Capacitor virtual lab

CAPACITORS

OBJECTIVES:

· To understand how a parallel plate capacitor works.

· To determine the dielectric constant for virtual paper used as the dielectric in virtual capacitor.

· To learn how capacitors connected in series and in parallel behave.

· To find equivalent capacitance for a complex combination of virtual capacitors.

EQUIPMENT:

Computer with Internet access.

INTRODUCTION AND THEORY:

Very common and important components in modern electrical devices are capacitors. They are what makes computer memory work. They are used with resistors in timing circuits, they occur as filters and coupling elements in every radio and TV set, they can eliminate ripples or spikes in DC voltages, they are used in flash units in photography.

A capacitor is considered a passive electronic element because it does not actively affect electrical currents in the circuit nor produce electrons or energy. Instead, it is used to store electrical charge (and hence electrical energy). A capacitor consists of a pair of conductors separated by a non-conductive material (or region) called dielectric which effectively insulates the two conductors.

The schematic symbol of a capacitor has two parallel vertical lines (representing the conductors) set a small distance apart, and two horizontal connecting wires:

                                                                         capacitor symbol

Any two conductors separated by an insulator (including vacuum) form a capacitor. When a voltage (potential difference) is applied across the capacitor, a charge is transferred to and from the conductors and an electric field develops in the dielectric. This field stores energy and produces a mechanical force between the conductors which can be released when needed. When a capacitor is charged the two conductors hold equal in magnitude but opposite in sign amount of charge so the net charge on the capacitor as a whole remains zero.

The capacitor’s ability to hold an electric charge is characterized by capacitance C defined as the ratio of the magnitude of the charge Q on either conductor to the magnitude of the potential difference ∆V between the conductors:

                                                                                                                                                 [Eqn. 1]

The SI unit of capacitance is one farad (1 F). One farad is equal to one coulomb per volt.

                                               1 F = 1 farad = 1 C/V = 1 coulomb/volt

The greater the capacitance C of a capacitor, the more charge Q can be stored on either conductor for a given potential difference ∆V and hence greater the amount of stored energy. One farad is a very large unit and we rarely see capacitors this big. In many applications the most convenient subunits of capacitance are the millifarad (1mF = 10-3 F), the microfarad (1µF = 10-6 F), the nanofarad (1nF = 10-9 F) and the picofarad (1pF = 10-12 F).

The value of the capacitance depends only on the shapes and sizes of the conductors and on the nature of the insulating material between them. The simplest way of making a capacitor is to build a unit with two parallel conducting fully overlapping sheets, each with area A, separated by a thin layer of air of thickness d.

Figure 1. Design of a parallel-plate

                 capacitor.

Air

                                              File:Parallel plate capacitor.svg

This arrangement is called a parallel-plate capacitor and its capacitance approximately (when d is small compared to the other dimensions and the field fringing effect around the periphery provides a negligible contribution) equals:

                                                                    C0 = , [Eqn. 2]

where is the permittivity of free space = 8.854-12 F/m. Please, note that A represents the area of overlap of the conducting surfaces.

The capacitance of a parallel plate capacitor is directly proportional to the area A of each plate (or in general to the area of overlapping) and inversely proportional to their separation d. Plates with larger area can store more charge. Similar effect takes place for the plates being closer together – according to Coulomb’s law when d is smaller the positive charges on one plate exert a stronger force on the negative charges on the other plate, allowing more charges to be held on the plates for the same applied voltage and this constitutes capacitor with larger C.

In commercial capacitors the layer of air is replaced by dielectric material such as Mylar, rubber, mica, waxed paper, silicone oil etc. If the space between the conducting plates is completely filled by the dielectric, the capacitance increases by the factor , called the dielectric constant (or relative permittivity) of the material which characterizes the reduction in effective electric field between the plates due to the polarization of the dielectric.

Figure 2. Charged parallel plate capacitor:

- air filled (top),

- with dielectric (bottom).

                                                  http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/diel3.gif

In general the capacitance of a parallel plate capacitor with a dielectric can be expressed as:

                                                           C = = , [Eqn. 3]

where is now the permittivity of the dielectric = κ0 .

Capacitors are manufactured with only certain standard capacitances and working voltages. If a different value is needed for a certain application, one has to use a combination (series, parallel or mixed) of those standard elements connected in such a way to achieve the required equivalent capacitance.

For a series connection, the magnitude of charge on all plates will be the same. Conservation of energy dictates that the total potential difference of the voltage source will be split between capacitors and apportioned to each of them according to the inverse of its capacitance. The entire series acts as a capacitor smaller that any of its components individually.

 = ∆VSource = ∆V1 + ∆V2 + ∆V3 + ….. = + + + …

  = + + + …. [Eqn.4]

                    Figure 3. Two capacitors in series. (a) Schematicillustration. (b) Equivalent circuit diagram.

Capacitors are combined in series mostly to achieve a higher working voltage.

In a parallel configuration all capacitors have the same applied potential difference. However, their individual charges might not necessarily be equal because the charge is apportioned among them by size (C). Since the total charge stored in such combination is the sum of all the individual charges, the equivalent capacitance equals the sum of the individual capacitances and is always greater than any of the single capacitance in this arrangment.

QTotal = Q1 + Q2 + Q3 + …. = C1∆V + C2∆V + C3∆V +….. = (C1 + C2 + C3 +…)∆V

  CEQ = C1 + C2 + C3 + … [Eqn. 5]

                Figure 4. Two capacitors in parallel. (a) Schematicillustration. (b) Circuit diagram. (c)Circuit

                                 diagram with equivalent capacitance.

PART I. Parallel plate capacitor.

Open the PhET Interactive Simulations web page http://phet.colorado.edu/en/simulation/capacitor-lab and download the Capacitor Lab.

The two parallel plates connected to the battery constitute the simplest capacitor. You can change the parameters of this capacitor by placing the cursor on the green arrows and moving it along the indicated directions (up and down to modify the plate separation, sideways to alter the area of plates).

From the right side tool bar menu select all options except the electric field detector. With the mouse left click grab the red test lead of the voltmeter and place it on the upper plate. Next, grab the black test lead and move it to the lower plate. The voltmeter is now ready to measure the potential difference ∆V applied to the capacitor. The potential difference between the capacitor plates will depend on the position of the vertical slider on the battery which allows for adjustment of the battery output.

1. “Design” your own air-filled parallel plate capacitor with plate separation d = 7 mm and having the plate area A of 250 mm2. Apply approximately 1.00 V to it. If the bar graphs displaying the capacitance, the plate charge and the energy go out of range, click the magnifying glasses icons positioned next to them. Capture the screen and paste it into MS Word file – you will have to attach this screen shot to your lab report.