PHYS 2426 – Engineering Physics II

Introduction to Capacitance

 

Leader: ___________________                      Recorder: __________________________

Skeptic: ___________________                     Encourager: ________________________

 

Materials

Laptop (for graphs)                                          Pasco Parallel Plate Capacitor

Genecon                                                           Set of Dielectric Materials

Light Bulb in Socket                                         2 x Alligator Clip cables

1 F capacitor                                                    15” Ruler or ˝ meter stick

LCR meter

 

Introduction

      In this activity we will examine some of the basic properties of capacitors.  We will first look at some simple qualitative ideas to examine the function of capacitors and then we will determine the factors that affect the capacitance of a capacitor.  This lab will also serve to introduce another common electrical measurement instrument, the LCR meter.  LCR meters are used for measuring inductance (L), capacitance (C), and resistance (R).

 

Part I – Capacitors and Energy Storage

Procedure

Turn the Genecon with nothing attached to it at about 1 turn per second.  Note the resistance the handle offers while turning.  Now, connect the terminals of the Genecon to the terminals of the socket. 

 

Q1)  Describe what happens.

 

 

Q2)  Why is it harder to turn the Genecon when it is connected to the light socket?

 

 

Q3)  Describe the energy transfer that occurs between you turning the handle and the light bulb lighting.

 

Connect the Genecon to the two leads on the 1 F capacitor.  Turn the handle at 1 turn per second for at least 20 seconds.

 

Q4)  Describe how the resistance of the handle changes as you continue to turn it.

 

 

Let go of the handle.

 

Q5)  Describe what happens when you let loose of the handle.

 

Put the Genecon flat on the table while the handle is still turning.

Q6)  Describe what happens.

 

 

When the Genecon handle offers resistance, you are doing work and thus transferring energy.

 

Q7)  Explain why when the Genecon is connected to the capacitor the resistance offered by the handle decreases over time.

 

 

Q8)  When you let loose of the handle, it continues to turn.  What provides the energy to continue turning the handle?

 

 

Q9)  Does the handle continue to turn indefinitely?

 

 

When we turn the handle, we are “charging” the capacitor and storing energy in it.  When we quit turning the handle, we extract the stored energy and use it to extract the stored energy.

 

Use the Genecon to charge the capacitor.  Quickly disconnect the Genecon and use the alligator clip cables to connect the leads of the capacitor to the light bulb.  Observe the light bulb for a while.

 

Q10)  Describe what happens.

 

 

Q11)  Why does the light bulb go out?

 

 

Replace one of the alligator clip cables with one lead from the Genecon to the capacitor and the other lead from the Genecon to the socket.  Turn the Genecon handle steadily at 1 turn per second for quite a while and observe the light bulb.

 

Q12)  What happens to the light bulb over time as you keep turning the handle?

 

Stop turning but continue to hold the handle and observe the light bulb.

 

Q13)  Describe what happens.

 

The light bulb indicates when there is energy transfer.

 

Q14)  As you turn the handle over time the light bulb goes out.  Can you transfer energy to the capacitor indefinitely?

 

Q15)  When you stop turning the handle, the light bulb lights but goes out.  Why?

 

Summary

Q16)  In terms of energy, what does a capacitor do?

 

 

Part II – The Dependence of Capacitance on Geometry:  Plate Spacing

Introduction

      In this part we will explore how capacitance depends on the geometric arrangement of the plates used to construct the capacitor.

 

Procedure

1.  Set-up

      The Pasco parallel plate capacitor consists of two circular parallel plates.  One of the plates slides and so the distance between the plates can be adjusted.  The scale gives the distance between the plates in cm.  Note that on one of the plates are some plastic tabs to keep the plates from touching completely.

      Connect the leads from the LCR meter to the terminals on the Pasco parallel plate capacitor.  Turn on the power by pushing the green button on the upper left of the meter.  The meter should come up in a mode to measure capacitance.  This will be indicated by the units in the lower right of the display being expressed in some multiple of F, possibly pF, nF, or μF.  If it doesn’t push the LCR button until the units indicate capacitance.

 

2.  Data Collection

      Record the capacitance read by the meter and the distance between the plates in the data table below.  Fill in the appropriate units in the column for capacitance.

