Electric Potential

The capacity of a charged body to do work is called electric potential. When a body is charged, work is done in charging it. This work done is stored in the body in the form of potential energy. The charged body has the capacity to do work by moving other charges either by attraction or repulsion. The ability of the charged body to do work is called electric potential.

Electric Potential, V = Work done/Charge = W/Q

Unit of electric potential is joules/coulomb or volt.

A body is said to have an electric potential of 1 volt if 1 joule of work is done to give it a charge of 1 coulomb.

 

Electric Current

The flow of free electrons is called electric current. When electric pressure or voltage is applied, then free electrons, being negatively charged, will start moving towards the positive terminal round the circuit. This directed flow of free electrons is called electric current.

The actual direction of current is from negative terminal to the positive terminal through that part of the circuit external to the cell. However, prior to Electron Theory, it was assumed that current flowed from positive terminal to the negative terminal of the cell via the circuit. This convention is so firmly established that it is still in use. This assumed direction is now called conventional current.

The strength of electric current I is the rate of flow of electrons i.e., charge flowing per second.

Current, I = Q/t

Unit of electric current is coulombs/sec or ampere.

One ampere of current is said to flow through a wire if at any section one coulomb of charge flows in one second.

 

Three Phase System

A three phase system is an arrangement of three windings producing three single phase voltages of the same magnitude and frequency but displaced 120° from one another. The three windings are suitably connected so that the three voltages act simultaneously in the circuit, each supplying power at different intervals of time to a common load. It is similar to a multi-cylinder engine in which each cylinder supplies power at different intervals of time to a common crankshaft. The following are the advantages of three phase system over single phase system:

1. Constant Power

In a single phase circuit, the instantaneous power varies sinusoidally from zero to a peak value at twice the supply frequency. This pulsating nature of power is objectionable for many applications. However, in a balanced three phase system, power supplied at all instants of time is constant. Because of this, the operating characteristics of three phase apparatus, in general, are superior to those of similar single phase apparatus.

2. Greater Output

The output of a three phase machine is greater than that of a single phase machine for a given volume and weight of the machine. In other words, a three phase machine is smaller than a single phase machine of the same rating. This is a distinct advantage of three phase system over single phase system.

3.Cheaper

The three phase motors are much smaller and less expensive than single phase motor because less material (copper, iron, insulation)  is required. Moreover, three phase motors are self-starting i.e, they do not require any special provision to get them started. However, single phase motors require internal starting device.

4. Power Transmission Economics

Transmission of electric power by three phase system is cheaper than that of single phase system, even though three conductors are required instead of two. For example, to transmit the same amount of power over a fixed distance at a given voltage, the three phase system requires only 3/4th the weight of copper than that required by the single phase system. This means a saving in the number and strength of transmission towers.

5. Three Phase Rectifier Service

Rectified three phase voltage is smoother than rectified single phase voltage. As a result, it is easier to filter out the ripple component of three phase voltage than that of a single phase voltage. This is especially useful where large a.c power is to be converted into steady d.c. power e. g. radio and television transmitters.

6 Miscellaneous Advantages

* A three phase system can set up a rotating magnetic field in stationary windings. This cannot be done with a single phase current.

* The three phase motors are more efficient and have a higher power factor than single phase motors of the same capacity.

Capacitor

A capacitor is a device that is capable of storing charge. It essentially consists of two conducting surfaces separated by an insulating material. The conducting surfaces are called plates of the capacitor and the insulating material is called dielectric. The most commonly used dielectrics are air, mica, paper,etc. A capacitor is generally named after the dielectric used e.g., air capacitor, mica capacitor, paper capacitor, etc. The capacitor may be in the form of parallel plates (parallel plate capacitor), concentric cylinders (cylindrical capacitor) or other arrangement.

Capacitace:

The ability of a capacitor to store charge is known as its capacitance. It has been found experimentally that charge q stored in a capacitor is directly proportional to the p.d. (V) across the plates i.e,

           q 

                   ________                =   constant C

           v              

The constant of proportionality C is called capacitance of the capacitor. The unit of capacitance is 1 C/V which is also called 1 Farad. By definition, capacitance is always a positive quantity. The p.d. across the capacitor increases linearly with increase in charge on capacitor plate. Therefore, the ratio q/V is constant for a given capacitor.

 

Corona

Corona is the ionization of air surrounding the power conductor due to the electrons normally present in free space because of radio activity and cosmic rays. Corona is the self sustained electric discharge in which the field intensified ionization is localized only over portion of the distance between the electrodes.

For maintaining the motion of charges produced by electric field, the energy required is derived from the supply system. In order to maintain the flow of energy over the conductor in the field where in this additional energy would have been otherwise absent, it is necessary to supply this additional loss from the supply system. This is referred to as corona effect.

Factors Affecting Corona Loss:

* Electrical Factors.
* Atmospheric Condition.
* Factors connected with conductors.
* Number of conductors/Phase.
* Profile of conductors.

Methods of Reducing Corona:

* Conductors having large diameters.

* Hollow conductors.

* Bundled conductors.

Network Theorems

Superposition Theorem:

The response in any element of linear, bilateral network containing more than one source is the sum of the responses produced by the sources, each acting independently.

Thevenin's Theorem:
Any combination of linear, bilateral circuit elements and active source, regardless of the connection or complexity, connected to a given load ZL, may be replaced by a simple two terminal network consisting of a single voltage source of VTh volts and a single impedance Zeq in series with the voltage source, across the two terminals of the load ZL.

Norton's Theorem:
Any combination of linear, bilateral circuit elements and active sources regardless of the connection or complexity, connected to a given load ZL can be replaced by a simple two terminal network consisting of a single current source of IN and a single impedance Zeq in parallel with it, across the two terminals of the load ZL.

Krichhoff's Laws

Gustav Krichhoff (1824 - 1887) , German Physicist developed two laws based on electric theories.

Krichhoff's First Law:

"The algebraic sum of currents flowing towards a junction in an electric circuit is zero"

An algebraic sum is one which the sign of the quantity is taken into account. For example, consider six conductors carrying currents a,b,c,d,e and f meeting at a common point as shown in the figure. If we take the signs of current flowing towards the point as positive, then the current flowing away from the point will be assigned negative sign. Thus applying Krichhoff's first law the junction in figure,

             a + b + c + d + (-e) + (-f) = 0
or                               a + b + c + d = e + f

i.e.,  Incoming currents = Outgoing currents

Hence Kirchhoff's first law can also be stated as under:

The sum of the currents flowing towards any junction in an electric circuit is equal to the sum of currents flowing away from the junction.

Krichhoff's law is true because electric current is merely the flow of electrons and they  cannot accumulate at any point in the circuit.

Krichhoff's Second Law:

"In any closed circuit or mesh, the algebraic sum of all the electromotive forces (e.m.fs) and the voltage drops is equal to zero"

ie, in any closed circuit or mesh, 

Algebraic sum of e.m.fs+Algebraic sum of voltage drops = 0

The validity of Krichhoff's second law can be readily established. If we start from any point in a closed circuit, and go back to that point after going round the circuit, there is no increase or decrease in the potential. This means that the sum of e.m.fs of all the sources met on the way plus the voltage drops in the resistances must be zero.

This law relates to e.m.f.s and voltage drops in a circuit and is sometimes called voltage law. 

A rise in potential should be considered positive while fall in potential should be considered negative.