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Electrical Theory

Electricity has been part of our lives since prehistoric times, so it would be misleading to say that anyone actually discovered it. Ancient man witnessed electricity in the form of lighting every time there was a thunderstorm. Some people see electricity as a powerful message from the gods, but today , electricity is more fully understood. We use electricity hundreds of times every day- when ever we flick a light switch, turn on the television or use a telephone. 

This section will help us to learn basic concepts of electricity, Voltage, Current, Resistance, Ohm's Law which connects them.

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We know that every matter is composed of molecules and molecules are composed of atoms. The atoms have neutrons, electrons and protons as its constituent element. The electrons carry negative charge while protons carry positive charge and neutrons are neutral in nature. Using these definitions, the electric charge is the extent to which it contains electrons and protons.

The matter is said to be positively charged if the number of protons are more than the number of electrons in an atom of the matter while the matter is said to be negatively charged if the number of protons are less than the number of electrons in an atom of the matter.

So, the charge of an object is equal to the sum of the charges of all the atoms while considering polarity. The electrical charge is measure in the coulomb (symbolized C), where 1-C is equal to 6.24 x 1018 electrons or protons. Generally it is written as 6.24 x 1018 e, where ‘e’ stands for electrons.
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The electric current is defined as the rate of change of electric charge with respect to time. The electric current flows in the direction opposite to the direction of flow of the electrons in the circuit. Since the electrons flows from negative (low potential) terminal to positive terminal (high potential), the electric current flows from positive terminal to the negative terminal. The electric current always follows the path of low resistance.
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The electric resistance is the measure of the opposition of the metal wire or conductor to the flow of the electric current. The electric current will flow with ease if the resistance of the metal wire or conductor is less. The resistance of the metal wire or conductor can be defined by: 

$R$ = $\frac{V}{I}$ 

where, R = resistance of the metal wire or conductor 
V = voltage applied to the metal wire or conductor
I = current flowing through the metal wire or conductor
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Ohm’s Law

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The electric current flowing through any circuit or conductor is directly proportional to the voltage applied across the conductor or circuit. This is known as Ohm’s law.

Mathematically, we can write ohm’s law as;

$I$ = $\frac{V}{R}$

here, R is proportionality constant and is known as resistance of the circuit or the conductor.
The Electromotive Force, or in short e.m.f., is the voltage generated by a energy source or by the varying magnetic field according to Faraday's Law. The Faraday’s Law states that when a conductor is placed in a time varying magnetic field, then due to induce effect an electric current is produced in it. 

Although from the name it appears to be force but the e.m.f. is the potential or the energy per unit of charge and is measured in volts.
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Electric Circuit is the closed path in which electric current flows from the high potential to the low potential point. The electric circuit is formed when the electric current finds a path with low resistance.

We have often seen that while working, without wearing proper insulator shoes, we experience an electric shock. This shock is due to the low resistance path offered by our body towards the ground. In this case our body is acting as the electric circuit.

Electric Circuit

The above shown diagram is the simple electric circuit containing voltage source E, and resistance R.
The Electric circuits plays a great role in electronics which makes the flow of desired current in the easier way.   → Read More Transistor is primarily used for two purposes:
  1. as an amplifier
  2. as a switch
The transistors are made of semiconductor material. Transistor is the crucial and important element in electronic circuit. It is a three terminal device, out of these three terminals one is used to ON or OFF the transistor. The three terminals are known as BASE, COLLECTOR and EMITTER. The transistor has two junctions of semiconductors.

The Transistors are of two types:
  1. NPN Transistors
  2. PNP Transistors
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The static electricity, as evident from the name itself is the electric field developed due to the stationary charges. The surface of material may contains some electric charges which constitutes the static electricity on that material. These static charges might come on the surface either through the contact with more charged body or through the extra ions presents in the air. 

