tag:blogger.com,1999:blog-19300111286167709912024-03-13T08:00:49.541-07:00gate online bitsAnonymoushttp://www.blogger.com/profile/08419430619289374918noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-1930011128616770991.post-957032673257045712016-07-25T02:25:00.004-07:002016-07-25T02:25:36.210-07:00networks<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<header>
<h1 class="title">
Introduction of Network</h1>
</header>
<br />
<div class="WordSection1">
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Electric Network: </b>A
physical electric network or electrical circuit, is a system of
interconnected components. The word components include source energy
such as voltage source or current source, electrical elements such as
resistors, inductors and capacitors.</div>
<ul>
<li class="MsoNoSpacing">Circuit elements can be classified in two categories, passive elements and active elements.</li>
<li class="MsoNoSpacing"><b>Passive Element:</b> The element which
receives energy (or absorbs energy) and then either converts it into
heat (R) or stored it in an electric (C) or magnetic (L ) field is
called passive element.
<ul>
<li class="MsoNoSpacing">Transformer is an example of passive element.</li>
</ul>
</li>
<li class="MsoNoSpacing"><b>Active Element:</b> The elements that supply energy to the circuit is called active element.
<ul>
<li class="MsoNoSpacing">Examples of active elements include voltage and
current sources, generators, and electronic devices that require power
supplies. A transistor is an active circuit element, meaning that it
can amplify power of a signal.</li>
</ul>
</li>
</ul>
<br />
A circuit which contains at least one source of energy is called <b>active</b>. An energy source may be a voltage or current source.<br />
<br />
A circuit which does not contain any energy source is called <b>passive circuit</b>.<br />
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Charge:</b> There
are two types of charge: positive (corresponding to a proton), and
negative (corresponding to an electron). Electric charge is
conservative. It can not be created or destroyed.</div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Current:</b>
The idea of “transfer of charge” or “charge in motion” is vital
importance to us in studying electric circuits because, in moving a
charge from place to place, we may also transfer energy from one point
to another.</div>
<ul>
<li>Electric current (i) = dq/dt, where i = current in amperes, q = charge in coulombs, t = time in seconds.</li>
<li>The unit of ampere can be derived as 1 A = 1C/s.</li>
<li>A direct current (dc) is a current that remains constant with time.</li>
<li>An alternating current (ac) is a current that varies sinusoidally with time.</li>
</ul>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Voltage:</b> Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V).</div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">Electric
potential difference (voltage) between two points can be defined as the
work dw done by the electric field in moving a small amount of positive
charge dq from one point to other.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">v= dw/dq, where v is voltage in volts, energy in joules, q= charge in coulombs</li>
</ul>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Power & Energy: </b>If
one joule of energy is expended in transferring one coulomb of charge
through the device in one second, then the rate of energy transfer is
one wait. The absorbed power must be proportion both to the number of
coulomb transferred per second (current), and to the energy needed to
transfer one coulomb through the element (voltage).</div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">Power is the time rate of expending or absorbing energy, measured in watts (W)</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">p=dw/dt=v.i</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">The law of conservation of energy ∑ p = 0</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">Energy is the capacity to do work, measured in joules (J)</li>
</ul>
<br />
<b>Symbol and Units of Electrical quantities:</b><br />
<a href="http://gs-blog-images.grdp.co/gate-exam/wp-content/uploads/2015/11/27114310/Units.jpg"><br /></a>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>The Classification of Network:</b></div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">A
circuit or network whose parameters i.e., elements like resistances,
inductances and capacitances are always constant irrespective of the
change in time, voltage, temperature etc., is known as <b>linear network. </b>The Ohm’s law can be applied to such network.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">A circuit whose parameters change their values with change in time, temperature, voltage etc., is known as <b>non-linear network. </b>The Ohm’s law may not be applied to such network.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">A
circuit whose characteristics, behaviour is same irrespective of the
