Capacitors
    Pre-lab:

No pre-lab exercise for this week.  However, please read ahead.  You may be interested in the java applet at http://www.phys.hawaii.edu/~teb/java/ntnujava/rc/rc.html


    Objective:

In this exercise we will discuss capacitors.  We would like to:
    Notes:
    A capacitor is an electrical device which stores charge.  There are many types of capacitors: parallel plate capacitors, cylindrical capacitors, tubular capacitors, etc.  Anything that stores charge is a capacitor.  You are a capacitor!  (If you weren't, you wouldn't be able to scuff your feet on carpet and zap your friends!)  You have a capacitance of about 100 pF (100 x 10 ^ -12 F).
    For all capacitors, there is a value which describes how much charge can be put on a capacitor, called capacitance.  Capacitance is measured in Farads (F = C / V)
    Capacitance is the amount of charge (Q) stored in a capacitor per unit voltage (V).
    or
C = Q / V
    The simplest type of capacitor is the parallel plate capacitor, which we have worked with in the last two labs.  A parallel plate capacitor is comprised of two metal plates a distance, d, from one another, and which has a voltage difference, V, between them.  We can describe this capacitor analytically.  (Other capacitors are much more complex!)
    We can determine quite easily with the equations that we've learned so far that the capacitance of a parallel plate capacitor is:
C = k * E0 * A / d
A is the area of the plate
E0 is the permittivity of free space = 8.85 x 10 ^-12 F / m
k is the dielectric constant
If there is no material between the plates of a capacitor (a vacuum) then k is 1.
Capacitors in AC circuits:
In an AC circuit, a capacitor has an effective resistance.  That is, energy is lost as the electric fields of the capacitors are created and destroyed.  We can treat the capacitors as resistors with a resistance of:
X = 1/wC,
where w is the angular frequency of the AC voltage source.  Instead of resistance, we call this quantity the reactance of the capacitor.
We can add resistances in series and parallel (please review your notes from the lecture class!) and the same rules apply for reactances:
series:         Xtotal  = X1 + X2
parallel:       1/Xtotal = 1/X1 + 1/X2
You can substitute in the definition of the reactance of a capacitor into the above equation to get equations (2) and (3) in your lab manual.
We will verify these two equations in our experiment.

   Procedure:
(In class, draw the circuit)
 
 
 
 
 
 
 
 

Part I: Measuring capacitance

1.  The circuit above is already constructed for you.  You only need to connect the oscilloscope and the frequency generator.  C1 = 0.22 micro-F.

2.  Attach capacitor A to the circuit.

3.  Vary the two resistances until the amplitude of the output on the oscilloscope is minimized (nearly flat line).

4.  Disconnect the scope and the frequency generator, being careful not to change the value of the resistors.  Measure the two resistances with a digital multimeter.

5.  Determine the capacitance of A. C2 = C1 * (R1 / R2).

6.  Repeat for capacitors B - E.

Part II: Effective Capacitance of Capacitors in Series and Parallel

1.  Using your values for A and B, analytically determine the total capacitance of A and B when they are placed in series.  (Use equation 2).

2.  Connect A and B in series.  Using the procedure in part I, experimentally determine the total capacitance of A and B.

3.  Calculate the total capacitance of A and B when they are placed in parallel (equation 3).

4.  Using the procedure in part I, experimentally determine the total capacitance of A and B.

Part III:  Homemade Capacitor
The homemade capacitor is a capacitor made out of two sheets of aluminum foil with a transparency between them.  The capacitance of our homemade device is, of course, quite small.  To determine the capacitance, we will have to make our capacitance-meter more sensitive.

To do this, we must put two capacitors in series.  Pick the smallest capacitor from part I and connect them in series to the orginal C1.  To aid you in your construction, draw the circuit below (given in class):
 
 
 
 
 

Determine the capacitance of the homemade capacitor in the same way that we did in the previous section.
Measure the length, width, and thickness of the capacitor (the aluminum foil).  You cannot answer question 1 if you do not measure this.
 

With your conclusion, answer the following questions:

1.  What is the value of k for our homemade capacitor? (Show your work)
 
 
 
 
 

2.  If I add a capacitor (C1) in series to another (C2), will I increase or decrease the capacitance of the overall circuit?  Justify your answer.
 
 
 

3.  If I add a capacitor in parallel to another, will I increase or decrease the capacitance of the overall circuit?  Justify your answer.