Next: About this document ...
Up: Physics 201/202 & 207/208 Lab Manual
Previous: Physics 201/202 & 207/208 Lab Manual
OBJECTIVES:
- I.
- Use the text-book model of capacitance to understand measurements of the behaviors of capacitors.
- II.
- Scrutinize how well this model describes real capacitors.
Preliminary Questions:
- A capacitor plate holds a given charge Q. Why is the voltage of this plate small when a grounded plate is near, but large (for the same Q) when it is alone?
- If the charge Q on a capacitor is doubled, what is the change in the voltage across the capacitor? (Remember that Q is the magnitude of the charge on each plate, both positive and negative.
- How could you double the positive charge on one capacitor plate
without changing the negative charge on the other plate?
APPARATUS:
- Conventional equipment: Parallel plate capacitor; Pasco electrometer &
power supply;
commercial capacitors & resistors on circuit board; aluminum paddle; low
capacitance lead, insulated cup and shield; coaxial lead & test probe;
digital multimeter (DMM); heat gun.
- Computer equipment:
Computer, monitor, keyboard, mouse; PASCO interface module;
PASCO voltage test leads (plug into PASCO input A).


INTRODUCTION:
- A capacitor consists of two electrodes
separated by an insulator. An electrode is just a fancy word for a piece of metal that can be connected to a voltage or current source. In part I you will study a parallel plate capacitor consisting of two circular metal plates held on lucite
insulators. In Part II you will study simple circuits and the charging behavior of capacitors using commercial capacitors. These are made from two long
strips of aluminum foil separated from each other by a thin plastic foil,
all rolled into a cylinder.
Part I: THE PARALLEL PLATE CAPACITOR
Introduction:
- For a fixed charge the potential of a conductor depends on
what bodies are nearby. If you charge a parallel plate
capacitor and then increase the plate spacing--leaving Q unchanged--you will find that
the potential difference increases.
- Q1.1)
- How do you reconcile this with the fact that
Q = CV remains constant? (Two good approaches are either using what you have learned about C, or using what you have learned about
for capacitors and the integral
).
- Q1.2)
- Preliminary calculation: Assuming air has a dielectric constant
estimate how many excess electrons electrons exist on one plate of the capacitorin front of you
when V is set to 30 V and the plates are separated by 1cm.
EXPERIMENT A: Potential Difference vs Separation for Fixed Charge on a Capacitor
- 1)
Referring to Fig. 1, connect the electrometer across
the capacitor, but use the special low capacitance lead and a separate
ground instead of the shielded coaxial cable.

Use the
movable plate as the grounded one, thereby shielding the other plate
from charges on your hand or clothing. Because this plate is at ground, you will only have to touch the other plate in order to charge the capacitor in step 2) below. This also reduces the effects of your presence in the configuration of conductors.
Figure 1
- 2)
- Start with the minimum plate separation. This is set by the spacers on the fixed plate, which are 1 mm thick.
Use the 30 V scale and output of the PASCCO DC power supply. Connect the negative terminal to the ground terminal of the electrometer. (Standby switch
must be in proper position or no voltage results even though meter reads).
Set the output of the DC power supply to 20 Volts using the Electrometer (not the meter on the supply; it is not as accurate. Watch out, the Electrometer can acquire and keep a voltage bias because of it's very high input impedance...how do you avoid this before setting the supply output?) Charge the
capacitor to 20 V by touching the appropriate plate with the positive voltage supply lead.
Now, change the plate spacing and observe the change of the voltage across the capacitor. Record your qualitative answer in your lab book, and then record readings of the voltage for different plate spacings. Does it make sense to make small changes to d when the plates are close? How about when they are far appart? Span 10cm in your measurements. Of course, zero on the cm scale will not be zero separation). Devise and report a way to make sure no charge has leaked off or been acquired by the plates during your measurements.
NOTE: In dry weather stray static charge on your body can adversely affect the
charge on the parallel plate capacitor. Keep body movement to a minimum.
There is an optional shielding screen which you may place in front of your body
to minimize this effect. In addition there is an optional extension handle
that attaches to the moving plate which will increase your arm to plate
distance.
In humid weather the charge may leak too rapidly off the plate to get reasonable
results. Use the heat gun to gently warm up the parallel plate capacitor and
eliminate some moisture.
- 3.)
- Analysis:
- Q 1.3.
- How do you expect the voltage between a parallel plate capacitor with a fixed charge to change with plate separation? (Use a formula.)
- 3.a)
- Plot the voltage on the capacitor vs. the distance d between the plates using the graphical analysis for windows software GAX. Double-click on the axis labels on the graph and change them to V and d.
- Q 1.4
- Which part of the plot is consistent with a parallel plate capacitor, and which is not? Print your plot and show your answer on the plot.
- Q 1.5
- Is the deviation from ideal behavior what you expect from what you know about capacitance? (Hint: a conductor has a lower capacitance when it is solitary than when a second conductor is nearby, and V = Q/C, so should you expect V to deviate above or below the value predicted by this equation?)
