Capacitance And Its Measurement

A capacitor is a device, which is used to store an electrical charge or electrical energy. Capacitor consists of 2 electrical conductors separated by a dielectric medium. Capacitance is the measure of the capacitor to store electrical charge. It is the property of an electric circuit which tends to oppose a change in voltage when a potential difference is applied. Capacitance exists when two electrical conductors are separated by a nonconducting medium or a dielectric material.

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Charging Of a Capacitor

When a battery is connected across 2 metal plates, the positive terminal attracts the negative  electrons in plate 1 of the plates. The excess of electrons on the negative of the battery rush to the plate 2 of the capacitor and gets accumulated. More and more electrons leave the plate 1 to the positive terminal of the battery and and more electrons crowd to the plate 2 from the negative terminal. A positive charge accumulates in the plate 1 and a negative charge gets accumulated in the plate 2.  The charges on the two plates increase in opposite directions until the difference between them is exactly equal to the difference in potential between the two terminals of the battery. At this point, the electrons stop flowing as there is a balance in forces of the charged plates. When a dielectric material such as glass or plastic is placed in between the plates, the capacitance increases as seen by the deflection of an ammeter connected in the circuit.

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The unit of capacitance is farad. A capacitor has a capacitance of 1 farad when 1 volt difference in voltage results in the storage of 1 coulomb of charge. Usually capacitors are denoted in micro farads, nanofarads, picofarads, etc. An ideal capacitor is characterized by a constant capacitance C, defined as a ratio of charge + or - Q on each conductor to the voltage V between them.

C = Q/V

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The charge build up in the capacitor affects the capacitor mechanically that varies its capacitance, where the capacitance is measured in incremental changes.

C = dq/dv 

Calculating current flow through the capacitor

Formula of current, I = dQ/dt

The formula for current with respect to time is dQ/dt = d(CV)/dt

it is expressed as I = C (dV/dt)

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Capacitors are used in electronic circuits for blocking DC voltage, allowing passage of AC, resonant circuits in radio, filter circuits, power supply smoothing, timing circuits, switching circuits, stabilizing power and voltage flow etc.

A capacitor has undesirable characteristics and limitations such as leakage current when the dielectric between the conductor plates of the capacitor passes a small leakage current through it. Capacitor has an electric field strength limit, resulting in a breakdown voltage for each. Also the leads and plates of the capacitor introduces some unnecessary inductance and resistance to the circuit.

Factors That Determine the Capacitance

The capacitance of a capacitor differs based on

1. The area of the plate surface that are directly opposite to each other. Increasing the plate area will increase the capacitance.

2. Distances between the plates. The smaller the distance between the plates, the bigger is the capacitance.

3. Type of dielectric. The type of dielectric that the capacitor is using does have an influence on the capacitance. Some dielectrics offers more capacitance than that using other types of dielectric.

The greater the surface area of the plates, the higher is the capacitance. The closer the distance between the plates, the higher is the capacitance. The greater is the dielectric constant of the dielectric, the higher is the capacitance.

Capacitance in Series and Parallel

Capacitors can be connected in series and parallel combination for various reasons. The need for connecting capacitance in combination are to increase or decrease the capacitance, reduce fluctuations due to heat, improved filtering, achieve higher voltage rating, obtaining high Q etc. Capacitors are combined in series to achieve higher voltage as in smoothing a higher voltage AC, the voltage rating of each capacitor adds up. Series combination is also used to connect polarized capacitors  connected back to back to form a bipolar capacitor.

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Capacitors Connected in Series

When capacitors are connected in series, the total capacitance can be reduced. The separation distance of the capacitor increases and not the plate area. Each capacitor stores the charge that is equal to that of every other capacitor in series. The voltage difference at the terminals of each capacitor is distributed among the capacitors according to the inverse of their capacitance. The effective capacitance is smaller than the smallest of any one of the capacitor connected to it.

The capacitors of capacitance C1, C2, C3,  - - - Cn are connected in series and the total capacitance is measured by the formula.

1/C = 1/C1 + 1/C2 + 1/C3 + - - - 1/Cn

For example, the three capacitors with capacitance 10 microfards, 5 microfarads, 5 microfarads are connected in series, it is written as

1/C = 1/10 + 1/5 + 1/5

1/C =  1+2+2/10

C = 2 microfarads

Capacitors Connected in Parallel

When capacitors are connected in parallel, the total capacitance is the sum of all the capacitors. All the capacitance adds up and the effective capacitance increases. Each capacitor have the same applied voltage across its terminals. There is equal distribution of charge through all capacitors depending on the size. Each capacitor contributes to the total surface area of the capacitor.

The capacitors of capacitance C1, C2, - - - C3 are connected in parallel and the total capacitance is measured by the formula.

C = C1 + C2 + C3 - - - + Cn

For example, the three capacitors with capacitance 10 microfards, 5 microfarads, 15 microfarads are connected in parallel, it is written as

C = 10 + 5 + 15

C =  30 microfarads