Basic Electrical Engineering

Sun Calculator (Sun angles calculator for Solar Photovoltaic Energy Sector)

2015-03-12T11:32:00.000+05:00

IE_DU PV Sun calculator

Institute of Energy of University of Dhaka has released the first version of IE_DU PV Sun Calculator. With this calculator you can easily find all the solar angles and you can also do time calculations and conversions.

We have also added some definitions. This version of sun calculator is a freeware and the source code can also be downloaded. And you can modify the software and use in commercial applications as well.

The download links of both the IE_DU PV Sun calculator and the source code of the sun calculator are given below. If you can not download it then leave us a comment.

Download IE_DU PV sun calculator software.

Download the source code of IE_DU PV Sun calculator.

Superconductors

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From the name we can guess that superconductors are such conductors which have a very high conductivity (theoretically infinite) or zero resistance. Usually in all conductors there are obstacles for electrons to flow like, collisions with other atoms of the material, repulsive forces between electrons (as we know like charges repel each other), impurities of the conductors, thermal disturbance created by temperature increase of the conductor etc. In a superconductor these obstacles are eliminated to have a perfect conduction.

Copper effect: In a superconductive state, electrons are paired together to help each other maintain a significantly higher velocity through the medium.

Superconductivity with years

History: Superconductivity was first discovered in 1911 but until 1986 it was of no use as it was only attainable at 23K (=-250C). In 1986 physicist Alex Muller and George Bednorz increased the temperature to 30K by using Lanthanum barium copper oxide. After few months of the same year professor Paul Chu and Man Kven Wu raised the temperature to 95K using a superconductor of Yttrium barium copper oxide.

Inferred absolute zero temperature:

2014-09-06T12:49:00.000+05:00

In a temperature-resistance curve of a metal (such as copper) the resistance gradually increases with the increase of temperature. Temperature has a profound effect on resistance and hence it is important that we determine a method to find the resistance at any temperature within the limit of operation. Although the temperature-resistance curve is not a straight line, we draw a best fit straight line to find the resistance at normal operating temperature range.

Figure: Temperature-Resistance curve of copper and inferred absolute zero temperature.

Although the actual curve extends to absolute zero (-273.15°C, or 0 K), the straight-line approximation is quite accurate for the normal operating temperature range.

Series Circuit

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Two or more electrical elements are connected in series if they have only one common node in between and no other electrical element is connected to that common node. So there are two conditions for being in series:

0 1. The elements should have only one common terminal (node). This means that they should be connected one after another.

0 2. No other current carrying electrical element should be connected to that common terminal (node).

To illustrate this lets have a look to the following circuit:

Series Circuit

In this circuit resistor R1 and R2 are in series as they have only b point common in between them and no other current carrying electrical element is connected at node b.

As there is no voltage source connected in between a series circuit, the voltage is shared among the resistors according to their values. So the ratio of voltage and resistor becomes constant and current does not change in the series circuit. For example see the following circuit:

Current is same throughout a series circuit

In this circuit, at R1, R2 and R3 voltage will be shared according to their resistance as there is no other voltage source in between them.

Total sum of their resistance = (6+3+1) Ω = 10 Ω

So, according to ratio: for 1 ohm resistance voltage will be = (20 / 10) volt = 2 V

Therefore, Voltage of R1 = 6 x 2 V = 12 V,

Voltage of R2 = 3 x 2 V = 6 V

Voltage of R3 = 1 x 2 V = 2 V

Total voltage = (12 + 6 + 2) V = 20 V = Voltage of the source.

Now let’s find the current in all the resistors.

Current through R1 = (Voltage of R1 / Resistance of R1) = (12 V / 6 Ω) = 2 A

Current through R1 = (Voltage of R2 / Resistance of R2) = (6 V / 3 Ω) = 2 A

Current through R1 = (Voltage of R3 / Resistance of R3) = (2 V / 1 Ω) = 2 A

So its clear that, current through a series circuit remains same throughout the circuit. But the voltage of the circuit drops and is shared by the resistors or electrical elements of the circuit.

