Physics 222
Lab #5
Capacitors
Objective: The objective of this laboratory is to study the properties of capacitors. You will build a parallel
plate capacitor and investigate how the charge, capacitance, and voltage across the capacitor are related.
Prelab: Due before the lab starts.
1. You create a parallel plate capacitor with circular plates of radius 9.0 cm and a plate separation
of 2 mm.
a. What is the theoretical capacitance of this capacitor?
b. What is the charge on this capacitor when the potential difference across the plates is 3000 V?
c. How does the capacitance change if the plate separation is increased to 4 mm?
2. a. Sketch the setup for Part 1 showing what you will change and what you will measure. (Show
the parallel plate capacitor, the addition of charge, and the electrometer.)
b. Sketch the setup for Part 2 showing what you will change and what you will measure.
c. Do the same for Part 3.
d. Do the same for Part 4.
Parallel Plate Capacitors
You will need an electrometer, Faraday Ice Pail, electrostatic voltage source, charge sphere, silver wand, and a
variable parallel plate capacitor. We will use this setup to make quantitative measurements of charge,
capacitance, and voltage for the capacitor. The electrometer measures voltage.
You should measure the radius of the capacitor plates, the radius of the silver wand, and the radius of the charge
sphere.
Part 1: How does the voltage across a capacitor (ΔVC) depend on charge on the capacitor (Q) when
capacitance (C) is held constant?
First, we will investigate how adding charge on the capacitor plates changes the voltage across the capacitor
plates. You will create a reservoir of constant charge density using the charge sphere and the electrostatic
voltage source. You will then transfer charge from the charge sphere to the capacitor using the silver wand.
1. Set up the capacitor: Attach the capacitor plates to the stand. When the plates are pushed together so they
are separated by the white dots, the spacing between the plates is 1.0 mm. Place the plates so that they are
1.0 mm apart and the marker on one plate is at the 1.0 mm mark on the base.
Connect the electrometer leads to the two sides of the capacitor and the electrometer ground wire to the
COM port on the electrostatic voltage source. Set the capacitor plate separation to around 2 mm.
YOUR CAPACITOR PLATES SHOULD BE PARALLEL – IF THEY ARE NOT, ASK FOR
ASSISTANCE.
2. Set up the charge sphere with a constant charge density: Connect the red lead on the voltage source to the
charge sphere. Keep the voltage source and charge sphere away from your capacitor. Charge the charge
sphere with the 3000 V outlet on the voltage source.
3. Investigate how the voltage across the capacitor depends on the charge on the capacitor: Make sure your
electrometer reads zero and then use the silver wand to transfer charge from the charge sphere to the
ungrounded capacitor plate. It is not necessary to touch the front surface of the capacitor plates – anywhere
on the plate will do. Record the voltage across the plates.
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Transfer more charge to the plates from the sphere and take additional readings so that you can construct a
graph of the voltage across the plates as a function of the charge on the plates. I recommend at least four
different readings.
What happens if you put some charge on the grounded capacitor plate?
The electrometer itself acts as a small capacitor in parallel with the parallel plate capacitor you created. The
capacitance of the electrometer is approximately 27 pF.
4. Use the radius of the capacitor plates, radius of the silver wand, radius of the charge sphere and the spacing
of the plates to calculate what the voltage on the capacitor plate should have been after each touch and
compare (with % error) to the actual electrometer readings.
Part 2: How does the voltage across the capacitor (ΔVC) depend on the capacitance (C) when charge on
the capacitor (Q) is held constant?
Now, let’s investigate how the voltage across the capacitor changes when we change the capacitance by
changing the separation of the plates. In these experiments we will maintain a constant charge on the plates.
1. Set up the capacitor: Discharge (zero) your electrometer and capacitor plates. Set the plate separation at 2
mm and use the voltage source set on 30 V to charge the parallel plates (just touch the two terminals of the
capacitor plates for a few seconds – touch the ground wire to one plate and the red wire to the other plate).