direction of current through various elements of it, is called <b>bilateral network.</b></li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">A circuit whose operation, behaviour is dependent on the direction of the current through various elements is called <b>unilateral network</b>.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">A network in which all the network elements are physically separable is known as <b>lumped network</b>.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">Most of the electric networks are lumped in nature, which consists elements like RLC voltage source etc.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">A
network in which the circuit elements like resistance, inductance etc.,
are not physically separable for analysis purposes, is called <b>distributed network</b>.</li>
</ul>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Circuit Elements</b></div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Resistor:</b> Resistance is the property of the material by which it opposes the flow of current through it.</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%; text-align: center;">
<b>R = ρ L / A</b></div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%; text-align: left;">
Where, l = Length in metre, A = Cross-sectional area in square-metre, ρ = Resistivity in ohm-metre, R = Resistance in ohm.</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%; text-align: center;">
<a href="http://gs-blog-images.grdp.co/gate-exam/wp-content/uploads/2015/11/27114310/Resistance.jpg"><br /></a></div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">4.186 joule = 1cal</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">1 joule = 0.24 cal</li>
</ul>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
Thus,
unit 1 ohm can be defined as that resistance of the circuit if it
develops 0.24 cal of heat, when one ampere current flow through the
circuit for one second.</div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Inductor:</b> An inductance is the passive element in which energy is stored in the form of electromagnetic field.</div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">An inductor consists of a coil of conducting wire.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">Inductance
(L) is the property whereby an inductor exhibits opposition to the
change of current flowing through it, measured in henrys (H).</li>
<li>The Inductance <b><i>L</i></b><b><i> </i></b>is a measure of the voltage drop across an inductor (e.g. a solenoid) per the rate change of current.</li>
</ul>
<div style="text-align: center;">
V= – L ΔI/Δt</div>
<ul>
<li>Since the magnetic field inside a solenoid is proportional to a
current, the rate-change of the magnetic flux is proportional to the
rate-change of the current.</li>
<li>The magnetic field inside a solenoid is: B = μ<sub>0 </sub>(N/ <i>l</i>) I</li>
</ul>
<div style="text-align: center;">
ΔB/Δt = μ<sub>0 </sub>(N/ <i>l</i>) ΔI /Δt</div>
<ul>
<li>The voltage across the solenoid is given by the rate-change of the flux times the number of loops:</li>
</ul>
<div style="text-align: center;">
V=-NA ΔB/Δt = -μ<sub>0 </sub><i>l</i> (N/ <i>l</i>)<sup>2</sup> A ΔI/Δt</div>
<ul>
<li>Therefore, the inductance <b><i>L</i></b> can be given in terms of the geometry of the solenoid.</li>
</ul>
<div style="text-align: center;">
<b>L= μ<sub>0 </sub><i>l</i> (N/ <i>l</i>)<sup>2</sup> A = μ<sub>0</sub> N<sup>2</sup>A/<i>l</i></b></div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
where, μ<sub>0</sub> = Permeability of the core, N = Total number of turns in coil, A = Area of cross-section of coil, and <i>l</i> = Length of the coil in metre.</div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Capacitor:</b> It is a passive element in which energy is stored in the form of an electrostatic field.</div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">A capacitor consists of two conducting plates separated by an insulator (or dielectric).</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">Capacitance
(C) of the capacitor is the ratio of the charge on one plate of a
capacitor to the voltage difference between the two plates, measured in
farads (F).</li>
</ul>
<div style="text-align: center;">
C = ε A/d</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
where A
is the surface area of each plate, d is the distance between the
plates, and is the permittivity of the dielectric material between the
plates.</div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">Capacitors are used extensively in electronics, communications, computers, and power systems.</li>
</ul>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Gyrator:</b></div>
An ideal gyrator is a two port network whose input (respectively
output) voltage (respectively output) is directly proportional to the
output (respectively input) current. The ratio α is usually called the
“gyration resistance”.<br />
In the case of an asymmetrical representation, a gyrator is illustrated by:<br />
<br />
The relations between current and voltage are : V<sub>1</sub>= α i<sub>2, and </sub>V<sub>2</sub>= -α i<sub>1</sub><br />
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Transformer: </b>A
transformer is a static electrical device that transfers energy by
inductive coupling between its winding circuits. A varying current in
the primary winding creates a varying magnetic flux in the transformer’s
core and thus a varying magnetic flux through the secondary winding.
