Capacitors and Capacitance

Capacitor

The capacitor is a component which has the ability or “capacity” to store energy in the form of an electrical charge producing a potential difference (Static Voltage) across its plates, much like a small rechargeable battery.

A capacitor is a system of two conductors separated by an insulator. The conductors have charges, say Q₁ and Q₂, and potentials V₁ and V₂.

· Usually, in practice, the two conductors have charges Q and – Q, with potential difference V = V₁ – V₂ between them. We shall consider only this kind of charge configuration of the capacitor. (Even a single conductor can be used as a capacitor by assuming the other at infinity.)

· The conductors may be so charged by connecting them to the two terminals of a battery. Q is called the charge of the capacitor, though this, in fact, is the charge on one of the conductors – the total charge of the capacitor is zero. The electric field in the region between the conductors is proportional to the charge Q. That is, if the charge on the capacitor is, say doubled, the electric field will also be doubled at every point. (This follows from the direct proportionality between field and charge implied by Coulomb’s law and the superposition principle.)

· Now, potential difference V is the work done per unit positive charge in taking a small test charge from the conductor 2 to 1 against the field. Consequently, V is also proportional to Q, and the ratio Q/V is a constant

The Capacitance of a Capacitor

Capacitance is the electrical property of a capacitor and is the measure of a capacitors ability to store an electrical charge onto its two plates with the unit of capacitance being the Farad (abbreviated to F) named after the British physicist Michael Faraday.

Capacitance is defined as being that a capacitor has the capacitance of One Farad when a charge of One Coulomb is stored on the plates by a voltage of One volt. Note that capacitance, C is always positive in value and has no negative units. However, the Farad is a very large unit of measurement to use on its own so sub-multiples of the Farad are generally used such as micro-farads, nano-farads and pico-farads, for example.

Standard Units of Capacitance

· Microfarad (μF) 1μF = 1/1,000,000 = 0.000001 = 10^-6 F

· Nanofarad (nF) 1nF = 1/1,000,000,000 = 0.000000001 = 10^-9 F

· Picofarad (pF) 1pF = 1/1,000,000,000,000 = 0.000000000001 = 10^-12 F

Then using the information above we can construct a simple table to help us convert between pico-Farad (pF), to nano-Farad (nF), to micro-Farad (μF) and to Farads (F).

Parallel Plate Capacitor

A Parallel Plate Capacitor is an arrangement of two metal plates connected in parallel separated from each other by some distance. A dielectric medium occupies the gap between the plates. The dielectric medium can be air, vacuum or some other non-conducting material like mica, glass, paper wool, electrolytic gel and many others.

Charging of Parallel Plate Capacitor

Circuit for charging capacitor

Let C be the two plates of capacitor, V be the potential difference and k be the switch in above figure.

Now when the key is closed then the electrons from the first plate start moving towards the positive end of the battery that is, there is flow of electrons from negative end to positive end of the battery

The electrons which moved towards to the positive end of battery from there they will start moving towards to the second plate. In this way both the plates will acquire charges, one will acquire positive charge while other will acquire negative charge.

This process will continue until the capacitor acquires potential difference V in the exact same amount that of the battery. Now the process will stop. At this time when the process has been stopped the capacitor has stored electric charge on it with the potential difference which is same as battery.

So now the charge can be written as:

Q = CV

Dependence of Charge Stored in a Capacitor

The amount of electric charge stored in any of the plate of parallel plate capacitor is directly proportional to the potential difference between the two plates of Parallel Plate Capacitor. This relation can be seen as:

Q α V

Q = (constant) V

Q = CV

where,

C = Capacitance of capacitor

Q = Amount of charge stored in one capacitor

V = Potential difference between the two plates

Capacitance of Parallel Plate Capacitor

The capacitance of parallel plate capacitor depends upon

· The distance d between two plates

· The area A of medium between the plates

· According to the gauss law, the electric field can be written as:

= V

Since we know that the capacitance is defined as V = Q/C, so capacitance can be rewritten as:

When the plates are placed very close and the area of plates are large we get the maximum capacitance.

Dielectric Material inserted between two plates

Dielectric placed between two electrodes

On the two plates, the microscopic dipole moment of the material will shield the charges. Thus will alter the effect of dielectric material which is inserted between the two plates Materials have a permeability which is given by the relative permeability k.

The capacitance is thus given by:

Capacitance of a parallel plate capacitor can be increased by introducing dielectric between the plates as the dielectric have permeability k, which is greater than 1. K is also sometimes known as Dielectric Constant.

Condition of parallel plate capacitor when medium is in air and in other substance

When in parallel plate capacitor the area between the who plates are partially filled with air and partially with other substance its Capacitance can be calculate.

Let there exist a parallel plate capacitor in which medium between the parallel plates is mainly the air and partially other substance as shown in figure below:

Dielectric and air between plates

Multi plate Parallel Plate Capacitor

The arrangement of parallel plate capacitor with dielectric material between them in groups fitting in each other is known as Multi plate Parallel Plate Capacitor.