# Experiment P43: RC Circuit (Power Amplifier, Voltage Sensor)

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1 PASCO scientific Vol. 2 Physics Lab Manual: P43-1 Experiment P43: (Power Amplifier, Voltage Sensor) Concept Time SW Interface Macintosh file Windows file circuits 30 m 700 P43 P43_RCCI.SWS EQUIPMENT NEEDED FROM AC/DC ELECTRONICS LAB* Interface capacitor, 330 microfarad (330 µf) Power Amplifier resistor, 100 ohm (100 Ω) Voltage Sensor LCR Meter (optional) (2) Patch Cords (*The AC/DC Electronics Laboratory is PASCO EM-8656.) PURPOSE The purpose of this laboratory activity is to investigate how the voltage across a capacitor varies as it charges and to find the capacitive time constant. THEORY 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 τ is 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 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. dg 1996, PASCO scientific P43-1

2 P43-2: Physics Lab Manual Vol. 2 PASCO scientific PROCEDURE In this activity, the Power Amplifier produces a low frequency 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. The Voltage Sensor measures the voltage across the capacitor as it charges and discharges. The program records and displays the data. You will measure the time for the capacitor to charge to the half-maximum voltage. Using the half-life time and the known value of the resistor, you can calculate the capacitance of the capacitor. PART I: Computer Setup 1. Connect the interface to the computer, turn on the interface, and turn on the computer. 2. Connect the Voltage Sensor to Analog Channel A. Connect the Power Amplifier to Analog Channel B. Plug the power cord into the back of the Power Amplifier and connect the power cord to an appropriate electrical outlet. 3. Open the document titled as shown: Macintosh P43 Windows P43_RCCI.SWS The document opens with a Graph display of Voltage (V) versus Time (sec), and the Signal Generator window which controls the Power Amplifier. Note: For quick reference, see the Experiment Notes window. To bring a display to the top, click on its window or select the name of the display from the list at the end of the Display menu. Change the Experiment Setup window by clicking on the Zoom box or the Restore button in the upper right hand corner of that window.) P , PASCO scientific dg

3 PASCO scientific Vol. 2 Physics Lab Manual: P The Sampling Options for this activity are: Periodic Samples = Fast at 1000 Hz and Stop Condition = Time at 4.00 seconds.. 5. The Signal Generator is set to output 4.00 V, positive only square AC Waveform, at 0.40 Hz. It is set to Auto so the Signal Generator will start automatically when you click MON or REC and stop automatically when you click STOP or PAUSE. PART II: Sensor Calibration and Equipment Setup You do not need to calibrate the Voltage Sensor or the Power Amplifier. 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 circuit 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. Battery + A B C 3.3 Ω 3 VOLTS MAX 3 VOLTS MAX E C CW B 100 Ω resistor Battery µf capacitor TO POWER AMPLIFIER VOLTAGE SENSOR (WITH CLIPS) dg 1996, PASCO scientific P43-3

4 P43-4: Physics Lab Manual Vol. 2 PASCO scientific 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 of the Power Amplifier to the banana jacks on the AC/DC Electronics Lab circuit board. Part III: Data Recording 1. Turn on the power switch on the back of the Power Amplifier. 2. Click the REC button ( ) to start collecting data. The Signal Generator output will automatically start when data recording begins. 3. Data recording will continue for four seconds and then stop automatically. Run #1 will appear in the Data list in the Experiment Setup window. 4. When data recording is complete, turn off the switch on the back of the Power Amplifier. ANALYZING THE DATA 1. Click the Autoscale button ( ) in the Graph to rescale the Graph to fit the data. 2. Click the Magnifier button ( ). Use the cursor 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. P , PASCO scientific dg

5 PASCO scientific Vol. 2 Physics Lab Manual: P43-5 This will give you an expanded view of the Voltage versus Time plot for that region. 3. Click the Smart Cursor button ( ). The cursor changes to a cross-hair when you move the cursor into the display area of the Graph. The Y-coordinate of the cursor/cross-hair is shown next to the vertical axis. The X-coordinate of the cursor/cross-hair is shown next to the horizontal axis. 4. Move the cursor to the point on the plot where the voltage begins to rise. Record the time that is shown in the area below the horizontal axis. 5. Move the Smart Cursor to the point where the voltage is approximately 2.00 volts. Record the new time that is shown in the area below the horizontal axis. 6. Find the difference between the two times and record it as the time to half-max, or t 1/2. dg 1996, PASCO scientific P43-5

6 P43-6: Physics Lab Manual Vol. 2 PASCO scientific ANALYZING THE DATA DATA Beginning time = s Time to 2.00 V = s Time to half-max (t 1/2 ) = s 1. Use t 1 2 = τ ln2 = RC to calculate the capacitance (C) of the capacitor. Capacitance = farad 2. If a capacitance meter is available, use it to measure the capacitance of the capacitor. Using the percent difference method, compare the measured value to the experimental value. (Remember, the stated value of a capacitor may vary by as much as ±20% from the actual measured value.) If a capacitance meter is not available, use the percent difference method and compare the stated value (e.g., 330 µf) to the experimental value. QUESTIONS 1. The time to half-maximum voltage is how long it takes the capacitor to charge half-way. Based on your experimental results, how long does it take for the capacitor to charge to 75% of its maximum? 2. After four half-lives (i.e., time to half-max), to what percentage of the maximum charge is the capacitor charged? 3. What is the maximum charge for the capacitor in this experiment? 4. What are some factors that could account for the percent difference between the stated and experimental values? P , PASCO scientific dg

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