Lab #4: The Capacitance of a Parallel Plate Capacitor.

Introduction:

Capacitance and Capacitors

A capacitor is a device used to store charge. The amount of charge a capacitor can store depends on two major factorsthe voltage applied and the capacitor's physical characteristics, such as its size. The capacitance is the amount of charge stored per volt, or

The capacitance of a parallel plate capacitor is

when the plates are separated by air or free space. ₀ is called the permittivity of free space.

Capacitors in Series and in Parallel

Total capacitance in series

Total capacitance in parallel

If a circuit contains a combination of capacitors in series and parallel, identify series and parallel parts, compute their capacitances, and then find the total.

Capacitors with dielectrics

A parallel plate capacitor with a dielectric between its plates has a capacitance given by

where k is the dielectric constant of the material. The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.

Energy stored in Capacitors

Capacitors are used in a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps, to supply energy. The energy stored in a capacitor can be expressed in three ways:

where is Q the charge, V is the voltage, and C is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads.

Objectives of this lab:

1. Using PHET simulation measure properties of parallel plate capacitor.
2. Explore the effect of the separation distance between the plates on the capacitance.
3. Explore the effect of the area of the plates on the capacitance.
4. Develop an understanding of how the dielectric affects the stored charge, energy, and voltage between the plates of the capacitor, when it is connected or disconnected from the battery

Instructions:

Go the PHET web site and select the Capacitor simulation. The following link will take you directly to the simulation:

https://phet.colorado.edu/en/simulation/legacy/capacitor-lab

If you click on the picture - it will prompt the following dialog window:

You can either download the simulator file (bottom) or you can run the lab from your browser (top). Once the Lab Sim is started you should see the following image.

Part I: Introduction

Try different setups - switching battery on and off, check off meters and observe what they do, try using voltmeter with the battery on and measure voltage for different points in the circuit, increase and decrease area of the plates and distance between the plates, observe meter readings.

Part II: Capacitance of the capacitor (middle tab - Dielectric)

1. Select "paper" from the choice of dielectrics in the menu on the right-hand side. Insert the dielectric completely inside the capacitor. Check the "Capacitance" to see the capacitance meter. The battery could be either connected or disconnected for this part.

1. Record the values of the plates' area A₀ (initially, it should be the smallest possible), distance between the plates d₀ (initially, it should be the largest possible), and corresponding capacitance.

1. Slowly increase the plates' area and measure the corresponding capacitance 4 more times (an increment of ~60 mm² is recommended). Record your results in the table in SI units (m, m², F).

Table 1:

Measurement #	A (area, m2)	C (capacitance, F)
1
2
3
4
5

1. Use Excel or other software of your choice to plot capacitance as dependent variable against the area. Then, use linear regression to draw the best-fit line to approximate the data with the linear model. Insert the screenshot of your graph below. It should contain:

• Labeled axes and units
• Data points and best-fit line (remember that the best-fit line does not necessarily go through all the points, but approximates the trend)
• Equation of the best-fit line

INSERT YOUR GRAPH HERE

...

1. Restore area to 100 mm². Now record the values of the plates' area A₀ (initially, it should be the smallest possible), distance between the plates d₀ (initially, it should be the largest possible), and corresponding capacitance.
2. Slowly decrease the distance between the plates area and measure the corresponding capacitance 4 more times (an increment of ~1 mm is recommended). Record your results in the table in SI units (m, m², F).

Table 2:

Measurement #	d (area, m2)	Calculated, 1/d	C (capacitance, F)
1
2
3
4
5

1. Use Excel or other software of your choice to plot capacitance as dependent variable against the reciprocalof the separation between the plates. Then, use linear regression to draw the best-fit line (also called trendline) to approximate the data with the linear model. Insert the screenshot of your graph below. It should contain:

• Labeled axes and units
• Data points and best-fit line (remember that the best-fit line does not necessarily go through all the points, but approximates the trend)
• Equation of the best-fit line

INSERT YOUR GRAPH HERE

...

1. Turn on the battery to +1.5 V. Slowly insert the dielectric inside the capacitor. As the dielectric fills more space in the capacitor, observe and record the changes in

• Capacitance

• Charge

• Voltage between the plates

• Energy stored by the capacitor

Part III: Capacitance of the circuit with multiple capacitors (tab - Multiple Capacitors)

In this part analyze 3 capacitor circuit in different combinations by checking the appropriate boxes on the right panel. Choose any arbitrary magnitude for individual capacitors, record in the table, record total capacitance of the circuit.

Table 3:

C combo	C1 (F)	C2 (F)	C3 (F)	Total C (F), measured	Total C (F), theoretical
3 in parallel
3 in series
2 in parallel and 1 in series
2 in series and 1 in parallel

Verify the measured values by calculating theoretical equivalent capacitance of C combinations.

Report calculated values in the table above.