To do this you may find it helpful to differentiate

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Unformatted text preview: through the circuit, and the charge stored on the capacitor plates. 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 circuit element. To do this, you may find it helpful to differentiate one of your equations. 7. 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. 8. Complete your solution by determining any arbitrary constants in your solution, using the initial value of the current you obtained in question 3. PREDICTION When the circuit is closed, with the capacitor initially uncharged, how does the current in the circuit change with time? How long does it take for the current to fall to zero? 94 CHARGING A CAPACITOR (PART A) – 1302Lab4Prob4 Sketch a graph of current against time for this circuit, assuming the capacitor is initially uncharged. 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. To discharge a capacitor, use an insulated wire to briefly connect one of the terminals to the other. If you have not done so, read about using 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? 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. Examine each element of the circuit before you build it. 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? After you are convinced that all of the circuit elements are working and that the capacitor is uncharged, build the circuit with a light bulb in place of the resistor, but leave the circuit open. Close the circuit and observe how the brightness of the bulb changes with time. What can you infer about the way the current in the circuit changes with time? From what you know about a battery, how does the potential difference (voltage) across the battery change over time? Check this using the DMM set for potential difference (Volts). From your observations of the brightness of the bulb, how does the potential difference across the bulb change over time? Check this using the DMM. What can you infer about the change of voltage across the capacitor over time? Can you check with a DMM? Use the concept of potential difference to explain what you observe. Now, discharge the capacitor, and reconnect the DMM in such a way that it measures the current in the circuit. Close the circuit and observe how the current changes with time? Is it as you expected? How long does it take for the current to fall to zero? 95 CHARGING A CAPACITOR (PART A) – 1302Lab4Prob4 Replace the light bulb with a resistor. Qualitatively, how will changing the resistance of the resistor and the capacitance of the capacitor affect the way the current in the circuit changes with time? How can you test this experimentally? Build the circuit, including a DMM in the circuit to measure the current. 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 value and a range of resistances that allow you to most effectively construct a graph to test your prediction. Complete your measurement plan. MEASUREMENT Measure the current flowing through the circuit for as many times as you deem necessary. Make your measurements using a resistor, not a bulb. What are the uncertainties in each of these measurements? ANALYSIS Use your measured values for the resistance of the resistor, the capacitance of the capacitor, and the voltage of the battery, along with your prediction equation, to construct a graph of your predicted current against time. Make a graph of the measured current flowing through the circuit against time. Compare these two graphs, noting any similarities and explaining any differences. CONCLUSION Describe which of your predictions were confirmed by experiments and draw conclusions accordingly. To continue conclusions, explai...
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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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