This varying magnetic flux induces a varying Electromotive Force (EMF),
or voltage, in the secondary winding.</div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Current-voltage relationship for a capacitor: </b>i = C dv/dt</div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Energy Sources: </b>Energy source is defined as the device that generates electrical energy. The classification of energy sources is given below.</div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;"><b>Independent Sources: </b>Independent sources are those in which source voltage or current are not dependent on a voltage or current.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;"><b>Ideal Voltage Source: </b>It is a voltage generator whose output voltage remains absolutely constant whatever be the value of the output current.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;"><b>Practical Voltage Source: </b>The voltage does not remain constant but falls slightly; this is taken care of by connecting a small resistance (R<sub>s</sub>) in series with ideal source.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;"><b>Ideal Current Source: </b>It produces a constant current value of the irrespective of the voltage across it.</li>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;"><b>Practical Current Source: </b>The output current does not remain constant but decreases with increase in voltage.</li>
</ul>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<a href="http://gs-blog-images.grdp.co/gate-exam/wp-content/uploads/2015/11/27114310/1.jpg"><br /></a></div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Ohm’s Law: </b>The
current flowing through the electric circuit is directly proportional
to the potential difference across the circuit and inversely
proportional to the resistance of the circuit, provided the temperature
remains constant.</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%; text-align: center;">
V ∝ I</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%; text-align: center;">
V/I= constant</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%; text-align: center;">
V/I = R</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
The
ratio of potential difference (V) between any two points of a conductor
to the current (I) flowing between them is constant, provided that the
temperature of the conductor remains constant.</div>
<ul>
<li>When R=0 (Short Circuit), V=0 Volts</li>
<li>When R= ∝ (Open Circuit), I=0 Amps</li>
</ul>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Note:</b> Ohm’s law can be applied either to the entire circuit or to the part of a circuit.</div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Limitations of Ohm’s Law:</b> It is not applicable to the non-linear devices such as diodes, zener diodes, voltage regulators etc.</div>
<ul>
<li>It does not hold good for non-metallic conductors such as silicon carbide.</li>
<li>The law for such conductors is given by <b>V = Ki</b><sup><b>m</b> </sup>where K and m are constants.</li>
</ul>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Kirchhoff’s Current Law</b> (KCL): The algebraic sum of all the currents meeting at a junction point is always zero.</div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">Mathematically, </li>
</ul>
where N is the number of branches connected to the node and i<sub>n</sub> is the nth current entering (or leaving) the node.<br />
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Note: </b>Current
flowing towards a junction point are assumed to be positive while
current flowing away from a junction point assumed to be negative.</div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Example-1:</b> Consider the following Node analysis of currents entering /leaving from node point p.</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
Using
KCL, entering a node p may be regarded as positive, while currents
leaving the node may be taken as negative or vice versa.</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%; text-align: center;">
i1 + (-i2) + i3 + i4 + (-i5) = 0</div>
<div class="MsoNormal" style="font-size: 16px; line-height: 150%; text-align: center;">
i1 + i3 + i4 = i2 + i5</div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%; text-align: left;">
<b>Note:</b> The sum of the currents entering a node is equal to the sum of the currents leaving the node.</div>
<br />
<div class="MsoNormal" style="font-size: 16px; line-height: 150%;">
<b>Kirchhoff’s Voltage Law </b>(KVL):
In any network, the algebraic sum of the voltage drops across the
circuit elements of any closed path (or loop or mesh) is equal to the
algebraic sum of the emfs in the path.</div>
<ul>
<li class="MsoNormal" style="font-size: 16px; line-height: 150%;">Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero</li>
