# Capacitors. Evaluation copy

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1 Capacitors Computer 24 The charge q on a capacitor s plate is proportional to the potential difference V across the capacitor. We express this relationship with q V =, C where C is a proportionality constant known as the capacitance. C is measured in the unit of the farad, F, (1 farad = 1 coulomb/volt). If a capacitor of capacitance C (in farads), initially charged to a potential V 0 (volts) is connected across a resistor R (in ohms), a time-dependent current will flow according to Ohm s law. This situation is shown by the (resistor-capacitor) circuit below when the switch is closed. Figure 1 As the current flows, the charge q is depleted, reducing the potential across the capacitor, which in turn reduces the current. This process creates an exponentially decreasing current, modeled by V()= t V e t The rate of the decrease is determined by the product, known as the time constant of the circuit. A large time constant means that the capacitor will discharge slowly. When the capacitor is charged, the potential across it approaches the final value exponentially, modeled by t V()= t V e 0 1 The same time constant describes the rate of charging as well as the rate of discharging. 0 Evaluation copy OBJECTIVES Measure an experimental time constant of a resistor-capacitor circuit. Compare the time constant to the value predicted from the component values of the resistance and capacitance. Measure the potential across a capacitor as a function of time as it discharges and as it charges. Fit an exponential function to the data. One of the fit parameters corresponds to an experimental time constant. Physics with Vernier 24-1

4 Computer 24 there is a discrepancy between the two quantities compared in Question 2, can the tolerance values explain the difference? 4. What was the effect of reducing the resistance of the resistor on the way the capacitor discharged? 5. How would the graphs of your discharge graph look if you plotted the natural logarithm of the potential across the capacitor vs. time? Sketch a prediction. Show Run 1 (the first discharge of the capacitor) and hide the remaining runs. Click on the y-axis label and select ln(v). Click to see the new plot. 6. What is the significance of the slope of the plot of ln(v) vs. time for a capacitor discharge circuit? EXTENSIONS 1. What percentage of the initial potential remains after one time constant has passed? After two time constants? Three? 2. Use a Vernier Current Probe and Differential Voltage Probe to simultaneously measure the current through the resistor and the potential across the capacitor. How will they be related? 3. Instead of a resistor, use a small flashlight bulb. To light the bulb for a perceptible time, use a large capacitor (approximately 1 F). Collect data. Explain the shape of the graph. 4. Try different value resistors and capacitors and see how the capacitor discharge curves change. 5. Try two 10 µf capacitors in parallel. Predict what will happen to the time constant. Repeat the discharge measurement and determine the time constant of the new circuit using a curve fit. 6. Try two 10 µf capacitors in series. Predict what will happen to the time constant. Repeat the discharge measurement and determine the time constant for the new circuit using a curve fit Physics with Vernier

5 Vernier Lab Safety Instructions Disclaimer THIS IS AN EVALUATION COPY OF THE VERNIER STUDENT LAB. This copy does not include: Safety information Essential instructor background information Directions for preparing solutions Important tips for successfully doing these labs The complete Physics with Vernier lab manual includes 35 labs and essential teacher information. The full lab book is available for purchase at: Vernier Software & Technology S.W. Millikan Way Beaverton, OR Toll Free (888) (503) FAX (503)

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