Name: ______

This worksheet is a pre-lab exercise for our class on 11/15/2010. You can expect that I will collect and grade it.

1. Neatly list all the formulas that you copied into your notes that relate to capacitance (review chapter 18 notes). Define each variable or constant and state the units. Draw diagrams that relate to the equations.

2. Review: Define Ampere.

3. Review: Define Coulomb.

4. Suppose you have a simple circuit with a 50V battery and a 8.2KΩ resistor. Calculate the…

(please use proper SI prefixes rather than scientific notation, e.g., G, M, K, m, μ, n, p, etc.).

a. …current flowing through the resistor

b. …power dissipated by the resistor

c. …number of Coulombs of that flow through the resistor in one second?

d. …number of electrons that that flow through the resistor in one second?

5. Every material has a permittivity (ε) that is larger than that of free space (εo). Oftentimes you will see a “relative” permittivity (or dielectric constant, k) for a given for a material rather than it’s permittivity. Relative permittivity is simply a ratio of the material’s permittivity compared to the permittivity of free space (k = εmaterial/ εo). For example, xylenol has a relative permittivity (or dielectric constant) of kxylenol = 17. In other words, xylenol’s permittivity is 17 times larger than that of free space. Go to the web site http://www.clippercontrols.com/pages/dielectric-values and look up dielectric constants for the following materials, then calculate their actual permittivities…

a. Dry Wood k = ______ε = ______

a. Wet Wood k = ______ε = ______(use largest value in table)

b. Wax k = ______ε = ______

c. Water k = ______ε = ______

d. Polyethylene k = ______ε = ______

(mylar is made of a type of this material we discussed in class)
6. The dimensions of the aluminum plates we used to demonstrate the concept of a parallel plate capacitor are 7 inches by 2.5 inches. Be careful with units! Once again, don’t use scientific notation; use SI prefixes to get numbers between 1 and 999 (e.g. 28.9 mF).

a. Calculate the capacitance if the plates are separated by 1 mm.

b. Now suppose you squeeze a piece a paper between the plates. I used calipers to measure the thickness of the paper to be 0.004 inches. Assuming paper has the same relative permittivity as wood, use your answer from 5.a. to calculate the capacitance.

c. I also have balsa wood that is 1/32” thick. If you soak it in water then use it between the plates, what is the new capacitance? Use your answer from 5.b.

7. It turns out that the voltage across the capacitor in the circuit below is proportional to , where t is time in seconds, and R and C are the values of the elements in the circuit. Another important fact that you probably already know from your math class is that an exponent must always be a unitless quantity . In our case, the exponent is . Given this bit of important information, what must the units of RC (resistance ´ capacitance, or Ω ×F) be?

8. In the circuit below, suppose you close the switch at time = 0 seconds. The voltage across the capacitor as a function of time is . VS is the source voltage, and VC,initial is the initial (starting value) of the voltage measured on the capacitor at time = 0 sec. Dust off your knowledge of exponential functions (think the the shape—is this growth or decay?) and answer the questions below…

a. What is the value of VC when time starts (t = 0). In other words, evaluate VC(0).

b. What is the value of VC when after a very long time has passed (e.g., t → ¥). In other words, evaluate VC(t = very large number) » . VC(¥).

9. Solve the equation

for . (e.g., isolate using algebra).

10. In the circuit to the right, use KVL and solve for VR.
11. Now let’s apply some numbers to the situation.

Let’s assume VC,initial = 0 (no charge on capacitor to

start). Use the VS, R, and C values to the right.

Suppose we close the switch at time = 0.

a. Fill in the values to your general equation

for :

VC(t) = ______

b. Now fill out the table below. I would highly recommend that you do this in excel and let excel handle the math for you. You can also enter the equations in your TI and have it calculate all the values using the “TABLE” button (use the TBLSET button to set up the 41 μs increment and starting value) and graph all at once using the GRAPH button. You can cut and paste this table directly in to Excel!

time, t (in μs) / VC(t) / VR(t) from #10 / Take ratio of VC:VR / Add VC(t) and VR(t) / Calculate IR(t) using VR(t) and Ohm’s law
0
41
82
123
164
205
246
287
328
369
410

c. Now make two graphs: (best to use Excel or have your TI do it using GRAPH and enter equations for each column above into Y1, Y2,, etc.)

(i) Graph VC(t), VR(t), and VC(t) + VR(t) versus time (all 3 on the same graph). This is the data from columns 2, 3, and 5 above.

(ii) Repeat for VC(t), IR(t) versus time (columns 2 and 6)