</ul>
<div style="text-align: center;">
<a href="http://gs-blog-images.grdp.co/gate-exam/wp-content/uploads/2015/11/27114310/kvl.jpg"><br /></a></div>
<ul>
<li style="text-align: left;">KVL can be interpreted as: Sum of voltage drops = Sum of voltage rises</li>
</ul>
</div>
</div>
Anonymoushttp://www.blogger.com/profile/08419430619289374918noreply@blogger.com0tag:blogger.com,1999:blog-1930011128616770991.post-3241813843577702962016-07-25T02:08:00.000-07:002016-07-25T02:20:14.173-07:00gate bits<div dir="ltr" style="text-align: left;" trbidi="on">
<strong>Model GATE Questions of Verbal Ability:</strong><br />
<br />
<b>
</b><strong>(i) Grammar: <span style="text-decoration: underline;">The professor</span>(1) <span style="text-decoration: underline;">Ordered to</span>(2) <span style="text-decoration: underline;">the students to go</span>(3) <span style="text-decoration: underline;">out of the class</span>(4). Which of the given underlined parts of the sentence is grammatically incorrect?</strong><br />
<b>
</b><strong>(ii) Sentence completion: Choose the most appropriate word from the options given below to complete the following sentence.</strong><br />
<b>
</b><b>A person suffering from Alzheimer’s disease____________ short-term memory loss.</b><br />
<b>
</b><b>(a) experienced (b) has experienced (c) is experiencing (d) experiences</b><br />
<b>
</b><strong>(iii) Pair of related words: Choose the pair of words similar to the following pair of related words. Unemployed : Worker</strong><br />
<b>
</b><b>(a) fallow : land (b) unaware : sleeper (c) wit : jester (d) renovated : house</b><br />
<b>
</b><b><span style="text-decoration: underline;"><strong>Numerical Ability:</strong></span></b><br />
<b>
</b><ul>
<li><strong>Numerical Computation: It involves the basic principles of arithmetic like addition, subtraction, multiplication, and division.</strong></li>
<li><strong>Numerical Estimation: It tests the individual’s
ability of solving straightforward questions as fast as they could. It
depends on how fast each individual answers.</strong></li>
<li><strong>Numerical Reasoning: These kinds of questions are
answered based on the reasoning done on the information provided. Such
reasoning is based on real time scenarios like financial data etc.</strong></li>
<li><strong>Critical reasoning: Information is provided that requires you to interpret it and then apply the appropriate logic to answer the questions.</strong></li>
<li><strong>Data Interpretation: It determines a person’s ability to extract the correct data from tables, graphs and charts.</strong></li>
</ul>
<b>
</b><strong>Important topics of Numerical Ability:</strong><br />
<b>
</b><b>Speed-distance-time, Number series, summation, Logical Inference,
cost-profit, Data Interpretation, Ages, Work (Days-workers), velocity,
Modulo problems, clock problems, Directions, Clock problems,
Distance-direction-east-west-north-south, Triangle problems, percentage,
probability, tangent, Base/Radix Numbers.</b><br />
<b>
</b><strong>Model GATE Questions of Numerical Ability:</strong><br />
<b>
</b><strong>(i) Speed-distance-time: A train that is 280 metres
long, travelling at a uniform speed, crosses a platform in 60 seconds
and passes a man standing on the platform in 20 seconds. What is the
length of the platform in metres?</strong><br />
<b>
</b><strong>(ii) Number series: The next term in the series: 81, 54, 36, 24, … is _____</strong><br />
<b>
</b><strong>(iii) Modulo problems: If x is real and |<sup>2</sup> − 2 + 3| = 11, then possible values of | − <sup>3</sup> + <sup>2</sup> – | include …</strong><br />
<b>
</b><strong>(iv) Clock problems: At what time between 6 .. and 7 .. will the minute hand and hour hand of a clock make an angle closest to 60°?</strong><br />
<b>
</b><strong>(v) Direction-distance: X is 1 km northeast of Y. Y
is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1
km east of P. What is the distance between X and Q in km?</strong><br />
<b>
</b><strong>(vi) Tangent: If y = 5x<sup>2</sup> + 3, then the tangent at x =0, y=3 …</strong><br />
<b>
</b><strong>(vii) Radix Numbers: Consider the equation: (7526)<sub>8</sub> − (Y)<sub>8</sub> = (4364)<sub>8</sub> , where (X)<sub>N</sub> stands for X to the base N. Find Y.</strong><br />
<b>
</b><div style="text-align: center;">
<b><em><strong>” The past is where you learned the lesson. </strong></em></b></div>
<b>
</b><div style="text-align: center;">
<b><em><strong>The Future is where you apply the lesson. </strong></em></b></div>
<b>
</b><div style="text-align: center;">
<b><em><strong>Don’t GIVE UP in the middle! “</strong></em></b></div>
<b>
</b></div>
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