# LAB 3: Capacitors & RC Circuits

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1 LAB 3: Capacitors & C Circuits Name: Circuits Experiment Board Wire leads Capacitors, esistors EQUIPMENT NEEDED: Two D-cell Batteries Multimeter Logger Pro Software, ULI Purpose The purpose of this lab is to determine how capacitors behave in -C circuits. The manner in which capacitors combine is also studied. Figure 1 A B C esistor Capacitor "Switch" V + - Procedure 1. Connect the circuit shown in Figure 1, using a 10 kω resistor and a 100 µf capacitor. Use one of the spring clips as a "switch" as shown. With the "switch" OPEN, connect the multimeter so that the black "ground" lead is on the side of the capacitor that connects to the negative terminal of the battery and set the meter for 2 volt, dc mode. 2. Close the "switch" and observe the voltage readings on the multimeter. Describe how the voltage changes (is it increasing or decreasing, is it changing at a constant rate, etc). Page 1 of 5

2 Make a graphical sketch that shows how you think the voltage changed with time. 3. If you now open the "switch", the voltage across the capacitor should remain at its present value (it may drop slowly due to leakage). This indicates that the charge that accumulated on the two plates of the capacitor (remember that q = CV) has no way to flow from one plate to the other to neutralize the capacitor (since the circuit is an open circuit). 4. Connect a wire from point A to point C and observe the multimeter. Describe how the voltage changes, as you did in Step 2. What is happening to the charge on the capacitor? 5. We can say that you have discharged the capacitor through the resistor. To make sure it is fully discharged, connect a wire from point B to point C. Why does this fully discharge it? 6. epeat Steps 2 through 4, until you have a good feeling for the process of charging and discharging a capacitor through a resistor. efine your descriptions and sketches as necessary and, finally, check your results with the instructor. 7. Before connecting the computer, disconnect the multimeter from across the capacitor and measure the battery voltage directly ("switch" open) and record it in the space below. Multiply it by and by and record the results in the spaces (include the units). = = = Page 2 of 5

3 Preparation for using the computer 8. Unplug all sensor inputs from the ULI box and plug the voltage probe connector into CH 1. Turn on the ULI box, the computer, and the display monitor in that order. 9. un the program Logger Pro. Change the vertical scale to 0.1 to Click the Experiment tab, click Data Collection and adjust the Sampling ate to 20 samples/sec. 10. Connect the two alligator clips of the voltage probe across the capacitor. The red clip connects to the + side and the black clip to the side. You can remove the multimeter. 11. Click on the Collect button. This will start data acquisition. As soon as you see points being plotted on the screen, close the "switch" (complete the circuit). You should see a curve representing a gradually increasing voltage that is similar to what you observed with the multimeter in Step 2. How closely does it resemble your sketch? If there is little or no resemblance, explain why. 12. After you have obtained an acceptable graph, click Analyze tab, find and click Examine in the popup menu, and determine the time interval from when you closed the "switch" until the voltage reached Enter your results in Table Obtain a graph of the voltage across the discharging capacitor. With the capacitor fully charged click the Start button, then open the "switch" to disconnect the battery, and connect a wire from point A to point C. This graph should resemble your sketch in Step 4. The initial voltage should agree with your value for. 14. After you have obtained an acceptable graph, click Analyze tab, find and click Examine in the popup menu, and determine the time interval from when you connected points A and C until the voltage reached Enter your results in Table epeat Steps 11 through 14 for the different capacitor (100 µf and 330 µf) and resistor (1 kω, 4.7 kω, and 10 kω) combinations. Print out one graph for the charging process and one for the discharging process for a combination of a resistor and a capacitor. Entitle the graphs and put the names of your group members on it. Page 3 of 5

4 Trial esistance Capacitance t charge t discharge t theoretical Capacitors in combination Table epeat Steps 11 through 14, but with the 10 kω resistor in series with the series combination of the 100 µf and 330 µf capacitors. ecord your results in Table epeat Steps 11 through 14, but with the 10 kω resistor in series with the parallel combination of the 100 µf and 330 µf capacitors. (You may need to increase the time axis.) ecord your results in Table 2. Type of combination t charge t discharge t theoretical Capacitors in series Capacitors in parallel Discussion Table 2 What is the significance of the numbers and 0.368? Compute the theoretically expected values for the characteristic times of the -C circuits for the values of and C used and enter them in the Tables. Do your charging and discharging times agree with the theoretical predictions? If not, explain why and if necessary repeat the experiments or theoretical calculations. What is the effective capacitance of capacitors connected in parallel? (Show for 3 capacitors) What is the effective capacitance of capacitors connected in series? Page 4 of 5

5 HOMEWOK ASSIGNMENTS 1. If the capacitor is initialy uncharged, calculate the time after the switch is closed necessary for it to acquire 63.2% of its final charge in this circuit? = 30 volts C = 35 µf C 2. If the capacitors are initialy uncharged, calculate the time after the switch is closed necessary for C 1 to acquire 63.2% of its final charge in this circuit? = 30 volts C 1 = 10 µf C 2 = 20 µf C 3 = 30 µf C 1 C 2 C 3 3. Switch S has been connected to the battery for a very long time. If S is then switched as shown calculate the time necessary for C 1 to have a charge of 36.8% of its initial charge in this circuit? = 30 volts C 1 = 10 µf C 2 = 20 µf C 3 = 30 µf C 1 C 2 C 3 S Page 5 of 5

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