Solving the equation may require an integral 98

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Unformatted text preview: cuit 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; (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. 98 CIRCUITS WITH TWO CAPACITORS – 1302Lab4Prob5 8. Complete your solution by determining any arbitrary constants in your solution, using the initial value of the current obtained above. Repeat the above steps for the other two circuits. PREDICTION For each of Circuits IX, X, and XI, draw a graph to qualitatively describe the current through the resistor (or the light bulb) as a function of time after the switch is closed, if the capacitors are initially uncharged. Compare the times it will take for light bulbs to go off in each circuit. For the comparison to be fair, do you think it is important that in each circuit (i) (ii) The resistances of light bulbs are the same, and The light bulb is connected in series with the battery? Having made necessary assumptions for a fair comparison, rank Circuits IX, X, and XI by the time it will take for the bulbs to go off. 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 before you use it and when you are finished using it. Review your exploration from the earlier problem, Charging a Capacitor (PartA). Before you start building a circuit, examine each element of it. How do you know if the battery is "good"? Are the capacitors charged? Carefully connect the two terminals of each capacitor to ensure it is uncharged. Make sure you that have two capacitors of the same capacitance. 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. Check that the polarity of the capacitor’s connection is correct and begin your observations by using bulbs instead of resistors. Build Circuit IX, but do not close the switch. Do you think the bulb will light when the circuit is closed? Record your reasoning in your journal. Close the circuit. Record your 99 CIRCUITS WITH TWO CAPACITORS – 1302Lab4Prob5 observations and explain what you saw using conservation of charge and the concept of potential difference. Build Circuit X, but do not close the switch. Do you think the bulb will light when the circuit is closed? Record your reasoning in your journal. Close the circuit. Record your observations and explain what you saw using conservation of charge and the concept of potential difference. Does it make a difference if you put the bulb in series with of one of the capacitors? Build Circuit XI, but do not close the switch. Do you think the bulb will light when the circuit is closed? Record your reasoning in your journal. Close the circuit. Record your observations and explain what you saw using conservation of charge and the concept of potential difference. Does the order in which you connect the two capacitors and the bulb in the circuit matter? Try following one capacitor with the other capacitor and then the bulb. Now, replace the light bulbs in your circuits with resistors. How can you determine the resistance of the resistor? Is there a way to confirm it? Connect a DMM in each of the circuits and observe how the current changes with time. For each circuit, decide how many measurements you will need to make in order to make a graph of current against time, and what time interval between measurements you will choose. Complete your measurement plan. MEASUREMENT Measure the current in each circuit for as many different times as you deem necessary. Make your measurements using resistors, not bulbs. What are the uncertainties in each of these measurements? ANALYSIS Use your measurements to plot the (measured) values of current as a function of time for circuits IX, X, and XI. CONCLUSION How well did your graphs drawn from your data compare to those in your predictions? Explain any differences. How did your predicted rankings of the time each bulb would remain lit compare to your measurements? Explain any differences. 100 PROBLEM #6: CHARGING A CAPACITOR (PART B) You are an electrical engineer working for a company designing ultrasonic bugrepellent devices. Your group has decided that in order to find the minimum power needed for the ultrasonic emitter to be effective, you should design a circuit in which the current to the emitter falls to half its initial value, then to half of that value, then to half again, all in equal time intervals. They will then observe the insects to see at what point they are no longer repelled. You tell your colleagues that a simple circuit consisting of a capacitor and a resistor in series will have this...
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