Now, create two new columns in GAX from your existing data by making a column of 1/V and a column of 1/d. Plot 1/V vs. 1/d.
- Q1.6
- If your capacitor were behaving as a single ideal capacitor, your data would follow a curve
. Derive this formula.
- Q1.7
- This formula will pass through the origin when d gets large (1/d goes to zero). What do you think is causing your data not to go through the origin? (Hint: if the capacitance of your cables is important, then it adds in parallel to the capacitance of the plates: C(plates) + C(cables) = Q/V.)
- Q1.8
- Why do we
need the low capacitance lead?)
EXPERIMENT B: (OPTIONAL after completing PART II)
Surface Charge Distribution on a Parallel Plate Capacitor
(at fixed Potential Difference)
SUGGESTIONS:
- 1)
- Ground yourself, the electrometer and the movable plate of the
capacitor. Turn the parallel plate capacitor so that you are
behind the movable plate. Set up electrometer and cup as in E1 but not
close to the capacitor. (Why?)
- 2)
- Connect 500 volts to the fixed plate.
Do NOT apply this voltage to electrometer directly.
(If properly configured the electrometer switch must be in the proper position or no voltage results!)
- 3)
- Use the aluminum paddle (as in experiment E1)
to probe the charge density on the capacitor's
surfaces, and then use the electrometer and cup to measure the charge on the
paddle. To avoid spurious effects from charges on the paddle's
insulator, touch the paddle to the bottom of the cup and remove the paddle
before taking the reading.
- 4)
- Record the relative charge density (sign and magnitude) on both
the inner and outer surfaces of the two plates for three radial positions:
center, halfway out, near edge of plate. Use plate separations of 2.5,
5, and 10 cm.
QUESTIONS for Experiment B:
- 1)
- Why are measurements for separations
2.5 cm not very
meaningful?
- 2)
- How does relative charge density,
, inside and outside the capacitor
depend on plate spacing? On distance from center of the plate? Explain.
EXPERIMENT C: (OPTIONAL)
- For a fixed spot inside the capacitor, find how
varies
with voltage.
Part II:
CAPACITORS IN PARALLEL, IN SERIES, AND CONNECTED TO RESISTORS
SUGGESTIONS:
- 1)
- Use the digital multimeter to test voltages in Part II: A and B experiments.
Use the
lucite circuit board containing different capacitors
and resistors. Although a push-button switch (plus connectors)
permits applying 30 V momentarily to any capacitor, you may prefer just to
touch the voltage supply leads directly to the capacitor being charged.
EXPERIMENT A: CAPACITORS IN SERIES
EXPERIMENT B: CAPACITORS IN PARALLEL
EXPERIMENT C: DISCHARGING OF CAPACITOR THROUGH A
RESISTOR
- In this experiment you will use the electroscope and computer interface to
observe discharging of a capacitor through a resistor. So far you have only
observed the ``steady state'' behavior. In this case, after charging the
capacitor, the transient flow of charge (current) through the resistor will be monitored
by measuring the voltage drop across the capacitor.
The basic relationships (as a function of time
during the discharge) are:
which upon solving gives the relation:
where
is the time constant for
a particular circuit. latex
SUGGESTED PROCEDURE:
- 1)
- Connect the
resistor (marked as
or
10 M
) across the large
capacitor (
) and set up the electrometer to measure the voltage on the
capacitor. Figure 4 show the nominal circuit configuration and a possible
wiring diagram while will achieve this desired circuit. Depressing the switch
will rapidly charge the capacitor and releasing the switch will initiate the
discharge.
Figure 4
- 2)
- Connect 30 V across the capacitor and observe the voltage V
on the
capacitor as a function of time after you disconnect the 30 volts and
switch in the resistance
. Qualitatively describe the discharge behavior
observed by watching electrometer display.
- 3)
- After making sure the PASCO interface is connected to the electrometer
output (through Channel A), CLICK on the ``Launch RC III'' icon below to
initiate the PASCO interface software. There should be a panel, a table and
a graphing display for V vs t.
- 4)
- CLICK the REC button, charge the capacitor, and record data
while the capacitor is discharging. CLICK on the STOP button.
Record six (or so) evenly spaced data points into your lab book.
- 5)
- Move the leads to the
resistor and repeat the
experiment.
(The interface should be configured to shown multiple data sets.)
- 6)
- Move the leads to the
resistor and repeat the
experiment.
QUESTIONS:
- 1)
- Do the curves have the expected function behavior?
- 2)
- By moving the curser over the inital voltage and time, and then over the voltage at
of the inital value, compare the product
to the time required for the voltage to drop to
of the initial
value (
).
Next: About this document ...
Up: Physics 201/202 & 207/208 Lab Manual
Previous: Physics 201/202 & 207/208 Lab Manual
Physics Laboratory
2000-09-28