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# Sustainability and the Practicalities of Design Accuracy (Lab Report Sample)

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Answering questions on electrical engineering and completing a laboratory report.

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Energy of a Photon
The energy of a photon is inversely proportional to its wavelength, that is the shorter the wavelength the higher the energy it possesses. The relationship is written as in the formula below.
E=hcλ
Where;
E is the photon energy in Joules,
h is a constant called the Planck’s constant,
c the speed of light and
λ is the wavelength of the photon.
h and c has got known values. h=6.626 × 10-34 Joule.s and c=2.998 × 108 m/s.
It is further clear that the photon’s energy is a function of its wavelength only. Other factors such as intensity doesn’t affect the energy in a photon.
Example 1:
The red light travels with a wavelength of 620 nm. The minimum photon energy for the red light is therefore calculated as below.
Since the Plank’s constant and the speed of light are known entities. It is also given that the wavelength is 620 nm therefore substituting into the formula for photon energy we get.
E=hcλ
E=(6.626 × 10-34)×(2.998 × 108)×(109)620
E=3.2× 10-19 Joules
Energy in electron-volt
Electron-volt(eV) is a unit of energy used to denote photon energy and one unit of it is the energy needed to raise an electron through 1 volt.
Hence
1 eV=1.602 × 10-19 J
Expressing this in terms of wavelength.
E(eV)=(6.626 × 10-34)×(2.998 × 108)×(109)×eVλ×1.602 × 10-19
EeV=1.2398×10-6 λ eV-m
Example 2:
Taking the wavelength for red light in the example 1 above as 620 nm.
The photon energy in Joules was
E=3.2× 10-19 Joules
The photon energy in electro-volt is given as in the substitution below.
EeV=1.2398×10-6 ×109620 eV-m
EeV=1.99967 eV
Atmospheric effects amount significantly to the reduction of the solar radiation from the edge of the atmosphere to the Earth's surface. The main effects for photovoltaic applications are:
* The radiations are absorbed, reflected and scattered as they travelling through the atmosphere hence reduce their power as they reach the earth’s surface;
* Certain wavelengths are absorbed and scattered in the atmosphere hence a change arise in their spectral content as they reach the surface of the earth;
* The radiations are embedded with diffuse and(or) indirect components as they travel down to the surface; and
* Variations such as water vapour and dust in the atmosphere add to the effects on the incident power, spectral content and direction of the rays.
A more detailed description of the effects is as outlined below.
Atmospheric absorption.
On its way to the earth’s surface through the atmosphere solar radiation are absorbed by suspensions such as gasses and dust. Such gases as ozone (O3), carbon (IV) oxide (CO2) and water vapour (H2O), have highly absorb of the photons that can surrender energy approximately
equal to the bond energies of these gases changing the spectral content of the radiation. Highest impact in reduction of the power from solar radiation is brought by the absorption and scattering of radiation due to presence of air molecules and smoke in the atmosphere.
Light with short wavelength is more susceptible to a scattering mechanism called Rayleigh scattering by molecules that exist in the atmosphere as it exhibits a λ-4 dependence. Another technique of scattering caused by dust particles particularly is referred to as Mie scattering.
This effect contributes to about 10 percent of the incident light being scattered and is known as Diffuse light and appears a blue from its origin the blue light.
Air Mass
Air Mass is the path length taken by light through the atmosphere normalized to path length it would have when the sun is directly overhead. It obviously gives value to the reduction in power of the radiation.
AM=1COSθ
θ is the angle from the vertical.
It is evidently true that the Air Mass is valued as 1 if the sun is directly overhead.Top of Form
Azimuth angle
Azimuth angle refers to the compass direction from where the sun rays are coming. At solar noon, the sun is always directly south in the northern hemisphere and directly north in the southern hemisphere. It varies throughout the day for instance at noon the sunlight is directly north in the southern hemisphere and directly south in the other half. It depends on the latitude and time of year.
