# Teacher s Guide - Activity P50: RC Circuit (Power Output, Voltage Sensor)

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1 Teacher s Guide - Activity P50: RC Circuit (Power Output, Voltage Sensor) Concept DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) Circuits P50 RC Circuit.DS (See end of activity) (See end of activity) Equipment Needed Qty From AC/DC Electronics Lab* Qty Voltage Sensor (CI-6503) 1 Capacitor, 330 microfarad 1 LCR Meter (SB-9754) 1 Resistor, 100 ohm 1 Patch Cords (SE-9750) 2 (*The AC/DC Electronics Lab is PASCO Model EM-8656) What Do You Think? The voltage across a capacitor varies as it charges. How can you investigate this relationship? Capacitors also have what is known as the capacitive time constant. How can this constant be calculated? Take time to answer the What Do You Think? question(s) in the Lab Report section. Background When a DC voltage source is connected across an uncharged capacitor, the rate at which the capacitor charges up decreases as time passes. At first, the capacitor is easy to charge because there is very little charge on the plates. But as charge accumulates on the plates, the voltage source must do more work to move additional charges onto the plates because the plates already have charge of the same sign on them. As a result, the capacitor charges exponentially, quickly at the beginning and more slowly as the capacitor becomes fully charged. The charge on the plates at any time is given by: q=q o 1 e t τ ( ) where qo is the maximum charge on the plates and τis the capacitive time constant ( τ = RC, where R is resistance and C is capacitance). NOTE: The stated value of a capacitor may vary by as much as ±20% from the actual value. Taking the extreme limits, notice that when t = 0, q = 0 which means there is not any charge on the plates initially. Also notice that when t goes to infinity, q goes to qo which means it takes an infinite amount of time to completely charge the capacitor. The time it takes to charge the capacitor to half full is called the half-life and is related to the capacitive time constant in the following way: t 1 2 = τ ln2 In this activity the charge on the capacitor will be measured indirectly by measuring the voltage across the capacitor since these two values are proportional to each other: q = CV. - + R C SAFETY REMINDER Follow all safety instructions. TP PASCO scientific p. 143

2 Physics Labs with Computers, Vol. 2 Teacher s Guide P50: RC Circuit C For You To Do Use the Output feature of the ScienceWorkshop interface to supply a voltage to the resistorcapacitor circuit. Use the Voltage Sensor to measure the voltage across the capacitor as it charges and discharges. Record the voltage in the secondary coil for two configurations: one with an iron core inside the inner coil, and one without the iron core inside the inner coil. Use DataStudio or ScienceWorkshop to control the voltage output of the interface and to record and display the voltage across the capacitor. Finally, measure the time for the capacitor to charge to the half-maximum voltage. Use the half-time constant and the known value of the resistance to calculate the capacitance of the capacitor. Compare the calculated value of the capacitor to the stated value of the capacitor. In this activity, the interface outputs a low frequency positive-only square wave (0 to 4 V). This waveform imitates the action of charging and then discharging a capacitor by connecting and then disconnecting a DC voltage source. PART I: Computer Setup 1. Connect the ScienceWorkshop interface to the computer, turn on the interface, and turn on the computer. 2. Connect the Voltage Sensor DIN plug into Analog Channel B. 3. Connect banana plug patch cords into the OUTPUT ports on the interface. 4. Open the document titled as shown: DataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win) P50 RC Circuit.DS (See end of activity) (See end of activity) The DataStudio document has a Graph display of voltage versus time and the Signal Generator window for controlling the Output of the interface. The document also has a Workbook display. Read the instructions in the Workbook. See the pages at the end of this activity for information about modifying a ScienceWorkshop file. Data recording is set to stop automatically at 4 seconds. The Signal Generator is set to output a 4 volt, positive only square wave at 0.40 Hz. The Signal Generator is set to Auto so it will start and stop automatically when you start and stop measuring data. POWER ScienceWorkshop A B C DIGITAL CHANNELS ANALOG CHANNELS (±10V MAX INPUT) OUTPUT (±5V / 300mA) p PASCO scientific TP50

3 PART II: Sensor Calibration and Equipment Setup You do not need to calibrate the Voltage Sensor. 1. Place a 100-ohm (Ω) resistor (brown, black, brown) in the pair of component springs nearest to the top banana jack at the lower right corner of the AC/DC Electronics Lab Board. 2. Connect a 330 microfarad (µf) capacitor between the component spring on the left end of the 100-Ω resistor and the component spring closest to the bottom banana jack. 3 VOLT BULBS KIT NO. + A B C 3.3 Ω 3 VOLTS MAX 3 VOLTS MAX Resistor E C CW B Capacitor + To interface OUTPUT Voltage Sensor 3. Put alligator clips on the Voltage Sensor banana plugs. Connect the alligator clips to the wires at both ends of the 330 µf capacitor. 4. Connect banana plug patch cords from the OUTPUT ports of the interface to the banana jacks on the AC/DC Electronics Lab Board. Part III: Data Recording 1. Start measuring data. (Hint: Click Start in DataStudio or REC in ScienceWorkshop.) The Signal Generator output will automatically start when data recording begins. Watch the plot of voltage versus time in the Graph display. 2. Data recording will continue for four seconds and then stop automatically. Run #1 will appear in the Data list. TP PASCO scientific p. 145

