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Unformatted text preview: estion 10. If not, you should answer the warm-up
questions 2-9 first.
2. Draw a circuit diagram, similar to the one 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 the capacitor.
3. Use energy conservation to write an equation relating the potential differences across
all elements of the circuit. Write an equation relating the potential difference across
the capacitor plates and the charge stored on its plates. What is the relationship
between the current through the resistor and the voltage across it? Are these three
equations always true, or only for specific times?
4. Describe qualitatively how each quantity labeled on your diagram changes with time.
What is the voltage across each element of the circuit (a) at the instant the circuit is
closed; (b) when the capacitor is fully charged? What is the current in the circuit at
these two times? What is the charge on the capacitor plates at these two times?
5. From the equations you constructed above, determine an equation relating the
voltage of the battery, the capacitance of the capacitor, the resistance of the resistor, the
current through the circuit, and the charge stored on the capacitor plates.
6. Write an equation relating the rate of charge accumulation on the capacitor plates to
the current through the circuit.
7. 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 circuit element. To
do this, you may find it helpful to differentiate one of your equations.
8. Solve the equation from step 6 by using one of the following techniques: (a) Guess the
current as a function of time, which satisfies the equation, and check it by substituting
your current function into your equation; (b) Get all the terms involving current on
one side of the equation and time on the other side and solve. Solving the equation
may require an integral. 106 CHARGING A CAPACITOR (PART C) – 1302Lab4Prob7
9. Complete your solution by determining any arbitrary constants in your solution,
using the initial value of the current you obtained in question 3.
10. Using your equation for the current, find the time it takes for the current to fall to
half its initial value. Sketch a graph of this time against the resistance of the resistor. PREDICTION
For a circuit consisting of a battery, a capacitor (initially uncharged), and a resistor, all
in series, how does the time it takes for the current in the circuit to fall to half its initial
value depend on the resistance of the resistor?
Use your calculation to graph the time it takes for the current to fall to half its initial
value against the resistance of the resistor. EXPLORATION
WARNING: A charged capacitor can discharge quickly producing a painful spark. Do
not handle the capacitors by their electrical terminals or connected wires by their metal
ends. Always discharge a capacitor when you are finished using it.
Before you build the circuit, examine each element of it. How do you know if the
battery is "good"? Is the capacitor charged? Carefully connect the two terminals of the
capacitor to ensure it is uncharged. How can you determine the resistance of the
resistor? Is there a way to confirm it?
If you have completed Charging a Capacitor (PartA) or (PartB), review your
exploration notes from your lab journal.
Note: Make sure the + terminal of the battery is connected to the + terminal of the
capacitor! These capacitors are only designed to charge one way. If you connect the
capacitors up the wrong way, the capacitance will change in an unpredictable manner.
Construct Circuit VIII, including a DMM in the circuit to measure the current. Check
that the polarity of the capacitor’s connection is correct and begin your experiment.
Close the circuit and observe how long it takes for the current in the circuit to halve.
How does changing the capacitance of the capacitor or the resistance of the resistor
affect this time? Choose a capacitor and a range of resistances that allow you to
effectively construct a graph and test your prediction. Complete your measurement
plan. 107 CHARGING A CAPACITOR (PART C) – 1302Lab4Prob7 MEASUREMENT
Measure the time taken for the current in the circuit to halve in value for different
resistances in the circuit. Be sure to make at least two measurements for each resistor. ANALYSIS
Construct a graph of the measured times it takes the current to halve against resistance,
using your experimental data. CONCLUSION
Compare your prediction graph with your graph showing your data. Explain any
How does the time taken for the current in the circuit to halve in value depend upon the
resistance of the charging circuit? Does this time depend upon the voltage of the
battery? If yes, then how?
What are possible sources of systematic uncertainty in...
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This document was uploaded on 02/23/2014 for the course MANAGMENT 2201 at University of Michigan.
- Spring '14