Laplace transforms pdf

CLICK THE LINK BELOW TO DOWNLOAD LAPLACE TRANSFORMS IMPORTANT FORMULAS IN THE FORM OF PDF

CLICK HERE

Friday, 22 July 2016

C program how to find the largest and smallest number in an ARRAY

#include<stdio.h>
void main()
{
int a[100];
int n,f,s,i;
printf("enter the number of elements in the array at least 2 \n");
scanf("%d",&n);
printf(" \n enter the elements and press enter\n");
for(i=0;(i<n);i++)
{
scanf("%d",&a[i]);
if(a[i]>f)
f=a[i];
else if(a[i]<s)
s=a[i];
}
printf("%d is the first largest number \n",f); printf("%d is the smallest number \n",s);
}

/*sample output is shown in the screen shot*/

Wednesday, 1 June 2016

Tuesday, 31 May 2016

GATE 2017 EEE SYLLABUS

Section1: Engineering Mathematics

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.

Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Green’s theorem.

Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.

Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals.

Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.

Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multi‐step methods for differential equations.

Transform Theory: Fourier Transform, Laplace Transform, z‐Transform.

Electrical Engineering

Section 2: Electric Circuits

Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and ac networks, Sinusoidal steady‐state analysis, Resonance, Passive filters, Ideal current and voltage sources, Thevenin’stheorem, Norton’s theorem, Superposition theorem, Maximum power transfer theorem, Two‐port networks, Three phase circuits, Power and power factor in ac circuits.

Section 3: Electromagnetic Fields

Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence, Electric field and potential due to point, line, plane and spherical charge distributions, Effect of dielectric medium, Capacitance of simple configurations, Biot‐Savart’s law, Ampere’s law, Curl, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits,Self and Mutual inductance of simple configurations.

Section 4: Signals and Systems

Representation of continuous and discrete‐time signals, Shifting and scaling operations, Linear Time Invariant and Causal systems, Fourier series representation of continuous periodic signals, Sampling theorem, Applications of Fourier Transform, Laplace Transform and z-Transform.

Section 5: Electrical Machines

Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency; Three phase transformers: connections, parallel operation; Auto‐transformer, Electromechanical energy conversion principles, DC machines: separately excited, series and shunt, motoring and generating mode of operation and their characteristics, starting and speed control of dc motors; Three phase induction motors: principle of operation, types, performance, torque-speed characteristics, no-load and blocked rotor tests, equivalent circuit, starting and speed control; Operating principle of single phase induction motors; Synchronous machines: cylindrical and salient pole machines, performance, regulation and parallel operation of generators, starting of synchronous motor, characteristics; Types of losses and efficiency calculations of electric machines.

Section 6: Power Systems

Power generation concepts, ac and dc transmission concepts, Models and performance of transmission lines and cables, Series and shunt compensation, Electric field distribution and insulators, Distribution systems, Per‐unit quantities, Bus admittance matrix, Gauss-Seidel and Newton-Raphson load flow methods, Voltage and Frequency control, Power factor correction,Symmetrical components, Symmetrical and unsymmetrical fault analysis, Principles of over‐current, differential and distance protection; Circuit breakers, System stability concepts, Equal area criterion.

Section 7: Control Systems

Mathematical modeling and representation of systems, Feedback principle, transfer function, Block diagrams and Signal flow graphs, Transient and Steady‐state analysis of linear time invariant systems, Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci, Stability analysis, Lag, Lead and Lead‐Lag compensators; P, PI and PID controllers; State space model, State transition matrix.

Section 8: Electrical and Electronic Measurements

Bridges and Potentiometers, Measurement of voltage, current, power, energy and power factor; Instrument transformers, Digital voltmeters and multimeters, Phase, Time and Frequency measurement; Oscilloscopes, Error analysis.

Section 9: Analog and Digital Electronics

Characteristics of diodes, BJT, MOSFET; Simple diode circuits: clipping, clamping, rectifiers; Amplifiers: Biasing, Equivalent circuit and Frequency response; Oscillators and Feedback amplifiers; Operational amplifiers: Characteristics and applications; Simple active filters, VCOs and Timers, Combinational and Sequential logic circuits, Multiplexer, Demultiplexer, Schmitt trigger, Sample and hold circuits, A/D and D/A converters, 8085Microprocessor: Architecture, Programming and Interfacing.