You might come across a scenario where on a dry weather day if you touch a door knob of metal, you might got slight electric shock, it is due to the static charges present on the surface of the door knob. The charges on the surface of door knob may be accumulated by the interaction with the more charged body.
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The coulomb’s law is the law of force between the charges. It states that when two charges are placed at a distance d, from each other than the force experienced by them due to each other is directly proportional to the multiplication of the charges and inversely proportional to the distance between them.If we consider two charges, Q1 and Q2 are placed at a distance of d then the force on each of them would be;
$F$ = $k$$\frac{Q_{1}Q_{2}}{d_{2}}$
We know that the electron and proton have equal magnitude but opposite polarity, so there are three conditions for force between them:
  1. Both the charges are electrons, the force in this case is positive and hence both the charges experience positive force. The positive force indicates that the charges repel each other.
  2. Both the charges are protons, the force in this case is positive and hence both the charges experience positive force. The positive force indicates that the charges repel each other.
  3. One of the charges is electron and the other is proton, so the force in this case is negative and hence both the charges experience negative force. The negative force indicates that the charges attract each other.
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It is the field surrounding the electrically charged particle or the time varying magnetic field. The electric field is the force experienced by a charge from the charge surrounded by the electric field. From this discussion we can say that charges generate electric field.

Michael Faraday introduced the concept of Electric Field. It is a vector quantity and is measured in Volts per meter (Vm-1) or Newton per Coulomb (NC-1).

So, mathematically electric field can be written as;

$E$ = $\frac{V}{d}$


$E$ = $\frac{F}{q}$

where, E = Electric field produced by charge Q
V = Voltage due to electric field E
d = distance at which test charge q is placed from the charge Q in the electric field E
F = force experienced by the test charge due to electric field produced by the charge Q placed at a distance of d
q = test charge placed in electric field E. → Read More

Gauss’s Law

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Gauss's law is also known as Gauss's flux theorem. It is relationship between distribution of electric charges to the resulting electric field through a closed surface. In other words, Gauss's law states that:
“The electric charge in an enclosed area is proportional to the electric flux flowing through it”.

Electrical Capacitance

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Capacitance is the ratio between the charge which is applied to the conductor and the increase in potential of the conductor.Capacitance value is based on the capacitor connection.

It is given as:
C = $\frac{Q}{V}$

Here the charge is Q and rise in potential is V. Its S.I unit is given by Coulomb/volt also called as Farad.

Equivalent Resistance

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Resistance is the property of the material by the virtue of which it opposes flow of electrons through the material. Equivalent resistance is the resistance offered by the sum total of all the resistance taken. 

There are two types of circuits:
  1. Series circuit
  2. Parallel circuit

Resistance in series

The circuit in which resistances are connected end to end so that the same current flows through all the resistances is called a series circuit as shown in the figure:
Series Resistance

By ohm’s law, voltage across various resistances is:                                                               V1 = IR1, V2 = IR2, V3 = IR3Now the total Voltage is given by
                            V = V1 + V2 + V3 = IR1 + IR2 + IR3V = I (R1 + R2 + R3)
$\frac{V}{I}$ = R1 + R2 + R3But $\frac{V}{I}$ is the total resistance RT between points A and B. RT is called the total or equivalent resistance given as:
$\therefore$ RT = R1 + R2 + R3Hence when a number of resistances are connected in series, the total resistance is equal to the sum of individual resistances.

Resistance in Parallel

When one end of each resistance is joined to a common point and the other end of each resistance is joined to another common point so that there are as many paths for current flow as the number of resistances, it is called parallel circuit.
The resistance in parallel circuit is:Parallel Resistance
Now, current through respective resistance is              

                                I1 = $\frac{V}{R_{1}}$

                                I2 = $\frac{V}{R_{2}}$

                                I3 = $\frac{V}{R_{3}}$

Now total current is given
I = I1 + I2 + I3
  = $\frac{V}{R_{1}}$ + $\frac{V}{R_{2}}$ + $\frac{V}{R_{3}}$
I = V ($\frac{1}{R_{1}}$ + $\frac{1}{R_{2}}$ + $\frac{1}{R_{3}}$)Or
$\frac{I}{V}$ = $\frac{1}{R_{1}}$ + $\frac{1}{R_{2}}$ + $\frac{1}{R_{3}}$.
But $\frac{V}{I}$ is the total resistance RT of the parallel resistances (see figure 2) so that [ $\frac{I}{V}$ = $\frac{1}{R_{T}}$]
$\therefore$ $\frac{1}{R_{T}}$ = $\frac{1}{R_{1}}$ + $\frac{1}{R_{2}}$ + $\frac{1}{R_{3}}$.Hence when a number of resistances are connected in parallel, the reciprocal of total resistance is equal to the sum of reciprocals of individual resistances.

More topics in Electrical Theory
Electric Charge Electric Current
Electrical Resistance Ohm's Law
Electromotive Force Electric Circuit
Transistors Static Electricity
Coulomb's Law Electric Field
Gauss Law Capacitor
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