Name: Partner: Date: RC Circuit Analysis Lab Experiment t RC

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1 Name: Partner: Date: RC Circuit Analysis Lab Experiment t RC VC () t = VS + ( VC, initial VS ) e ε A 0 q C = C = τ = ReqC d V 1. Solve the V C (t) equation above for t. 2. Solve the V C (t) equation above for R. t e -t/τ 1 - e -t/τ 1τ τ τ τ τ Solve the V C (t) equation above for C. Suppose in the circuit above that C = 0.1 μf, R = 25KΩ, and V S = 12V. When the switch is pushed to the left, the capacitor charges. When the switch is pushed to the right, it discharges. When the switch is in the middle, neither circuit is complete. 4. Calculate the time constant for the RC circuit. State your response using appropriate SI prefixes. 5. Suppose you push the switch to the left and the capacitor voltage is zero initially. a. What is V S for this situation? b. How long will it take for the capacitor to charge to 99.3% of V S? c. Suppose you discharge the capacitor completely by switching right. How long will it take for the capacitor to charge to 6V when you switch to the left again?

2 d. Now that the capacitor is charged to 6V, how long will it take to go from 6V to 9V? 6. Now suppose that someone switches out the resistor to another unknown value. Assuming the capacitor is still charged to 9V from the last problem, suppose you flip the switch to the right and you find that it takes 1.3 seconds to drop to 1V. What is the value of R? 7. Now suppose someone swaps in a new uncharged capacitor and the original resistor. If it takes 22 ms to charge to 86.5% of the source voltage, what is the value of the capacitor? Solve this problem two ways, please. 8. Now choose a partner and choose a resistor and capacitor from the bins with an RC value in the 3 10 second range. Show your calculations and record your values below. R = Partner = C = τ = SAFETY PRECAUTIONS: WEAR SAFETY GOGGLES If you use an electrolytic capacitor, make sure it has an appropriate voltage rating and that you place the negative lead toward the low voltage side of your circuit. 9. Using a 9V battery w/ clip, alligator clips, a single-pole-double-throw (SPDT) knife switch, and your resistor and capacitor, build your circuit. Use a DMM to measure your resistor value and battery level before you put them into the circuit. Quickly check your circuit to see the capacitor charges and discharges properly (use voltmeter to watch V C ). Battery voltage: Measured R value: Check V C charge/discharge:

3 10. Use Vernier Data Logger & TI to collect 200 data samples for V R Charging/Discharging: a. Get a Vernier Data Logger & TI-84 and an analog voltage probe. b. Make sure the data cable is plugged between the top of the TI and the bottom of the Data Logger (push into the small round jack completely at both ends). c. Turn ON the TI. d. Plug in a voltage probe into one of the analog channels 1 4 (CH1 CH4). e. Press APPS, scroll down to EasyData, and press ENTER. Now the EasyData app should come up on the screen and show CHx:Voltage +/- 10V with a real-time voltage reading. At the bottom of the screen you will see 5 tabs that correspond to the 5 buttons along the top of your TI. f. Touch the probes to the terminals of your 9V battery and record your battery voltage. V battery = g. Connect the red and black leads to read the voltage across the resistor (V R ). h. For technical reasons we are unable to read the voltage across the capacitor with the TI/Vernier, but you will monitor that voltage using your DMM (set up your DMM to monitor V C now). i. How long will it take your RC circuit to charge (or discharge) to 99.3% of it s maximum (minimum) value? What are max in min V C values and what position should the switch be in to achieve these values? Time to charge (or discharge) 99.3%: Maximum V C possible in this circuit: Switch position: Voltage rating of capacitor (higher than number above!) Minimum V C possible in this circuit: Switch position: j. Here s the sequence of events you will record (fill in the table with times): Event Description Approx. time to complete event Wait Start recording V R value with switch in center position, V C,initial = 0V. 5 s Charge Throw switch to left position and charge capacitor to approximately 99.3% of its maximum possible voltage. Hold Return switch to center position and wait. 10 s Discharge Throw switch to left position and discharge capacitor to drop approximately 99.3% of its previous. Total time + add 10 extra seconds to be safe: k. You need the data logger to record 200 V R data points over the time span above. Calculate the time interval you need to use: Time interval: l. Click the SETUP tab at the bottom of the TI EasyData screen, select Time Graph, click on the Edit tab, then follow the instruction to enter your time interval and number of data samples. m. Click the START tab to begin recording V R data. Use a stopwatch to move knife switch at appropriate times.

4 n. Make a sketch of your TI-84 s graphed data below. Accurately label your axes. o. Bring your Data Logger to Mr. Rhine and have him upload your group s data into excel and post on the wiki for you to complete excel analysis of data. 11. Data Analysis: Each student must create their own spreadsheet, but you may discuss and work alongside your partner and other groups. Use a blank copy of the RC Pre-Lab Excel spreadsheet as a starting point for this exercise. Be prepared to replicate all or part of this exercise as a practical exam. a. Fill in your name and the given data cells with your circuit s actual values. You need two given values for V S one for the charging circuit, and one for the charging circuit. Make that change and enter the data for each. Save the file with your name as part of the file name. b. Cut & paste your time and V R data from the class data sets posted on the wiki into the appropriate places into the template spreadsheet (into columns A and C). c. Rename the column title in cell D9 to read Event, then in the cells below type in WAIT, CHARGE, HOLD, or DISCHARGE (type the word once, then use AUTOFILL tool to fill in the rest of the values. Record the time that each of these events began in Table 1. d. Using KVL, find an equation for V C for the charging circuit, then use that equation to calculate the V C (t) values in column B. e. Create a properly labeled graph of V C (t) and V R (t) on the same axes. Use the title Attachment 1: Graph of Actual Capacitor Voltage Versus Time a. Print the graph and attach it to this lab. b. Did the shapes of these curve mach your expectations? Why or why not? Explain the shape of each portion of the curve with your comments in Table 1.

5 Table 1: Analysis of V C (t) Graph Event Actual Event Start Time (seconds) After you complete steps 11 d & e: Describe shape the V C curve in this event region and explain how it matches (or does not match) your expectations based on RC circuit theory. Use proper physics and mathematics terminology in your discussion. The size of the box is indicative of the amount of writing necessary for a proper answer! Step 11 x: Theoretical Equation for the V C (t) curve in this event region Wait Charge Hold Discharge