PHYS 2426 – Engineering Physics II

Introduction to Capacitance II – Area

 

Leader: _________________________          Recorder: __________________________

Skeptic: _________________________         Encourager: ________________________

 

Materials

Laptop (for graphs)

Aluminum foil

1 sheet acrylic

LCR meter

Micrometer (2 shared between tables)

1 x Pasco Parallel Plates capacitor on instructor’s with dielectric sheet for comparison.

 

Introduction

      This lab will continue the investigation of capacitance that we started in the previous lab.  In that lab we investigated the dependence of a parallel plate capacitor on the distance between the two plates.  In this activity we will investigate the dependence of the capacitance on the area of overlap between the two plates. 

 

Part IV – The Dependence of Capacitance on Area

1.  Set-up

      Cut two strips of aluminum foil 15 cm long.  Use a straight edge and cut your strips perpendicular to the sides of the aluminum foil.  Place one of the sheets of aluminum foil on the lab table.  Place the sheet of acrylic on top of the foil so that one of its short edges lines up with but is 1 cm beyond the corresponding edge of the foil.  Connect one of the leads of the LCR meter to the exposed corner of the aluminum foil.  Be gentle in handling the foil, it will rip.

      Place the other sheet of aluminum foil so that it is oriented the same as the first but that it overlaps the first sheet by only 2 cm on the side opposite the exposed end of the first sheet.  Your set up should look something like figure 1.  Connect the other lead of the LCR meter to the top piece of aluminum foil opposite the other lead.  Try to keep the sheets of foil smooth and flat.

 

Figure 1  Schematic of Experimental Setup

 

2.  Qualitative Observations

While observing the LCR meter, slowly slide the top sheet of aluminum foil so that the area of overlap increases between the two sheets.

 

Q1)  As the area of overlap increases how does the capacitance change?

 

 

Q2)  Does the change seem to be proportional to the area or does it seem to change in some other way?  Explain.

 

Being careful not to rip the foil, place your textbook on top of the top sheet of foil.

 

Q3)  Did the capacitance read by the meter change?  In what way?

 

 

Q4)  Why do you think the capacitance changed when you placed the textbook on top?  Illustrate your answer with a sketch.

 

Remove the textbook.

 

3.  Data Collection

You should have observed that the capacitance increased as the area of overlap between the sheets of foil varied.  Here we will look at that quantitatively.  Measure and record the width of the foil.

 

Width  =  ___________

 

Keeping the sheets parallel, arrange them so that they overlap by approximately 1 cm.  Measure and record the actual distance in the data table below.  Determine the area of overlap and record that in the table.  Measure and record the capacitance read by the meter.

 

Length

Area

Capacitance

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Repeat 6 more times each time increasing the amount of overlap by 1 cm.

 

      Use LoggerPro or Excel to construct a properly labeled graph of Capacitance vs. Area.

 

Q5)  Do your data seem to agree with your answer to Q2)?

 

 

Q6)  Add a best fit line and record the equation of the best fit line for later reference.

 

 

Print and attach a copy of your graph.

 

We can treat our capacitor like a parallel plate capacitor.  The capacitance of a parallel plate capacitor with a dielectric is C = ε0κA/d + C0 (1), where we have added an additive constant to account for the capacitance of the leads. κ is the dielectric constant and ε0 is the permittivity of free space 8.85 x 10-12 F/m.

 

Use the micrometer to measure the thickness of the sheet of acrylic.

 

Thickness of sheet of acrylic = ________________

 

Q7)  Use Equation (1), the measured value of the thickness, and your fit (Q6) to determine the dielectric constant of acrylic.

 

Q8)  The textbook value for the dielectric constant of acrylic is 2.5.  Is the value you determined comparable, less, or greater than the accepted value?

 

 

Q9)  When you measured the dielectric constant in the previous part of this lab you probably got a value of around 1.3 or so - noticeably less than the accepted value.  Is this consistent with your measured value here?

 

 

Our determination of the dielectric constant seems to be consistently too small suggesting that we have a systematic error.

 

Q10)  What effect did placing the textbook on top of the capacitor have? 

 

It is true that it probably decreased the distance slightly, but not enough to account for the change.

 

Q11)  Did anything else change about the capacitor when the textbook was added?  Draw a picture to illustrate your answer.

 

 

Q12)  Will the answer to Q11) change the capacitance?  In what way.

 

 

Q13)  Examine the apparatus you used last time.  When the dielectric sheet is in and the capacitor is closed is the interior completely filled with the dielectric?

 

Q14)  Explain why this will give you a measured value of the dielectric constant which is too small.