Resistance

Ohm's Law

For any conductor in constant temperature, when current flows the current that flows in the conductor is proportional to the voltage different between the conductor.
V α I
V = kI // k is the proportional constant

by practicals the scientists sow that k is constant for the same conductor. They called it Resistance of the conductor.
V = IR
The resistance of the conductor depend on the three factors.
1. Resistivity of the conductor ( ρ ).
2. Length of the conductor ( l ).
3. Cross area of the conductor ( A ).

The Resistance of the conductor can be given as below.
R = ρl / A
When the temperature changes the resistance of the conductor given in following format.
R_θ = R₀ (1+αθ)
In here,
R₀ - resistance in 0⁰ centigrade s
R_θ - resistance in θ⁰ centigrade s
α - temperature coefficient of resistance in 0⁰ centigrade s( metric unit is K^-1 )

Start with semi-conductors

      Materials can be catagorised into conductors ( Conduct Electricity very well) , insulators (don't conduct electricity) or semiconductors ( Relative to the conductors semiconductors don't conduct electrecity and relative to the insulators conduct Electricity very well) by their ability to conduct electricity.

/* these are advanced readings*/

      In an insulator there are as many electrons as there are energy levels for them to occupy. If an electron swaps place with another electron no change is made since electrons are indistinguishable. There are higher energy levels, but to promote the electrons to these energy levels requires more energy than is usually practical.

/* these are advanced readings*/

     Metals conduct electricity easily because the energy levels between the conduction and valence band are closely spaced or there are more energy levels available than there are electrons to fill them so very little energy is required to find new energies for electrons to occupy. The resistivity of a material is a measure of how difficult it is for a current to flow.

/* these are advanced readings*/

      Semiconductors have a resistivity between 10^-4 < ρ < 10⁸ Ohms per meter (Ω m^-1) although these are rough limits. The band theory of materials explains qualitatively the difference between these types of materials. Electrons occupy energy levels from the lowest energies upwards. However, some energy levels are forbidden because of the wave like properties of atoms in the material. The allowed energy levels tend to form bands. The highest filled level at T=0 K is known as the valence band . Electrons in the valence band do not participate in the conduction process. The first unfilled level above the valence band is known as the conduction band . In metals, there is no forbidden gap; the conduction band and the valence band overlap, allowing free electrons to participate in the conduction process. Insulators have an energy gap that is far greater than the thermal energy of the electron, while semiconductor materials the energy gap is typically around 1eV.

Intrinsic semiconductors

Essentially pure semiconductor material. The semiconductor material structure should contain no impurity atoms. Elemental and compound semiconductors can be intrinsic semiconductors. At room temperature, the thermal energy of the atoms may allow a small number of the electrons to participate in the conduction process. Unlike metals, where the resistance of semiconductor material decreases with temperature.
As the temperature increases, the thermal energy of the valence electrons increases, allowing more of them to breach the energy gap into the conduction band. When an electron gains enough energy to escape the electrostatic attraction of its parent atom, it leaves behind a vacancy which may be filled be another electron. The vacancy produced can be thought of as a second carrier of positive charge. It is known as a hole . As electrons flow through the semiconductor, holes flow in the opposite direction. If there are n free electrons in an intrinsic semiconductor, then there must also be n holes. Holes and electrons created in this way are known as intrinsic charge carriers. The carrier concentration or charge density defines the number of charge carriers per unit volume. This relationship can be expressed as n=p where n is the number of electrons and p the number of holes per unit volume.

Extrinsic semiconductor

Consists can be formed from an intrinsic semiconductor by added impurity atoms to the crystal in a process known as doping.As an example, consider Silicon. Since Silicon belongs to group IV of the periodic table, it has four valence electrons.In the crystal form, each atom shares an electron with a neighboring atom. In this state it is an intrinsic semiconductor.B, Al, In, Ga all have three electrons in the valence band. When a small proportion of these atoms,(less than 1 in 10⁶ ),is incorporated into the crystal the dopant atom has an insufficient number of bonds to share bonds with the surrounding Silicon atoms.One of the Silicon atoms has a vacancy for an electron. It creates an a hole that contributes to the conduction process at all temperatures. Dopents that create holes in this manner are known as acceptors.This type of extrinsic semiconductor is known as p-type as it create positive charge carriers. Elements that belong to group V of the periodic table such as As, P, Sb have an extra electron in the valence band.When added as a dopant to intrinsic Silicon, the dopant atom contributes an additional electron to the crystal.Dopants that add electrons to the crystal are known as donors and the semiconductor material is said to be n-type.

* If one As atom dopent to the 10⁶ Ge atoms the conductivity of the material increasing by 10³ times.

Capasitance

Capacitance

Capacitor

A parallel plate capacitor consists of two conductors separated by a non-conductive region. The non-conductive region is called the dielectric medium. The dielectric is an electrical insulator(glass, air, paper, vacuum, etc; even a semiconductor depletion region chemically identical to the conductors).
A capacitor is assumed to be self-contained and isolated, with no net electric charge and no influence from any external electric field. The conductors thus hold equal and opposite charges on their facing surfaces, and the dielectric media develops an electric field. In SI units it measures by a farred(F).

Farred

One coulomb of charge on each conductor causes a voltage of one volt across the device.
The formula for calculate capacitance of the capacitor,
     C=Q/V
In here,
   C - Capacitance of the capacitor
   Q - Charge of a plate
   V - Voltage different between two plates
Sometimes charge build-up affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance is defined in terms of incremental changes:
   C=dC/dV
Also capacitance of the capacitor is give by,

C = ƐA/d

Here,
Ɛ - permittivity of the media
A - Area of the plates
d - Distance between two plates

Energy storage of the capacitor

The work done in establishing the electric field, and hence the amount of energy stored, is given by,

    W= VQ/2