Effect of Temperature on the Resistance

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Temperature has a significant effect on the resistance of any electrical element. There are three types of electrical substance:

0 1. Conductors,

0 2. Semiconductors, and

0 3. Insulators.

Conductors: In metals or in any good conductor there are many free electrons. Actually for these free electrons electron flow can occur and conduction of current happens. But when we heat a conductor or raise its temperature the molecules of the conductors start to move and vibrate at a much higher rate than before. So the free movements of the free electrons are hampered and current cannot pass as easily as before. Thus the resistance of the conductor increases. In summary:

Increase in temperature will increase the resistance of a conductor. Therefore conductors have a positive temperature coefficient.

Conductors have a positive temperature coefficient

Semiconductors: In semiconductors like silicon increase in temperature will help to increase the number of free electrons or carriers. So increase in temperature will decrease the resistance of the semiconductor. Therefore they have a negative temperature coefficient.

Semiconductors and insulators have negative temperature coefficient

Insulators: In insulator there is no or very less number of free electrons. Increase in temperature will help some of the electrons to get free from their outer shell and conduct electricity. So increase in temperature of an insulator will decrease its resistance. Thus it has a negative temperature coefficient.

Resistance of Circular wire

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Resistance is the property of an element to resist current and to convert this current in another form of energy like heat. A circular wire has a uniform cross-sectional area. The resistance of a substance which has a uniform cross-sectional area is determined by the following four factors.

1. Material: The material of any particular substance has a unique molecular structure. The number of free electrons and pressure of charge flow is different for each and every substance. So resistance depends on the molecular structure of the material. This property of the substance to resist current is called the resistivity (ρ). The higher the resistivity, the more the resistance.

2. Length: The relationship between the length and resistance is proportional. That is the higher the length, the higher the resistance.

3. Cross-sectional area: There is an inverse proportional relationship among cross-sectional area of the wire and resistance. If the cross-sectional area is high then the resistance will be low.

4. Temperature: Hot material is more resistive and thus temperature has a proportional relationship with resistance. If the temperature of the circular wire is high then it will show more resistance.

Now let’s write these relationships in a formula:

R = ρ x (l / A)

Where,

R is the resistance of the wire, ρ is the resistivity, l is the length of the conductor, and A is the cross sectional area of the wire.

Nodal Analysis with Supernode

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From our previous discussion of Nodal Analysis we have seen, how voltage sources affect nodal analysis. We have also seen how a voltage source makes it easier for us to calculate the node voltages when connected with a reference node. But things get complicated when a voltage source cannot be referenced i.e. it comes in between two non-reference node. This voltage source along with two non-reference nodes forms a supernode.

In summary, When a voltage source comes in between two non-reference node then these two non-reference nodes and the voltage source form a supernode and we take this supernode as a single node and apply KCL and KVL to solve the circuit.

To solve a problem of supernode follow these steps:

01. Mark a reference node such that a supernode can’t be formed. Try to avoid supernode at first hand. If it’s not possible then at least make a voltage source referenced.

02. Then mark other non-referenced nodes as you do in normal nodal analysis.

03. Next, mark the supernode with a dotted circle to remind you that it’s a supernode.

04. Now apply KCL at the supernode.

05. At the end apply KVL at the supernode loop to find the node voltages in supernode.

Let us explain this procedure with an example:

First of all we have marked a reference node V0. Then we marked all other nodes as we do normally for nodal analysis.

Now we have given a dotted circle to remind us that this is a supernode along with V1 and V2.

Now we apply KCL at the circuit:

2 = (V1 – 0) / 2 + (V2 – 0) / 4 +7

8 = 2 V1 + V2 +28 (multiplying both sides by 4)

2 V1 + V2 = -20 ………………………………………………. (a)

Now we apply KVL at the supernode loop:

-V1 - 2 +V2 = 0

V2 = V1 + 2 ……………………………………………………. (b)

Putting this value of V2 in equation (a):

2 V1 + (V1 + 2) = -20

3 V1 = -22

V1 = -22/3 V

Now from (b): V2 = -22/3 +2 = -16/3V

Note that the 10 Ohm resistor connected across the supernode does not make any difference in the calculations as it is connected across the supernode.

