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Capacitors
(Using Charge sensor)
Introduction
In this lab, we use a “charge-sharing” technique to determine the capacitance of various conductor –
dielectric geometries. Text Reference Young & Freedman §§24.1-2
Procedure
1) 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, which has more than million times higher internal resistance than the digital multimeter
and draws less than one picoamp current.
1a) 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.
1b) Now mount the 0.1 µF capacitor leads to the input of the charge sensor (select “Gain” switch to the
position 1 to measure up to 10 V). Again use the power supply to charge this capacitor to a voltage of
5.0 V; then disconnect the power supply; this time the reading should show a constant 5.0 V on the
computer display. Discharge the capacitor by using “Zero” button or 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.
1c) 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.
1d) Now discharge the 1.1 µF capacitor. Repeat the above steps using a 0.1 µF capacitor as the chargetransfer
capacitor (instead of a 1.0 µF capacitor). Once again compare the reading to what is expected
from a theoretical calculation.
1e) 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
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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
1.1 µF capacitor? Do the experiment and report your results.
1f) 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.
2) Finally, we wish to measure the capacitances of a parallel-plate capacitor and of a length of coaxial
cable.
2a) 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.
2b) 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.
2c) 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.
2d) 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 parallel- plate
capacitor and of a length of coaxial cable.
1. Charge the standard capacitor to V1 = 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 V2 across capacitors in parallel: the standard capacitor and parallelplate
capacitor.
5. Calculate the capacitance of the parallel-plate capacitor.
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How would pressing the two parallel plates together more tightly affect their capacitance? Try it by
adding another 1 kg mass 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).
Questions for self-assessment
1. What does a capacitor store?
2. What is the unit of the capacitance?
3. How to compute the total capacitance for the capacitors connected in series and parallel?
4. Why we are using the charge sensor (or voltage follower) in this experiment?