i.e., W= (F cos q) S=F S cos q or W=\[\overrightarrow{F.}\,\overrightarrow{S}\]
In terms of rectangular components, work done
W=\[\overrightarrow{F.}\,\overrightarrow{d}\]
\[W=(\hat{i}\,{{F}_{x}}+\hat{j}\,{{F}_{y}}+\hat{k}\,{{F}_{Z}}).(\hat{i}\,\,dx+\hat{j}\,dy+\hat{k}\,\,dz)\]
\[={{F}_{x}}dx+{{F}_{y}}dy+{{F}_{Z}}dz\]
Units of work
SI unit: joule (J). One joule of work is said to be done when a force of one newton displaces a body by one metre in the direction of force
\[1\,\,joule={{10}^{7}}erg\]
Dimensions of work:
Work = force, displacement
\[=[ML{{T}^{-2}}][L]=[M{{L}^{2}}{{T}^{-2}}]\]
Work Done in Pulling and Pushing an Object
\[F=\frac{\mu \,\,Mg}{\cos \theta +\mu \sin \theta }=force\,\,required\,to\,pull\,on\,object\] force required to pull an object \[W=F\,\,d=\frac{\mu \,\,Mg\,\,d}{\cos \theta +\mu \,\,\sin \,\theta }\]
Similarly, work done in pushing an object
\[W=\frac{\mu \,\,Mg\,\,d}{\cos \theta +\mu \,\,\sin \,\theta }\]
Work Done by a Variable Force
\[W=\int\limits_{{{x}_{1}}}^{{{x}_{2}}}{Fdx=}\]area under F-x curve with proper algebraic sign.
Work done by external force when spring is elongated from \[{{x}_{1}}to\,{{x}_{2}}\]
Work done in small displacement dx, dW = Fdx
Total work done, W=\[\int\limits_{{{x}_{1}}}^{{{x}_{2}}}{Fdx=k\,\,\int\limits_{{{x}_{1}}}^{{{x}_{2}}}{xdx}}\]
\[F=kx\]
The constant k is the spring constant or force constant.
\[W=\frac{1}{2}k{{x}_{2}}^{2}-\frac{1}{2}k{{x}_{1}}^{2}\]
Conservative Force
A force is said to be conservative, if the work done, by or against the force
(i) is independent of path and depends only on initial and final positions.
(ii) does not depend on the nature of path followed between the initial and final positions.
Examples of conservative force: All central forces are conservative like gravitational, electrostatic, elastic force, restoring force due to spring etc.
SPECIAL POINTS
(a) Work done along a closed path or in a cyclic process is zero. i.e.\[i.e.\,\,\oint{F.dx=0}\]
(b) If \[\overrightarrow{F}\] is a conservative force, then \[\overrightarrow{\Delta }\times \overrightarrow{F}=0\]
Non-conservative Force
A force is said to be non-conservative, if work done, by or against the force in moving a body depends upon the path between the initial and final positions.
The work done in a closed path is not zero in a non-conservative force field.
Examples of non-conservative force: Air resistance, viscous force etc.
Energy
The energy of a body is defined as the capacity of doing work or ability of the body to do work.
It is a scalar quantity.
The dimensional formula of energy is \[[M{{L}^{2}}{{T}^{-2}}]\]. It is the same as that of work. The unit of energy are the same as that of work Le,, joule in S. I. system and erg in CGS system.
Kinetic Energy
It is the energy possessed by a body by virtue of its motion. If v be the velocity acquired by the block after travelling a distance x,
then kinetic energy
\[K=W=Fx=m.a.x=\frac{1}{2}m{{v}^{2}}\] \[[\therefore {{v}^{2}}=2ax]\]
Work Energy Theorem for a Variable Force
The work done by the resultant force in displacing the particle from\[{{x}_{0}}\] to x is
\[W=\frac{1}{2}m{{v}^{2}}f-\frac{1}{2}m{{v}^{2}}_{i}\]
'The work done by more... 
CLASSIFICATION OF ELECTRIC DRIVES
The classification of electrical drives can be done depending upon the various components of the drive system. Now according to the design, the drives can be classified into three types such as single-motor drive group motor drive and multi motor drive.
The single motor types are the very basic type of drive which are mainly used in simple metal working, house hold appliances etc Group electric drives are used in modem industries because of various complexities. Multi motor drives are used in heavy industries or where multiple motoring units are required such as railway transport. If we divide from another point of view, these drives are of two types:
ELECTRICAL MOTOR
The electrical motor is a device that has brought about one the more... 
AMPLITUDE MODULATION (AM)
The method of varying amplitude of a high frequency carrier wave in accordance with the information to be transmitted, keeping the frequency and phase of the carrier wave unchanged is called Amplitude Modulation. The information is considered as the modulating signal and it is superimposed on the carrier wave by applying both of them to the modulator. The detailed diagram showing the amplitude modulation process is given below.
Modulation Index (m)
The ratio between the amplitude change of carrier wave to the amplitude of the normal carrier wave is called modulation index-
It is represented by the letter 'm'.
It can also be defined as the range in which the amplitude of the carrier wave is varied by the modulating signal.
\[m={{V}_{m}}/{{V}_{c}}\]
Percentage modulation, \[%\,\,m={{m}^{*}}100={{V}_{m}}/{{V}_{c}}*100\]
The percentage modulation lies between 0 and 80%.