Kirchhoff’s Laws

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We have already gain understandings of nodes, branches and loops. German physicist Gustav Robert Kirchhoff gave two laws which alongside with Ohm’s laws give us a powerful tool of circuit analysis.

Kirchhoff’s Current Law (KCL):

Kirchhoff stated that, amount of current entering or leaving a node should be equal. That means the algebraic sum of currents with respect to a node should always be zero.

A water pipe analogy would make it easier for us to understand this law. Suppose in a network of water pipes, water comes and leaves through different branches. At a single point of this network the amount of water coming to that node or point from different branch is always equal to the amount of water leaving from that point or node. If we think water as current then the amount of current coming through different branches at a node in a circuit must be equal to the amount of current leaving that node. This is Kirchoff’s Current Law (KCL).

To illustrate KCL look at the figure below:

At figure A, current I is entering node X and I1 and I2 is leaving node X. And at node Y, I1 and I2 is entering node Y and I is leaving node Y.

Hence, according to KCL:

I=I1+I2=I-I1-I2 = 0

Here current I1 and I2 has opposite polarity of I. So we can express it as: I+I1+I2=0

At figure B, same thing happens. Current I1 and I2 are entering node Z and I3, I4 and I5 is leaving node Z.

Hence, according to KCL:

I1+I2+I3+I4+I5=0

Kirchoff’s Voltage Law (KVL):

The statement of KVL is: In a closed path or loop the algebraic sum all voltages must be zero. That means simply, the voltage sources will generate voltages and other elements will consume it.

We already know the resistors have always a voltage drop, i.e they consume voltage. Other elements like capacitors and inductor also have voltage drops as they consume real or reactive power from the source.

To illustrate KVL, let us see the figure below,

The voltage source E generates voltage or potential. Whereas Resistors have drops of E1, E2, E3 and E4. According to KVL,

E = E1 + E2 + E3 +E4

As we can see from the figure, the signs of potential of resistors is opposite of voltage source. So,

E= -E1-E2-E3-E4

E+E1+E2+E3+E4=0

Hence, the algebraic sum of voltages in a loop is zero.

Nodal Analysis

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Nodal analysis is a procedure to analyze circuits. It uses node voltages as circuit variables. It is a very easy procedure for calculation as it reduces equations and makes it convenient to solve large networks. In nodal analysis we don’t take element voltages rather we take node voltages which actually reduces number of equations to be solved simultaneously. Nodal analysis is basically the implementation of KCL (Kirchoff’s Current Law).

We are interested in node voltages in nodal analysis, and after finding out node voltages we form independent circuit equations to solve the circuit. We should follow the steps below to solve a circuit using nodal analysis:

01. First of all, select a reference node. Show it with a ground notation. You can select any node as a reference node. At that reference node, node voltage will be zero. Now assign voltages like v1, v2 ….. vn-1 etc for remaining nodes. These voltages are referenced with respect to the reference node.

02. Now apply KCL to all other nodes except reference node. You have to use Ohm’s law and using it express branch currents in terms of node voltages.

03. Finally, solve all the simultaneous equations to find the unknown node voltages.

Now let’s explain these three steps using an example. Look at the following circuit.

It’s a simple circuit with a voltage source of 10V and a current source of 1 mA and three different resistors. We have to find the voltage across the resistor R3. Now let us assign a reference node first. Here we can see three nodes are there. We choose the lowermost one as the reference node and assign it Vo = 0V. We also define other nodes having voltages as V1 and V2.

Now as we can see, node V1 has a voltage source of 10V and the other terminal of the source is connected to the reference node. Hence we can say that the whole 10V should appear at V1.

Therefore V1=10V.

