Capacitors

Figure 115.

As you can imagine, the equipotential lines are evenly spaced and parallel to one another in the case of a uniform electric field and parallel conducting plates. In such a case, the voltage potential at the positive plate will be the highest and the voltage potential at the negative plate will be at the lowest.

CAPACITORS

A capacitor is a device that is used to store electric charge. Capacitors do a great deal in electric systems by filtering static in radio reception and will store energy in heart defibrillators. These commercial capacitors will have two conducting parts that are close together but do not touch. Often, an insulator is used between the two plates in order to create the separation.

While the capacitor’s overall charge is, of course, zero, there will be split of charge between two conducting plates. A battery can be used to charge the capacitor into positive and negative plates. The amount of charge that can be stored depends on the capacitor’s size and on the voltage applied. The electric field strength is directly proportional to the overall charge of Q. The greater the charge applied by a battery, the greater the amount of charge it can hold.

So, what is capacitance? This is proportional to the charge that is stored in the capacitor. The charge stored in the capacitor is the capacitance multiplied by the applied voltage. It is defined as the amount of charge stored per volt applied. The unit of capacitance is the Farad, which goes by the initial F. One Farad is one coulomb per volt. A one-farad capacitor is one that will store one coulomb when one volt is applied. A one-Farad capacitor would be huge and most are in the range of 1 x 10-12 Farads to 1 x 10-3 Farads.

The parallel plate capacitor will have two identical conducting plates separated by a distance d with no material between the plates. When voltage V is applied to the capacitor, an amount of charge Q is held by it. Capacitance depends on the surface area of the two plates and by distance between them. The bigger the plates, the more charge can be stored. The force between the charges will decrease with distance. What this means is that, the larger the surface area of the capacitor and the closer they are to one another, the more charge can be stored.

The capacitance can be defined as a constant multiplied by the area divided by the distance. The constant is called the “permittivity of free space”, which is 8.85 x 10-12 Farads per meter. This is such a small number because a farad is a very great number.

The problem with capacitors is that they have to be big in order to work unless some modifications are done. Some modifications include using plates that can be rolled up so that they can be bigger and can use up less physical space. Another modification is to introduce a dielectric, which is an insulating material between the plates of the capacitor in order to allow the distance to be as small as possible. These can hold greater electric fields that can be gotten through air without breaking down.

The other benefit of using a dielectric is that the equation doesn’t use the permittivity of free space constant but uses the dielectric constant also referred to by the letter k. This gives the capacitor a greater degree of capacitance. The dielectric constant for air is nearly one, while for a vacuum, it is set at one exactly. Other dielectrics will have different dielectric strengths, above which the material will break down and conduct.

The dielectric strength is the maximal electric field above which the dielectric begins to break down and conduct electricity. The more easily a dielectric is polarized, the greater

is its dielectric constant. Water is highly polar as a molecule and therefore it has a dielectric constant of 80, which is relatively high. It will increase the Coulomb force between the two plates. The dielectric constant is the ratio of the electric field in a vacuum to that in the dielectric material. It is highly related to the polarizability of the material.

Some molecules are polar and will have a separation of charges within the molecule. Hydrogen ions are partly positive, while oxygen molecules are slightly negative. This molecule and similar molecules have higher dielectric constants because they are more polarizable. In a sense, water has an electric field and a charge separation. It provides a screening or shield of the electric fields in biological systems. Figure 116 shows the polar water molecule:

Figure 116.

What’s true of capacitors is that they can be linked together in a variety of situations in physics. Many capacitors together can act like a single capacitor with the total capacitance depending on the capacitance of the different capacitors. These can be done in series and parallel or in combination of both.

Remember that the capacitance is the charge divided by the voltage. The combination of capacitors in series resembles a single capacitor with an effective plate separation greater than that of the individual capacitors alone. Large plate separation means a

smaller capacitance. This will mean that capacitors in series doesn’t add to the capacitance of a system but subtracts from it. One divided by each capacitance and added together leads to one divided by the total series capacitance when in series.

Capacitors in parallel have the same voltage applied to each capacitor with conductors being equipotential from each other. These capacitors have the same charges on them as they would if they would have been connected individually. The total charge is the sum of the individual charges. In such cases, the capacitance is the sum of the capacitance of each capacitor. This leads to the appearance of a much larger capacitor. If there is a combination of parallel and series capacitors, the capacitors in series are added as in the equation, while capacitors in parallel are added together so the sum is given.

Figure 117 shows how to add capacitors in series and in parallel. When adding capacitors in series and in parallel, the C total will be the C in series plus the C in parallel added together:

Figure 117.

In reality, capacitors are used to store energy in things like defibrillators, calculators, and camera flash lamps. This is electrical potential energy of the system. Capacitors start with zero voltage and go up to a full voltage when charged. This makes the change in voltage the same thing as the total voltage on the capacitor. The average voltage on

the capacitor during the charging process is half of the total voltage so the energy stored will be the total charge multiplied by the voltage divided by two. Figure 118 shows several ways to describe the energy stored in a capacitor:

Figure 118.

In this case, the energy stored by a capacitor is in Joules and is proportional to the square of the charge while being inversely proportional to the capacitance of the capacitor. The equations in figure 118 are simply rearranging what we know of the values of total voltage, total charge, and capacitance.