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Unformatted text preview: n what was incorrect in those
of your predictions that your laboratory observations or measurements did not support
(or what went wrong with the experiment that failed to verify your prediction). Finally,
use theory and your experimental results from this problem to answer the following
question: Does the current in the circuit change linearly with time? 96 PROBLEM #5: CIRCUITS WITH TWO CAPACITORS
You are modifying the design of a sturdy, low-cost beeper to be used as a safety device
on children’s bicycles. The sound-producing component of the beeper will not pass
current or make noise until after the potential difference across it reaches a certain
value. This component is connected in parallel to the capacitor in an RC circuit. When
the threshold voltage is reached, the capacitor discharges through the sound-producing
component, and then begins to charge again. The time between beeps is thus
determined by the time it takes for the capacitor to charge to a certain value. You wish
to shorten the amount of time between beeps and decide to modify the capacitance.
You don’t want to buy new capacitors because the original ones are extremely cheap
and reliable. You decide to use two of the original capacitors for each beeper. There are
at least two different ways to arrange the capacitors in the circuit: in series with each
other, or in parallel. How would you arrange the capacitors in order to reduce the time
between beeps? In order to understand the quantitative behavior of each circuit, you
decide to make some measurements on the circuits with the sound emitter removed.
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, Sections 24.3 and 25.6. EQUIPMENT
You will build the circuits shown below out of wires, resistors, 2 uncharged capacitors
of equal capacitances, and a battery. To visualize the presence of electric current in the
circuits, you will replace resistors with light bulbs. (Note, however, that you cannot
fairly compare capacitances in the circuits unless the bulbs are identical. Using the
same bulb in all circuits is a possible way to ensure that.) You will have a stopwatch
and a digital multimeter (DMM) for measurements. Circuit IX Circuit X Circuit XI 97 CIRCUITS WITH TWO CAPACITORS – 1302Lab4Prob5
Read the section The Digital Multimeter (DMM) 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
firstname.lastname@example.org. Include the room number and brief description of the
problem. If you are unable to, ask your TA to submit a problem report. WARM UP
1. For each of the circuits, draw a circuit diagram, similar to those shown above. Decide
on the properties of each of the elements of the circuit that are relevant to the problem,
and label them on your diagram. Label the potential difference across each of the
elements of the circuit. Label the current in the circuit and the charge on each
capacitor. What is the relationship between the charges on the two capacitors of
Circuit X? What about the two capacitors of Circuit XI? Under what conditions will
the bulb go out?
2. Write an equation relating the potential difference across each of the elements of the
circuit. What is the relationship between the potential difference across the plates of
each capacitor and the charge stored on its plates? What is the relationship between
the current through a resistor (in the place of each bulb) and the voltage across it? Are
these equations always true, or only for specific times?
3. Explain how each of the quantities labeled on your diagram changes with time. What
is the voltage across each of the elements of the circuit (a) at the instant the circuit is
closed, (b) when the capacitor is fully charged? What is the current through the
resistor at these two times? What is the charge on each of the capacitors at these two
4. From the equations you constructed above, determine an equation relating the
voltage of the battery, the capacitance of each of the capacitors, the resistance of the
resistor, the current through the resistor, and the charge stored on each of the
5. Write an equation relating the rate of charge accumulation on the capacitor plates to
the current through the circuit.
6. Use the equations you have written to get a single equation that relates the current
and the rate of change of current to the known properties of each cir...
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This document was uploaded on 02/23/2014 for the course MANAGMENT 2201 at University of Michigan.
- Spring '14