Well, here is an important thing to mention: most of the time we assign the node which connected to a voltage source’s negative terminal as a reference node which in turn simplifies our calculation by giving the other node voltage value directly from the voltage source’s value.

Now, let us apply KCL at node V2:

(V2 – V1) / 20 k + V2 / 10 k – 1 m = 0

(V2 – V1) / 20 k + V2 / 10 k = 1 m

V2 –V1 + 2 V2 = 20 (multiplying both sides by 20k)

3 V2 – V1 = 20

3 V2 – 10 = 20 (putting the value of V1)

3 V2 = 20 + 10

3 V2 = 30

V2 = 30 / 3

V2 = 10V

Now, we have all the node voltages. We can find the voltage Vr3 easily.

Vr3 = V1 – V2 = 10 V – 10 V = 0V

We have taken arbitrary values of resistors and sources which lead the voltage across R3 to be zero.

Wye-Delta Transformations:

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Most of the time we can solve the circuit using our idea of series and parallel connection and ohm’s law or KCL or KVL. But sometimes we encounter some circuit where the formations of elements are neither in series nor in parallel. For example look at the figure of bridge network below:

Now look at the following two formations which look like Wye and Delta. These formations usually found in three phase connections, filters, or in matching networks.

(a) Y netwrk (b) Delta Network

(a) Delta Network

(b) Pie Network

When we analyze a circuit we may find a certain formation to be helpful. And we might want to change one formation into other. Suppose it might helpful for us to work with Wye formation in three phase rather in Delta formation. So we have to know how to transform a Delta network into Wye network.

Delta to Wye conversion:

Look at the figure below:

Now for Delta to Wye conversion:

R1 = (Rb . Rc) / (Ra + Rb + Rc)

R2 = (Rc . Ra) / (Ra + Rb + Rc)

R3 = (Ra . Rb) / (Ra + Rb + Rc)

We don’t have to memorize these formulas rather we can easily remember these. Each resistor of the Wye network is the product of the two adjacent resistors of Delta network, divided by the sum of all three resistors of the Delta network.

Wye to Delta Conversion:

Look at the figure again:

Now for Wye to Delta conversion:

Ra = (R1.R2 + R2.R3 + R3.R1) / R1

Rb = (R1.R2 + R2.R3 + R3.R1) / R2

Rc = (R1.R2 + R2.R3 + R3.R1) / R3

We don’t have to memorize this also. The easy way to remember is, each resistor in the Delta Network is the sum of all possible product formation of Wye network’s resistors taken two at a time, divided by the opposite Wye resistor.

Nodes, Branches and Loops

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When we discuss network topology we have to understand certain terms. Among these terms node, branch or loops are used most of the time. Let’s see what they mean.

Branch: A single element with its terminals is usually called a branch. For example a voltage source or a resistor is a branch.

Node: When two or more branches are connected at a point then that point is called a node.

Loop: A closed path in a circuit is called a loop.

Mesh: Mesh is a kind of loop which has no loop inside it. But you have to remember that all meshes are also loops. But all loops are not meshes.

For example let’s have look at the following figure:

In a network or circuit, number of loop, nodes and branches has to satisfy the following fundamental relationship:

b=l+n-1

where, b = number of branches,

l = number of loops and

n = number of nodes.

There is another important thing to remember in circuit analysis.

01. In a series connection two or more elements are connected sequentially, so they carry the same current I , that is in a series connection current will always remain constant where as voltage will have a drop after each element.

02. In a parallel connection, all the branches are connected at two common nodes. So, they apparently have the same voltage at each node but the current is divided according to ohm’s law.

Static electricity

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Without flowing anywhere charge carriers, specially electrons can build up on anything. Anyone can experience this charge storage when he/she walks on a carpeted floor in winter or in a dry place where humidity is low. When charges forms on body, an excess of shortage of electrons makes your body to be charged positively of negatively. This charge formation or storage is called static electricity.