Disconnect the voltage source from the capacitor. As long as nothing touches the plates, the charge on the
capacitor should remain constant. Adjust the setting of the electrometer so that this initial reading is
approximately 1/5 scale (probably the 100 volt setting).
2. Investigate how the voltage across the capacitor depends on the separation distance of the plates: Record
the electrometer reading. Increase the plate separation and record the electrometer readings at various
separations. Take enough data so you can create a graph of ΔVC as a function of d (the plate separation).
How does the voltage across the capacitor depend on the plate separation? According to the theoretical
equation for the capacitance of a parallel plate capacitor, how does the capacitance depend on the plate
separation? Combining these two relationships, how does the voltage across the capacitor depend on the
capacitance when the charge on the capacitor is held constant?
Compare the theoretical voltage across the capacitor plates to the measured voltages. In calculating the
theoretical voltage, you will need to include that the electrometer is a capacitor (C = 27 pF) in parallel with
your parallel plate capacitor. As you move the plates apart, the charge on these two capacitors will move
between the capacitors keeping the voltages across the capacitors equal to each other. (The electrometer
capacitance becomes drastically more important as the parallel plates are separated since the parallel plate
capacitance goes down dramatically with distance.)
Part 3: How does the charge (Q) on the capacitor depend on the capacitance (C) when voltage across the
capacitor (ΔVC) is held constant?
In this set of experiments, you will hold the voltage across the capacitor plates constant. You will change the
capacitance by changing the separation of the plates and measure how the charge on the plates changes. You
will use the Faraday ice pail to measure charge.
When using the Faraday ice pail, I strongly recommend that the person holding the silver wand keep one hand
on the outer (grounded) cylinder of the ice pail at all times, and that this person not move any more than
absolutely necessary.
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1. Set up the ice pail and the parallel plate capacitor: The electrometer should be connected to the Faraday ice
pail with the red lead connected to the inner cylinder and the black lead to the outer cylinder. The ground
wire goes to COM port on the electrostatic voltage source. Set the plate separation on the parallel plate
capacitor to approximately 6 cm. Connect the 3000 V voltage source connection to one capacitor plate and
the ground wire (COM on the voltage source) to the other plate. Since we want the voltage across the
capacitor to remain constant, you will keep the voltage source connected to the capacitor. Discharge (zero)
the electrometer and the silver wand.
2. Measure the charge density near the center of each capacitor plate: Use the silver wand to touch a plate near
the center and then put the wand inside the Faraday ice pail (do not touch the sides of the pail) to measure
the relative charge density.
3. Now determine how the charge density on a plate changes as you change the capacitance: Change the
distance between the plates (you will want at least 4 different distances, some less than 6 cm and some more
than 6 cm) and measure the charge density at the center of a plate again. By changing the plate separation,
you have changed the capacitance (but the voltage across the plates has remained constant). Measure the
charge density at several separations so that you can create a graph of charge density as a function of the
plate separation.
What happened to the charge density as you moved the plates? Calculate what should happen to the charge
density when the capacitor plates are moved. You should show this by deriving an equation for the charge
density in terms of the plate separation distance. You may assume the charge density is uniform over the
surface of the plates for this calculation. (You don’t need to calculate values in this case, only a general
relationship – should the charge density go up or down as the plates are moved? Should it be proportional
or inversely proportional to the separation? Does this agree with your measurements?)
Part 4: How does the charge (Q) on the capacitor depend on the voltage across the capacitor (ΔVC) when
the capacitance (C) is held constant?
To finish our investigation of parallel plate capacitors, let’s vary the voltage across the capacitor plates and see
how the charge on the capacitor changes. In this case, we will hold the capacitance constant by not changing the
dimensions of the capacitor.
1. Set the plate separation back at 6 cm again, with the 3000 V setting on the voltage source. Use the silver
wand to measure the charge density at the center of the plate. Measure the charge density at 2000 V, at
1000 V, and at 0 V so that you can graph the charge (or charge density) as a function of the voltage across
the plates.
How does charge (or charge density) vary with the voltage across the capacitor plates? Compare this with
the theoretical predictions.
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