(Using Charge sensors) Introduction In this lab, we use a “charge-sharing” technique to determine the capacitance of various conductor – dielectric geometries. Procedure You will use a power supply to charge a capacitor; then carefully touch that capacitor’s leads to the leads of a second capacitor (uncharged in most cases) so that the charge on the first capacitor is shared with the second. Before beginning the formal experiment, you must learn how to measure the voltage across a charged capacitor. Digital voltmeters, due to finite internal resistance, always draw some current when connected across a charged capacitor, thereby leaking charge. To overcome this problem, we will use a charge sensor. Mount a 0.1 µF capacitor on the Styrofoam block. Use the power supply to charge this capacitor to a voltage of 5.0 V; then disconnect the power supply. Attempt to measure the capacitor voltage directly with a digital voltmeter (DVM). You should observe the voltage on the DVM dropping rather quickly to zero. Now mount the 0.1 µF capacitor leads to the input of the charge sensor. Again use the power supply to charge this capacitor to a voltage of 5.0 V; this time the reading should show a constant 5.0 V on the computer display. Discharge the capacitor by touching both capacitor leads simultaneously with an alligator clip. Once again the voltage should drop rather quickly to zero. You may observe some short-lived “rebound” in the voltage due to a lingering polarization in the dielectric of the capacitor. For the formal experiment, begin with a pair of capacitors in parallel. Leave the 0.1 µF capacitor mounted on the charge sensor and mount a 1.0 µF capacitor on the Styrofoam block; connect the two capacitors (the connectors with small hooks are useful here) to create 1.1 µF capacitor. Make sure the 1.1 µF is completely discharged. Charge a second 1.0 µF capacitor to 5.0 V (you can do this by holding the second capacitor by its plastic cover and inserting its leads into the power-supply outlets) and touch it to the uncharged 1.1 µF capacitor (be sure to connect positive to positive). For safety, discharge the “charge-transfer” capacitor before putting it down. Compare the measured voltage to what is expected from a theoretical calculation. Now discharge the 1.1 µF capacitor. Repeat the above steps using a 0.1 µF capacitor as the charge-transfer capacitor (instead of a 1.0 µF capacitor). Once again compare the reading to what is expected  from a theoretical calculation. This time, do not discharge the 1.1 µF capacitor. Recharge the 0.1 µF charge – transfer capacitor to 5.0 V and connect it again across the 1.1 µF capacitor, taking care to maintain the proper polarity. You should observe that the increase in the voltage is a little less this time. Compare the voltage reading to what is expected from a theoretical calculation and explain why the increase in voltage is a little less for the second charge transfer. What do you expect for a third charge transfer without discharging the Page 2 of 2 1.1 µF capacitor? Do the experiment and report your results. Now charge the 1.1 µF capacitor to 5.0 V. Share the charge on this capacitor with an uncharged capacitor of unknown capacitance (the capacitor covered with black electrical tape), and from the final reading of the voltage determine the unknown capacitance. You can share the charge by holding the uncharged capacitor and touching its leads to the leads of the charged 1.1 µF capacitor. Report this measurement of capacitance and compare with a second measurement taken directly with the capacitance capability of the DVM. Finally, we wish to measure the capacitances of a length of coaxial cable and of a parallel-plate capacitor. Construct the parallel-plate capacitor by inserting the waxed paper between the aluminum plates; press the combination together by putting a 1.0 kg weight on top of the top plate. Both of these capacitances are quite small, so we will need to alter our standard capacitor. Remove the 0.1 µF capacitor and mount a 0.01 µF capacitor (the smaller brown capacitor: check with capacitance capability of the DVM) on the charge sensor; disconnect the capacitor mounted on the Styrofoam. We must take into account the small capacitance of the charge sensor, which we have thus far ignored. Use the capacitance capability of the DVM to measure the combined capacitance of the 0.01 µF capacitor and the charge sensor (it should be approximately twice the capacitance of the 0.01 µF capacitor alone); this is our standard capacitor. Charge the standard capacitor to 5.0 V using the power supply. Use the charge-sharing method (as summarized below) to determine the two unknown capacitances: capacitances of a length of coaxial cable and of a parallel- plate capacitor. 1. Charge the standard capacitor to V 1 = 5.0 V. (Fig. 1). 2. Disconnect one wire between power supply and the charge sensor. 3. With a quick touch, share the charge of the standard capacitor and a parallel-plate capacitor (Fig. 2). 4. Record the resultant voltage V 2 across capacitors in parallel: the standard capacitor and parallelplate capacitor. 5. Calculate the capacitance of the parallel-plate capacitor. How would pressing the two parallel plates together more tightly affect their capacitance? Try it and report your results. Follow the same procedure to measure the capacitance of a length of coaxial cable. Compare your results to direct measurements of those two capacitances with the capacitance capability of the DVM (the DVM internally performs a similar experiment).