This type of electricity is called static as they don't move like other type of electricity (AC or DC). If the carrier body or thing touches or comes across some metallic body then a discharge happens with a spark. The body or object seems to jump during the discharge. It is the static discharge which makes it happen.

We see lightning occurring at a stormy day or night. Lightning might occur between clouds, or between clouds and ground in the atmosphere. This lightning is nothing but a magnified version of static electric discharge. Before the lightning happens, there is a static charge in the clouds, between different clouds of parts of clouds. In the following figure cloud to cloud (A) and cloud to ground (B) static charge build ups are shown. At figure (A) when two different clouds come sufficiently close to each other then the static discharge happens and lightning occurs. In case of (B) the positive charge in the earth attracts the negative charges of cloud and then discharge happens.

The interesting thing is that, the current flow in a lightning stroke is very high. Its about several tens of thousands or hundreds of thousands, of amperes. But this huge current can't do that much damage as it lasts for only a fraction of second.

Ohm’s Law

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In circuit analysis, current, voltage and resistance and their interdependence play a vital rule. The relationship among them is called Ohm's Law. It was named after the scientist who expressed it first. This law can be denoted by three formulas:

V=IR

I =V/R

R =V/I

Where V stands for voltage, I for current and R for resistance.

One have to remember only one and he/she can derive the others by simple mathematics.

Ohm's Law can be represented by a triangle, as shown in the figure. One can cover the required one to get the relationship between them.

For example, we know E and I, and wish to determine R, we have to just cover R from the picture and see what's left:

Suppose, we know E and R, and wish to determine I, we have to just cover I from the picture and see what's left:

Lastly, if you we know I and R, and wish to determine E, we have to just cover E from the picture and see what's left:

Ideal Voltage and Current Sources

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Ideal Voltage Sources

An electrical device which can generate prescribed voltage irrespective of the current supplied to other elements is called an ideal voltage source. The ability to provide constant voltage will not be harmed by any other means like heavy load. Since load always destabilizes voltage sources and at full load no source can produce prescribed voltage so ideal voltage sources are imaginary. Ideal voltage sources are not available in real world. We use this idea of Ideal voltage source to make comparison among other voltage sources.

In summary we can say, An ideal voltage source is an electric device which maintains a constant voltage whether we change the load or not, or we can say irrespective of the current flowing throw it. The amount of the current supplied by the source depends on the circuit connected to it.

Ideal Current Sources

An electrical device which can generate prescribed current irrespective of the circuit or other elements connected to it, is called an ideal current source.To maintain a constant current the voltage in the circuit will vary. Thus it will produce arbitrary voltage across its terminals. The figure below shows symbol of ideal current sources.

We can say: An ideal current source maintains a prescribed or constant current irrespective of the circuit connected to it. The circuit connected to the ideal current source determines the voltage generated.

BRIEF HISTORY OF ELECTRICAL ENGINEERING

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Electrical engineering has a evolution which was done by few people who needs to be remembered. Among them here are some. We show our gratitude to their effort and work. Hats off to them.

01. William Gilbert (1540–1603): He was an English physician. He is the founder of magnetic science and he published De Magnete in 1600.

02. Charles A. Coulomb (1736–1806): He wan a French engineer and physicist. He published the laws of electrostatics in between 1785 and 1791. Unit of charge Coulomb was named after him.

03. JamesWatt (1736–1819): He was an English inventor. He developed the steam engine. Unit of power is named after him.

04. Alessandro Volta (1745–1827): He was an Italian physicist. He discovered the electric pile. His name is used to represent the unit of electric potential and the alternate name of this quantity (voltage).

05. Hans Christian Oersted (1777–1851): He was a Danish physicist. He discovered the connection between electricity and magnetism in 1820. His name is used to represent the unit of magnetic field strength.

06. Andr´e Marie Amp`ere (1775–1836): He was a French mathematician. He was also a chemist, and physicist. The relationship between electric current and the magnetic field was first electrically quantified by him. His name is used to represent the unit of electric current.