Section 10: Power Electronics

Characteristics of semiconductor power devices: Diode, Thyristor, Triac, GTO, MOSFET, IGBT; DC to DC conversion: Buck, Boost and Buck -Boost converters; Single and three phase configuration of uncontrolled rectifiers, Line commutated thyristor based converters, Bidirectional ac to dc voltage source converters, Issues of line current harmonics, Power factor, Distortion factor of ac to dc converters, Single phase and three phase inverters, Sinusoidal pulse width modulation.

Saturday, 25 July 2015

How to type mathematical equations in MS WORD

If you want to insert an equation in your documents using MS WORD follow these  steps.
Step1: Open MS WORD.
Step2: click n INSERT.
Step3: click on MATHEMATICAL EQUATION.
Step4: you can see different patterns on the top click on the pattern type which you want to insert.

Distribution factor

It is defined as the ratio of EMF PRODUCED PER PHASE in Distributed winding to that of Concentrated winding. It is  denoted by Kd.
Let us derive the equation for kd.
Let us consider a 2 Pole synchronous machine with 12 slots in stator and with full pitch winding(i.e coil span is equal to 180°electrical. The total electrical angle is equal to 360° (180*2).
Electrical angle is calculated by formula
   Electrical angle=(number of poles*180°)
Number of slots per pole is equal to 6 ((12/(2)).
[Formula:
Number of slots per pole is given by the ratio of number of slots to that of number of poles.]
Number of slots per pole per phase is equal to 2 (6/3).
[Formula:
Number of slots per pole per phase is given by the ratio of number of slots per pole to that of number of phases.]
Slot angle is equal to 30° ((180*2)/12)
[Formula:
Slot angle=
((No of poles*180)/(total no of slots))]
Let us draw armature winding(only for one phase).
It is shown clearly in the photographs.
The emfs  E1 and E2 in the coil side 1 and 2 will be in same phase.
And the emfs E3 and E4 are in the same phase and their resultant will be lagging by an angle with the resultant of E1 and E2.
Their vectors are shown in the figure 2.
Let us assume that their are n turns and'Q' (some times represented as alpha during explanation)be  the slot angle then the vector diagram is shown in the figure. Let us draw perpendicular bisectors of all the vectors.Perpendicular bisectors meet at a point O as shown in the figure 3.
Let Er be the total emf induced in the distributed winding per phase and From Fig3
Er=ci=2yc=2*oc*sin(nQ/2)[from fig 3]
In case of concentrated winding the they use only two slots and hence emf induced in the coil sides are equal(coil span=180°).
Let ct is the emf induced in each coil side
Hence each phase has 2 coil sides and n turns, So total emf induce is given by
E=2*n*ct=2*n*oc*sin(Q/2).[from fig3]
Distribution factor(Kd)=((emf induced per phase in case of distributed winding)/(emf induced in case of concentrated winding))
Kd=[(2*oc*sin(nQ/2))]/[2*oc*n*sin(Q/2)]
=[sin(nQ/2)]/[n*sin(Q/2)]
By using above formula we can calculate distribution factor where
n = the number of slots per pole per phase.
Q=slot angle.

How to calculate the multiplication factor of a wattmeter

Multiplication factor=(Voltage range*current range*power factor)/(full scale deflection)

Thursday, 23 July 2015

Cost of printing different Indian currency

In our daily life we are using different Indian currency. Have you ever thought about the amount our government   is spending in printing different kinds of notes(Rs50 note,Rs100 note,etc.)

It costs 50paise for printing 5RS note.
It costs 96paise for printing 10RS note.
It costs 1.5Rupees for printing 20Rupees note.
It costs 1.81Rupees for printing 50Rupees note.
It costs 1.70Rupees for printing 100Rupees note.
It costs 3.58Rupees for printing 500Rupees note.
It costs 4.06Rupees for printing 1000Rupees note.