The formula for Azimuth angle is given by;
Azimuth= cos-1(sin(δ)cos(θ)-cos(δ)sin(θ)cos(HRA)cos(α))
Whereby;
α is the altitude angle
Elevation angle
Elevation angle is the height of the sun from the horizontal axis when it is travelling through the sky. It has a value 90 degrees when the sun is overhead and zero degrees when the sun is rising. Its proportional to the time of the day. It is dependent on the latitude and the day of the year.
It has a formula given as
α=90+φ-δ
where;
α is the elevation angle in degrees
φ denotes the latitude of the location and
δ is the day of the year.
Semiconductor
Semiconductor is a device that partially conducts current, that is it has the conductivity between that of an insulator and a conducting metal. Recalling the periodic table, they are mostly materials from group IV, combination of group III and V and combinations of group II and group VI elements. Silicon a group IV element is the most applicable semiconductor in practice.
Silicon (Si) structure is has each of its atoms bonded together to form a regular, periodic structure whereby each atom has eight electrons surrounding it. From basic concepts it is stated that an atom is made up of positively charged protons, neutral neutrons and surrounded by negatively charged electrons thus an atom is electrically neutral. The electrons in this arrangement in a semiconductor constitutes a covalent bond. The concept of sharing an electron by atoms is foundation of covalent bond. In silicon therefore the four atoms form four covalent bonds with eight electrons shared as shown below.
Fig1. Silicon crystal lattice representation diagram with each line representing an electron being shared.
Doping
Doping is the addition of impurities to an intrinsic semiconductor intentionally to alter its conduction properties. It varies the number of electrons and holes in the resulting semiconductors.
The materials are said to be N-type when they are doped using group V elements and increases conductivity due to addition of electrons as only four valence electrons are used in bonding with the fifth free electron from the group 5 element used for conduction. P-type semiconductor are as a result of doping with group III elements and boosts conduction by addition of holes as only three valence electrons are available to bond leaving an absence of electron called a hole.
P-N junction and P-N junction diode
P-N junction is formed by joining the P-type and N-type semiconductors. At this junction electrons flow by diffusion from the N-type to the P-type side while holes diffuse from the P-type side to the N-type side and the process continues until the number of electrons equals the number of holes on either side. This leads positive ion cores and negative ion cores in the N-type and P-type respectively being exposed resulting into an electric field in the region which is known as the depletion region that sweeps away carriers.
Though the impending action of electric field in the depletion region is active some majority carriers with enough velocity still diffuse through causing diffusion current whereas minority carriers are swept causing drift current bringing to life the p-n junction diode which is used in solar cells.
Band Gap
Band Gap with reference to a semiconductor is the minimum energy it would take to break an electron from non-conducting bound state to a conducting free state. When this happens the electron is free to move throughout the semiconductor. A hole is created where the electron moved to be filled by another electron and this action continues all over the semiconductor.
Operation of Solar Cell
A solar cell converts the light from the sun directly to electricity. It does this by two processes. The incident photon having energy higher than the band gap is first absorbed and used to create electron-hole pairs. These carrier pair are then collected by the p-n junctions and separated spatially by the junction. Connection of emitter to base of the solar cell the carriers flow through the external circuit.
Short circuit current
Short circuit current denoted Isc is the current through the solar when given the voltage across the solar cell is zero. It arises due to the process of generation and collection of the electron-hole pairs(carriers).
Open circuit voltage
Open circuit voltage often denoted as VOC is the voltage from the solar cell at the instance when the current is zero. It is the maximum value of voltage attainable from the solar cell and is due to biasing by the light generated current.
Fill factor
Fill factor denoted as FF is the ratio of maximum power from the solar cell to the product of open circuit voltage and short circuit current. It is used to aid determine the maximum power possible from a solar cell.
Solar cell efficiency
Solar cell efficiency, η corresponds to the output energy from the solar cell to the input energy from the sunlight. It is also affected by intensity of the sunlight absorbed and the temperature of the cells. It is given as
η=VocIscFFPin
Where;
Pin is the power input from the sunlight.
Construction of the solar cell
Fig 2. The schematic of a solar cell.
Each...
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