07. Georg Simon Ohm (1789–1854): He was a German mathematician. He investigated the relationship between voltage and current and quantified the phenomenon of resistance. First results of his work were published in 1827. Unit of resistance is named after him.

08. Michael Faraday (1791–1867): He was an English experimenter. He demonstrated electromagnetic induction in 1831. Beginning of the age of electric power was marked by his electrical transformer and electromagnetic generator. Unit of capacitance was named after him.

09. Joseph Henry (1797–1878): He was an American physicist. He discovered self-induction at around 1831. Unit of inductance was named after him. Essential structure of the telegraph was first recognized by him. Later on Samuel F. B. Morse perfected it.

10. Carl Friedrich Gauss (1777–1855): He was a German mathematician. He and Wilhelm Eduard Weber (1804–1891), a German physicist, first published the measurement of earth's magnetic field in 1833. Unit of magnetic field strength is Gauss, while unit of magnetic flux is Weber.

11. James Clerk Maxwell (1831–1879): He was a Scottish physicist. He discovered the electromagnetic theory of light. He also discovered the laws of electrodynamics. Maxwell's equations are the base of modern theory of electromagnetics.

12. ErnstWerner Siemens (1816–1892) andWilhelm Siemens (1823–1883), both were German inventors and engineers. They perfected selectrical science and contributed to the invention and development of electric machines. Their name is used to represent the modern unit of conductance.

13. Heinrich Rudolph Hertz (1857–1894): He was a German scientist and experimenter. He discovered the nature of electromagnetic waves. He then published his findings in 1888. The unit of frequency is named after him.

14. Nikola Tesla (1856–1943): He was a Croatian inventor. But in 1884 he immigrated to the United States. He invented poly-phase electric power systems. The modern AC electric power system and induction motor was his work. The unit of magnetic flux density is named after him.

Dependent (Controlled) Sources

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Usually the voltage and current sources have the ability to generate specific voltage or current irrespective of any other element in the circuit. So, they are not dependent on any other circuit element and termed as independent sources.

But the sources, whose output (current or voltage) is a function of some other voltage or current at a point in a circuit, are called dependent (or controlled) sources.

Dependent sources are represented by a symbol in the shape of a diamond. The symbol is shown in the figure. In the following table the relationship among source voltage and the dependent voltage or the source current or the dependent current is shown:

Voltage and Current:

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Like static electricity, electrons can be motivated to flow through a conductor. The force is the same force manifested in static electricity.

When electrons moves through a closed path then it is called a circuit. When the specific potential energy is different in two location of a circuit then electron flow from high potential to low potential. The measure of specific potential energy (potential energy per unit charge) between two locations at a circuit is called voltage. Voltage is an expression of potential energy. Hence it is always relative between two locations, or points. Most of the time it is called a voltage "drop."

If we connect a voltage source to a circuit, then because of the potential difference, electrons will flow uniformly through that circuit. This uniform flow of electrons is called current.

The amount of current is always same at a single loop circuit. The current will not change anywhere in the circuit. But the voltage drop will be different.

In a broken circuit, where there is a voltage source connected, then the full voltage of that source will appear across the points of the break.

The + sign shows the positive polarity in a circuit and the - sign shows the negative polarity. This convention is also relative.

Resistance of Resistor

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Resistance is the property of an electrical element which defines the measure of obstacle or how much the element will resist the flow of current. Most of the electrical elements in a circuit has some resistance.

There are elements in a circuit which are specially made to increase the resistance of a circuit which are called resistors. Resistors resist the current to flow. Resistors are very important in circuit construction as they resist the flow of current, so they are used to allow specific amount of current at specific element as designed by the engineer.

In industry resistors are made by adding impurities in carbon. Clay to a carbon paste, or by winding a thin wire into a coil can be used as impurities.

The unit of resistance is Ohm (Ω). The upper class Greek letter omega (Ω) is used to denote ohms. One ohm is defined as "if 1 A current is passed through a circuit having a potential difference of 1 V then the circuit has a resistance of 1 ohm".