4 Physics Labs with Computers, Vol. 2 Teacher s Guide P50: RC Circuit C Analyzing the Data 1. Rescale the Graph display if needed. 2. Expand a region of the Graph display. Use the Zoom Select tool in DataStudio ( ) or the Magnifier tool in ScienceWorkshop ( ) to click-and-draw a rectangle over a region of the plot of Voltage versus Time that shows the voltage rising from zero volts to the maximum volts. Result: Your selected region expands to fill the Graph display. 3. Use the built-in analysis tools in the Graph display to find the time to half-max. In DataStudio, click the Smart Tool. Move the cursor to the point on the plot where the voltage begins to rise. Drag the corner of the Smart Tool to the point where the voltage is about 2 volts. The time to half-max is the x-coordinate. In ScienceWorkshop, click the Smart Cursor. The cursor changes to a cross hair when you move the cursor into the display area of the Graph. Move the cursor to the point on the plot where the voltage begins to rise. Click-and-drag the cursor to the point where the voltage is about 2 volts. The time to half-max is displayed under the horizontal axis. 4. Use t 1 2 = τ ln2 = RC to calculate the capacitance (C) of the capacitor. Put your results in the Lab Report section p PASCO scientific TP50

5 Lab Report- Activity P50: RC Circuit What Do You Think? The voltage across a capacitor varies as it charges. How can you investigate this relationship? Capacitors also have what is known as the capacitive time constant. How can this constant be calculated? Answers will vary. Students may predict that they can use the plot of voltage versus time as the capacitor charges to find the relationship of the voltage across the capacitor and the amount of charge. They may predict that they can calculate the capacitive time constant ( τ = RC) after they find the capacitance, C, of the capacitor. They can use the resistance, R, and the time to half-max to find the capacitance. Data Time to half-max (t1/2) Capacitance = 388 x 10-6 farad = s = 388 micro f arad t 1 2 (Remember, C = ln2 R) Percent Difference between stated capacitance value of 330 microfarad = 17.5 % 1. The time to half-maximum voltage is how long it takes the capacitor to charge halfway. Based on your experimental results, how long does it take for the capacitor to charge to 75% of its maximum? Answers will vary. In this example, R = 100 Ω and C = 388 µf. The time to 75% of maximum is two half-life times or seconds. V = V 0 1 e t τ t τ 0.75 = 1 e t τ 0.25 = e ln(0.25) = t RC t = RC ln(0.25) 2. After four half-lifes (i.e., time to half-max), to what percentage of the maximum charge is the capacitor charged? Answers will vary. The capacitor charges to fifteen sixteenths of maximum charge in four halflife times or 93.75%. 3. What is the maximum charge for the capacitor in this experiment? Charge equals capacitance multiplied by voltage, or farads x 4.00 volts, or coulombs or 1552 microcoulombs. TP PASCO scientific p. 147

6 Physics Labs with Computers, Vol. 2 Teacher s Guide P50: RC Circuit C 4. What are some factors that could account for the percent difference between the stated and experimental values? The percent difference between the stated and experimental values is within the manufacturer s specifications. One factor for the difference is the extreme difficulty in maintaining a capacitance to within a few microfarads p PASCO scientific TP50

7 Appendix: Modify a ScienceWorkshop File Modify an existing ScienceWorkshop file. Open the ScienceWorkshop File Open the file titled as shown: ScienceWorkshop (Mac) P43 RC Circuit ScienceWorkshop (Win) P43_RCCI.SWS This activity uses the Output feature of the ScienceWorkshop 750 interface to provide the output voltage. Remove the Power Amplifier in the Experiment Setup window. Remove the Power Amplifier Icon In the Experiment Setup window, click the Power Amplifier icon and press <delete> on the keyboard. Result: A warning window opens. Click OK to return to the setup window. Results The ScienceWorkshop document has a Graph display of Channel A voltage. Plug in the Voltage Sensor Connect the Voltage Sensor DIN s plug into Channel A on the interface (rather than Channel B). TP PASCO scientific p. 149

8 Time Estimates Preparation: 15 min Activity: 30 min Objectives Students will be able to use the Output feature of the ScienceWorkshop interface to supply the voltage (low frequency positive only square wave) for a resistor-capacitor circuit use the Voltage Sensor to measure the voltage across the capacitor as it charges and discharges use the Graph display to determine the time for the capacitor to charge to one-half of its maximum voltage calculate the capacitance based on the time to half-max calculate the capacitive time constant based on the capacitance and resistance of the circuit compare the measured capacitance of the capacitor to the stated value Safety Alert! Remind students to be especially careful when they remove the capacitor from the circuit board after the activity is finished. They should fully discharge the capacitor by using a patch cord as a bridge to each end of the capacitor. Notes The industry standard for capacitors allows a ±20% difference between the stated capacitance and the actual capacitance. DataStudio Sample Data Note: DataStudio and ScienceWorkshop results were obtained during separate data runs and can not be compared to each other. TP PASCO scientific p. 151

9 Physics Labs with Computers, Vol. 2 Teacher s Guide P50: RC Circuit C ScienceWorkshop Sample Data p PASCO scientific TP50

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