Instructions before lab read the laboratory in its

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Unformatted text preview: property. They are unconvinced, so you decide to demonstrate to them that the time required for the current in the circuit to decrease to half its value is independent of the time that you begin measuring the current. You build a circuit consisting of a battery, a capacitor (initially uncharged), and a resistor, all in series in order to demonstrate this property. 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, Section 25-6. EQUIPMENT Build the circuit shown below using wires, resistors, capacitors, and batteries. Use the accompanying legend to help you build the circuits. You will also have a stopwatch and a digital Circuit VIII multimeter (DMM). \ 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 labhelp@physics.umn.edu. Include the room number and brief description of the problem. If you are unable to, ask your TA to submit a problem report. 101 CHARGING A CAPACITOR (PART B) – 1302Lab4Prob6 WARM UP 1. If you have done Charging a Capacitor (PartA), you will already have the equation that describes the way in which the current in the circuit changes with time and depends upon the capacitance of the capacitor and the resistance of the resistor. You should skip to Warm-up question 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. 102 CHARGING A CAPACITOR (PART B) – 1302Lab4Prob6 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 taken for the current to fall to half its initial value. Now find the time taken for the current in the circuit to halve again, and so on. How does the time for the current to be cut in half depend on the amount of time after the circuit was closed? PREDICTION In a circuit consisting of a battery, a capacitor (initially uncharged), and a resistor, all in series, calculate the time it takes for the current to fall to half its initial value. Sketch a graph of current against time for this circuit, assuming the capacitor is initially uncharged. Indicate on your graph the time taken for successive halving of the current in the circuit (the time at which the c...
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