When there is no resistance along a path of a circuit we call it as 'short'. Short circuit can be dangerous as high current will pass through the short circuit. And if there is a high voltage source connected then short circuit can cause fire and severe damage.

The opposite of short circuit is 'open' circuit where the path of the current is broken at any point of the circuit or network. So at an open circuit current can not flow. But the voltage will appear as it is at the two open terminal of the open circuit.

Electric circuits:

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An unbroken loop which consists of conductive material and along which electrons can flow is a circuit.

When conductive materials no longer form a complete path and continuous flow of electron is hampered then the circuit is called broken or open.

Conductors, insulators, and electron Flow

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From basic chemistry, we all know that different types of atoms have different energy levels or different degrees of freedom to move around. In metals, the outer shell atoms are loosely bound and they move chaotically in between the space of the atoms. In room temperature they are so loosely bound or unbound that they can move freely and leave their respective atoms. And they can float around the space between the adjacent atoms. So they are called free electrons.

In non-metals or insulators such as glass, the electrons of the atoms are heavily bound or they have a very little freedom to move. But if external energy or force is applied such as rubbing or application of heat then the electrons are excited enough to move and leave their respective atoms and transfer to the atoms of any other material. But they do not have the ability to move between atoms within that material like metals.

Conductivity is the measure of relative mobility of electrons within a material.

Conductivity depends on various feature of an atom. Such as, the type of the atom in a material, the atomic mass, the formation of the atoms etc. The materials which has a high mobility of electrons are called conductors. On the other hand, the materials with low electron mobility are called insulators.

Few common examples of conductors and insulators are given below:

Conductors: silver, copper, gold, aluminum, iron, steel etc.

Insulators: glass, rubber, oil, asphalt, fiberglass, porcelain, ceramic, quartz etc.

Conductance and the Siemens

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When a substance can conduct better, we say that its resistance is less. When it conducts less, we say that its resistance is high. But most of the time electrical engineers don't mention resistance or a material rather they prefer to speak about conductance of a material.

Conductance is the ability of a substance or material to pass electricity. The measure of the opposite of resistance is conductance. Siemens, S is the unit of conductance. When a the resistance of a component is 1 ohm then its conductance is also 1 Siemens. When the resistance is increased to double, the conductance is decreased to half and vice-versa.

The relation between Siemens and ohms can be written as:

Siemens = 1/ohms, or

ohms =1/Siemens

Transformer

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Transformer: Transformer is an electrical device which transfers electrical energy through inductively coupled conductors. These inductive conductors are called coils. From Faraday's Law, we know if we give a varying current in the first or primary winding then in the core a varying magnetic flux will be induced. Thus it will induce a varying magnetic field in secondary winding. This varying magnetic field induces a varying electromotive force (EMF), or "voltage". This effect is known as inductive coupling.

Current will flow in the secondary winding, if a load is connected to it, and from the primary circuit through the transformer to the load electrical energy will be transferred . The induced voltage of an ideal transformer in the secondary winding (V_s) is in proportion to the primary voltage (V_p). It is given by the ratio which is usually called as transformer's turns ratio. The turns ratio is ratio of the number of turns in the secondary (N_s) to the number of turns in the primary (N_p) as follows:

By appropriate selection of the turns ratio, a transformer enables an alternating current (AC) voltage to be "stepped up" or "stepped down" by making N_s greater than N_p, or by making N_s less than N_p respectively. In most of the transformers, the windings are coils wound around a ferromagnetic core.

Transformers can be of different sizes. One can be size of a thumbnail hidden inside a stage microphone, while other can be huge units weighing hundreds of tons used to interconnect portions of power grids. But all of them operates according to the same principles.

Now-a-days new technologies have somehow eliminated the need for transformer in some electronic circuit. But still transformers are found in almost all electronic devices which are designed for household use. Transformer are must for high voltage electric power transmission. It makes long distance transmission economical and practical.