Move the plates to a separation of 4 cm and record the separation and the capacitance in the table.  Repeat three more time each time increasing the separation by 4 cm.

 

Distance between Plates (cm)

Capacitance

(      )

 

 

 

 

 

 

 

 

 

 

 

Q17)  As you increase the plate spacing how does the capacitance change?

 

 

Q18)  Does the capacitance change the same amount each time or does the change get smaller with larger spacing?

 

Q19)  What does this suggest about the type of relationship between the capacitance and the plate spacing?

 

Disconnect the leads from the capacitor and lay them on the table.

 

Q20)  When the leads are disconnected does the meter read 0?

 

Try moving the leads around, closer, further and so on.

 

Q21)  Does the reading on the meter change as you move the leads around?

 

This is an important point in making measurements.  The meter itself will have capacitance and this capacitance will add to the measured value.

 

Reposition the leads in approximately the position used while measuring the capacitance of the plates. (Still not connected.)

 

Q22)  Record the reading of the meter.

 

 

Q23)  As a first approximation, we can treat the meter capacitance as a constant which we can subtract from our readings above, or alternatively which we can allow for in the fit we make to our data.  In this procedure we will allow for it in the fit we make to our data.

 

      From class we expect the capacitance of a parallel plate capacitor to be
 (1), where Area is the cross sectional area of one of the plates, d is the spacing between the plates, and ε0 = 8.85 x 10-12 C2/(Nm2).  From this result we expect the capacitance to vary inversely with the distance. 

      Use LoggerPro to construct a properly labeled graph of Capacitance vs. Plate Spacing.  Click on the curve fit button , and scroll down the list to Nth Inverse.  Click on the radio button and enter 1 in the box for the Power.  Click on the Try Fit button and then on OK to accept the fit.

 

Print and attach a copy of your graph to the report.

 

Q24)  Record the equation given by the fit.

 

 

Q25)  The constant B given by the fit represents a constant capacitance added to the data.  How does the value given from your fit compare to the value you measured in Q22?  Compute the percent difference taking the measured value as the correct value.

 

 

 

Q26)  Based on your answer to Q25), did treating the capacitance of the meter as a constant amount seem like a reasonable procedure?

 

Q27)  Compare the fit to the expression for the capacitance of the parallel plate capacitor given in equation (1).  What combination of variables does the coefficient A give?

 

 

Q28)  Determine and record the area of the plates.

 

 

Q29)  Use your fit and your answers to Q27) and Q28) to determine a measured value of ε0.  Show your work and record the measured value in the space below.  Be very careful about units!

 

 

Q30)  Compute the percent difference between the value you determined in Q29 and the accepted value of ε0. 

 

 

Q31)  Equation (1) was derived for an infinite parallel plate capacitor.  Does it seem to do a good job of describing the parallel plate capacitor we used in this lab?  Justify your answer.

 

 

 

Part III – Dielectrics

Procedure

You should have several pieces of insulating material.  Another term for insulator is dielectric.  In the context of capacitors, we usually refer to insulators as dielectrics.  Reconnect the LCR meter to the terminals of the parallel plate capacitor.  Place one of the sheets of dielectric material between the plates of the capacitor and close the plates onto the dielectric.  Record the material and the capacitance in the table below.

 

Carefully remove the dielectric so that you don’t change the plate spacing.  Record the value of the capacitance in the table.  Place the appropriate units in the column heading.

 

Material

Capacitance with Dielectric (      )

Capacitance without Dielectric (       )

Dielectric Constant

 

 

 

 

 

 

 

 

 

 

 

 

 

Q32)  How does the value of the capacitance compare with and without the dielectric between the plates?

 

 

Repeat the measurements with the other dielectric materials.  Add your results to the data table.

 

Q33)  Is the trend the same for the other materials as it was for the first?

 

 

When you add a dielectric material to a capacitor, the capacitance increases by a multiplicative factor known as the dielectric constant.

 

Q34)  How can you use the data above to determine the dielectric constant for each material?

 

 

Q35)  Use your answer to Q34)  to determine the dielectric constants for each of the materials.  Record your values in the table above.  (As a check, dielectric constants are greater than 1.)