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Materials The following materials are required for the experiment: • multimeter with capacimeter electrolytic capacitor two resistors (R1 and R2) connecting wires with clips • banana plugs • stopwatch Procedure INSTITUTE 2 A. Resistance and Capacitance Measurements 1. Measure the actual resistance of the resistor. 2. Measure the actual capacitance of the capacitor using the capacimeter. Record the actual values in Table W1. B. RC Circuit (Charging) 1. Set the power supply voltage to 12.0 V. Record this value as Vo in Table W2. 2. Connect two banana plugs to the power supply. For convenience, use the red banana plug in the positive terminal of the power supply, and the black banana plug in the negative terminal. Make sure the plugs are snugly fit to the terminals of the power supply. DILIMA 3. Using alligator clips, connect one end of the R1 resistor to the red banana plug, and the negative terminal of the capacitor to the black banana plug. (Make sure this has been done correctly. Reversing the connections in the capacitor may cause the capacitor to explode!) On the free ends of the resistor and capacitor, attach alligator clips, but do not complete the circuit yet. 4. Connect the voltmeter in parallel with the capacitor. Make sure that the voltmeter is in DC setting, and the RANGE is set at one decimal setting. 5. Turn on the power supply and ready the stopwatch. Start the stopwatch as soon as the circuit is closed by placing the free ends of the alligator clips in contact. 6. While the stopwatch is running, observe the increase in the voltage reading across the capacitor. Record the voltage across the capacitor every 5.0 seconds in Table W2. Do not stop the stopwatch in the duration of data collection.
7. If, somehow, a mistake has been incurred during measurement and it has been decided that a new set of data will be recorded, turn off the power supply and short the leads of the capacitor using alligator clips. Repeat step 5 afterwards. 8. Perform data collection for at least 90 seconds. 9. By linearizing equation 2 (which describes the voltage across the charging capacitor over time), we derive the following: In(1-1)=-RC where the product RC is the time constant. To experimentally determine the time constant, generate a plot of In (1-) versus time. Perform a linear fit to the In (1-) versus time data using a spreadsheet program. From the best fit line, identify the time constant which is the negative reciprocal of the slope of the best fit line (according to equation 4). 10. Compare the experimentally determined time constant with the theoretical time constant (to be calculated using the measured values from Table W1). 11. Replace the R1 resistor with the R2 resistor. Repeat steps 2-6 and record your data in Table W3. Observe the difference in the rate of charging. C. RC Circuit (Discharging) 1. Connect one lead of the R1 resistor to one lead of the capacitor using an alligator clip. Likewise, connect the remaining free leads of both components using another alligator clip. 2. Using alligator clips and banana plugs connect the negative terminal of the multi- meter to the negative terminal of the capacitor. Also, connect the positive terminal of the multimeter to the positive terminal of the capacitor. 3. Make sure that the voltmeter is in DC setting, and the RANGE is set at one decimal setting. 4. Make sure that the power supply is off. Using alligator clips and banana plugs, connect the positive terminal of the power supply to the positive terminal of the capacitor. Likewise, connect the negative terminal of the power supply to the negative terminal of the capacitor. 5. Set the power supply voltage to 12.0 V. Turn on the power supply and notice that the multimeter reading (of the voltage across the capacitor) will go up from zero. Allow the capacitor to fully charge. The capacitor is fully charged when the voltage reading is no longer increasing over time. Record the voltage reading when the capacitor is fully charged as Vo in Table W4. 6. Ready the stopwatch. As soon as you pull the banana plug from the positive/negative terminal of the power supply, start the stopwatch.
7. While the stopwatch is running, observe the decrease in the voltage reading across the capacitor. Record the voltage across the capacitor every 5.0 seconds in Table W4. Do not stop the stopwatch in the duration of data collection. 8. If, somehow, a mistake has been incurred during measurement and it has been decided that a new set of data will be recorded, reconnect the pulled banana plug in step 6 to the power supply and repeat steps 1-7. 9. Perform data collection for at least 90 seconds. 10. By linearizing equation 3 (which describes the voltage across the discharging ca- pacitor over time), we derive the following: (5) RC where the product RC is the time constant. To experimentally determine the time constant, generate a plot of In () versus time. Perform a linear fit to the In () versus time data using a spreadsheet program. From the best fit line, identify the time constant which is the negative reciprocal of the slope of the best fit line (according to equation 5). In( Vo 11. Compare the experimentally determined time constant with the theoretical time constant (to be calculated using the measured values from Table W1). 12. Replace the R1 resistor with the R2 resistor. Repeat steps 2-9 and record your data in Table W5. Observe the difference in the rate of discharging.