Quiz 01: Basics of Circuit Theory

2012-04-11T15:28:00.014+05:00

Quiz 01: Basics of Circuit Theory

Given each of the questions below, check the most appropriate response.

All about Capacitors

2011-08-06T01:35:00.002+05:00

Capacitor

A capacitor was formerly known as condenser. It is a device for storing electric charge. Practical capacitors are made using various methods. But in all of them there are at least two conductors separated by an insulation.

A pair of conductors separated by a dielectric or insulator forms a capacitor. If we apply a potential difference or voltage across these two conductors, then a static electric field is formed across the insulator or dielectric. Hence, positive charges are stored in a plate or conductor and negative charges in the other. The unit of capacitance is Farad. It is the ratio of electric charge to the potential difference on each conductor.

Capacitors are widely used in electronic circuits. It is used to block direct current while allowing alternating current to pass. It is also used in filter networks, for smoothing the output of power supplies. It is also used in the resonant circuits.

To increase the capacitance of a capacitor we have to do two things:

01. Increase the area of the conductors by any means and

02. Narrow the separation between them as much as possible.

Operation of Capacitor:

Capacitors are the general model for electric fields. An ideal capacitor is the one which has a constant capacitance C. Capacitance C, can be defined as the ratio of charge on each conductor to the voltage between them.

C = Q/V

where C is capacitance, Q is charge and V stands for voltage.

In fact, charge build up is a continuous process. And sometimes discharge happens. Or a leakage current may flow. Hence we represent capacitance as the derivative of small charge, q with respect to small voltage v.

C = dq/dv.

Energy storage

To 'move' charges between the conductors of a capacitor, work must be done. This work is done by a voltage source. When this external influence is removed the capacitor starts discharging and comes to its equilibrium position. The amount of energy stored in a capacitor is the work done in establishing the electric field. It can be expressed as:

Networks

Capacitors in parallel:

When we connect capacitors in parallel connection then all the capacitors get same applied voltage. Hence their capacitances add up. Actually the plate area of the capacitors are added up in parallel connection.

Capacitors in series:

But in series connection the plates are much more separated. From the diagram above it is very clear that the separation distance is added up. So the total voltage difference is calculated as sum of the inverse of their capacitance. Hence the total series capacitance must be smaller than any other capacitor in the network.

High working voltage is achieved by combining capacitors in series. For example, a high voltage power supply can produce voltage spikes. Series capacitors are used for smoothing the spikes of a high voltage power supply.

Resistor Colour Code

2011-08-05T13:02:00.002+05:00

Resistor Color Code:

The value of a resistor’s resistance is indicated on its body by a color band. This band indicates the resistance with percentage of tolerance.

Using color code gives reliability of resistance calculation and enhances look of the resistor. It is also called the “Color Band”. The color band on a resistors body looks like below:

Figure: 1

You can see there are four coloured lines on the body of the resistor. Look at the picture below to see which band means what.

Figure: 2

So the first band means a simple integer number which is the first digit of the number of ohomic resistance. The second band means also another integer which is the second digit of the number of ohomic resistance. Third one is the multiplier of the number. And the last one is the tolerance which is usually silver or gold coloured.

The value of the colours in the band is given below:

To remember the colour code I would like to give you a tremendous way. That is remembering this word “BB ROY Good Boy Very Good Worker” which means:

B = Black

B = Brown

R = Red

O = Orange

Y = Yellow

Good = Green

Boy = Blue

Very = Violet

Good = Gray

Worker = White

Now to find the value of the resistance of the resistor at figure 2 calculate like this:

A = First band = Red = 2

B = Second Band = Violet = 7

C = Third band (multiplier) = Green = 5

D = Tolerance = Gold = +/- 5%

Hence, The value of the resistance = (AB)*10^C +/-D = (27*100000)+/-5%

= 2700000 +/- 5% Ohm

Sometime it is very confusing from which side you should start counting the first digit. The correct procedure in this case is to start with the opposite side where tolerance bands (silver of gold) are drawn.