Power Relations in an AM wave
A modulated wave has more power than had by the carrier wave before modulating. The total power components in amplitude modulation can be written as:
\[{{P}_{total}}={{P}_{carrier}}+{{P}_{LSB}}+{{P}_{USB}}\]
Considering additional resistance like antenna resistance R.
\[{{P}_{carrier}}={{[({{V}_{c}}/\sqrt{2})/R]}^{2}}={{V}^{2}}_{C}/2R\]
ANGLE MODULATION
In the angle modulation, again there are two different types of modulations.
Frequency modulation.
Phase modulation.
.
Zigbee Module
Zigbee is a wireless technology developed as an open global standard to address the unique needs of low-cost, low-power wireless M2M networks. The Zigbee standard operates on the IEEE 802.15.4 physical radio specification and operates in unlicensed bands including 2.4 GHz, 900 MHz and 868 MHz Zigbee builds upon the physical layer and medium access control defined
In IEEE standard 802, 15.4 (2003 version) for low-rate WPAN's.
The specification goes on to complete the standard by adding four main components: network layer, application layer, Zigbee device objects (ZDO's) and manufacturer-defined application objects which allow for customization and favor total integration.
Radio waves
Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared-light. Radio waves have frequencies as high as 300 GHz to as low as 3 kHz, though some definitions describe waves above 1 or 3 GHz as microwaves, or include waves of any lower frequency. At 300 GHz, the corresponding wavelength is 1 mm (0.039 in), and at 3 kHz is 100 km (62 mi). Like all other electromagnetic waves, they travel at the speed of light. Naturally occurring radio waves are generated by lightning, or by astronomical objects.
The basic building block of radio communications is a radio wave. Like waves on a pond, a radio wave is a series of repeating peaks and valleys. The entire pattern of a wave, before it repeats itself, is called a cycle. The wavelength is the distance a more... 
Fig.: PN Junction Diode
Modes of Operation
There are generally two types of modes of operation for diodes:
(i) Forward Bias: When an external voltage source is applied to one end of the junction in such a manner that it overcomes the potential barrier and permits current to flow, it is called Forward Biasing.
In case of a PN junction Diode, in order to operate the diode in the forward biasing mode, the p-type semiconductor (anode) is connected to the positive terminal, while the n-type semiconductor (cathode) is connected to the negative terminal of an external voltage source as shown in the fig.
Fig.: Forward Biasing
(ii) Reverse Bias: This acts opposite to the forward biasing mode i.e. in this mode an external voltage source is connected in such a manner, that it will increase the potential barrier and resist the flow of current, m this mode the p-type semiconductor (anode) is connected to the negative terminal and the n-type semiconductor (cathode) is connected to the positive terminal as shown in fig.
Fig.: Reverse Biasing
V-I Characteristics
Fig.: V-I Characteristics
Effect of Temperature on Diode Characteristic
In the last section, we had discussed about diode current equation, in which it is clearly mentioned that diode current is a function of temperature and since the coefficient of temperature\[\left( {{V}_{T}} \right)\]is in the denominator of the power of the exponential term:
\[I={{I}_{0}}({{e}^{V/{{\eta }^{V}}T-1}})\]
therefore, with an increase in the temperature, the diode current exponentially decreases and vice versa. However, there is one more term mentioned in this equation, which is the saturation current\[({{I}_{0}})\], the variation for which is much greater than the exponential term.
ZENER DIODE
Zener Diode is a special purpose silicon PN junction diode which differs from other diodes in the sense that it operates in the reverse biased mode.
Zener diode is also known as a voltage regulator or voltage reference or breakdown diode. The Fig. shows the symbol for a zener diode:
Fig.: Symbol of Zener Diode
The breakdown voltage of a Zener diode is carefully controlled by maintaining the doping level during manufacturing. So, if the doping level is high, then depletion layer is thin and breakdown occurs at a low reverse voltage. When reverse voltage is increased, a critical voltage called breakdown voltage is reached at which reverse current will sharply increase.
Zener more... 
Statics deals with forces in terms of their distribution and effect on a body at absolute or relative rest. Dynamics deals with the study of bodies in motion. Dynamics is further divided into kinematics and kinetics. Kinematics is concerned with the bodies in motion without taking into account the forces which are responsible for the motion. kinematics deals with the bodies in motion and its causes.
Force System: A force system may be coplanar/non-coplanar. in a coplanar force system, all the forces act in the same plane. In a non-coplanar force system, all the forces act in different planar.
Classification of force system: (For coplanar forces)
(Complete classification of force system)
Let \[\theta \]=Angle between the two forces 'P' and 'Q'
\[\alpha \]= Angle between resultant 'R' and one of the force
('Q' in this case)
= direction of the resultant then,
Then,
Resultant' \['R'=\sqrt{{{P}^{2}}+{{Q}^{2}}+2PQ\cos \theta }\]
Angle made by resultant \['R'=\left( \frac{P\sin \theta }{Q+P\cos \theta } \right)\]
or,
\[\tan \,\,\alpha =\left( \frac{P\sin \theta }{Q+P\cos \theta } \right)\Rightarrow \alpha ={{\tan }^{-1}}\left( \frac{P\sin \theta }{Q+P\cos \theta } \right)\]Land's theorem:
According to Lam is theorem, if three forces are acting at a point and the forces are in equilibrium, then the each of the three forces is directly proportional to the sine of the angle between the other two forces.
Let, P, Q, R = Three forces in equilibrium
\[\alpha \],\[\beta \], \[\gamma \]= Angles included between three forces P, Q and R then,
\[\frac{P}{\sin \alpha }=\frac{Q}{\sin more... 
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