evaluate a design change. In order to improve the reliability of a circuit for the
next shuttle flight, a navigation electronics team has suggested adding a second battery.
The proposed design is shown below. You worry about the heat generated by the
circuit since it will be located next to an experiment that uses liquid oxygen. Your
manager asks you to calculate the rate of thermal energy output by the proposed circuit.
As a first step, you decide to calculate the current through each resistor. You consult
with the team to build a prototype circuit and test your calculation.
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 25.5. Pay attention to the examples 2510, 2514 and 2516. EQUIPMENT
Build the circuit shown to the right with
wires, resistors, and a voltage source
(batteries or a power supply).
You have a digital multimeter (DMM) for
measuring resistance, current and voltage. R1
+
 V2 V1 + R3 R2 C ircuit XII
Read the sections The Digital Multimeter (DMM) and Resistor Codes in the Equipment
appendix.
Read the appendices Significant Figures, Review of Graphs and Accuracy, Precision
and Uncertainty to help you take data effectively.
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. 113 QUANTITATIVE CIRCUIT ANALYSIS (PART A) – 1302Lab4Prob9 WARM UP
1. Draw a circuit diagram, labeling all voltages and resistances. For this problem, the
voltages and the resistances are the known quantities and the currents in the resistors
are the unknowns.
2. Assign a separate current for each leg of the circuit, indicating each current on the
diagram. Identify the number of circuit paths (loops) and label them on the diagram.
3. Apply conservation of current to each point in the circuit at which wires come
together (a junction). Use conservation of energy to get the sum of the potential
differences across all of the elements in each loop, ensuring your signs are correct.
Does the potential difference increase or decrease across each circuit element, in the
direction you have chosen to traverse the loop? Use Ohm's law to get the potential
difference across each resistor.
Check that the number of equations you wrote above matches the number of
unknowns.
4. Complete the calculations and write your solution. Simplify your equations as much
as possible, but be warned that your final solutions may look quite complicated. PREDICTION
To predict currents through resistors in the circuit under study, you will need to use
Kirchoff’s laws. The goal is to derive theoretical formulas for the currents. Once you
have the formulas, you can plug in the parameters of your circuit, such as voltages of
the batteries and resistances of resistors, and calculate the currents. These (predicted)
values will be compared with the currents measured in the experiment. EXPLORATION
If necessary, read about how to use the DMM in the Equipment appendix. Pay special
attention to the connections and settings that are used to measure voltages and currents,
and why the DMM should be connected in the circuit differently for voltage and current
measurements. Do you know why we should connect them in these ways?
Build Circuit XII. How can you tell if there is current flowing through the circuit?
What happens to the current at each junction? What is the resistance of each resistor?
What is the potential difference provided by each of the batteries? What is the potential
difference across each resistor? Use the DMM to check your answers to each of these
questions. 114 QUANTITATIVE CIRCUIT ANALYSIS (PART A) – 1302Lab4Prob9
Complete your measurement plan. MEASUREMENT
Measure the resistance of the resistors, the current flowing through each resistor and
the potential difference provided by each battery in the circuit. So that you can check
your measurements, measure the potential difference across each resistor. ANALYSIS
Calculate the current through each resistor from your prediction equations, using your
measured values of the resistance of each resistor and voltage of each battery. Compare
those results to the measured va...
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This document was uploaded on 02/23/2014 for the course MANAGMENT 2201 at University of Michigan.
 Spring '14

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