Ch-1 Fundamentals of Alternating Voltage & Current

8/12/2019 Ch-1 Fundamentals of Alternating Voltage & Current

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IntroductionDC QUANTITY : A dc quantity is one which has a constant magnitudeirrespective of time.

Uses: Electroplating, charging of batteries, electric traction, refining ofcopper.An alternating voltage is any voltage that varies in both magnitude and

polarity wrt time.An alternating current is any current that varies in both magnitude and

direction wrt time .


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Introduction of AC AC circuit means that, electrons do not flow in one direction. Theymove forward and back constantly. As a result of this changing motionof the electrons voltage of the system is also not constant. AC circuitsshow sinusoidal graphs as given below.

Most of the electrical devices in our homes work with alternatingcurrent, TV, washing machines, hair drier etc.You can convert AC to DC with transformer which decreases theamount of voltage, and you can use diodes in your circuits.


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Advantages of alternating current over direct current:-

AC generators have no commutator and can thus be built in verylarge units to run at high speeds producing high voltage.

Alternating current can be stepped up and down efficiently bymeans of a static machine called transformer, which makes thetransmission and distribution of electrical energy economical.While in case of direct current the use of transformer is not

possible. AC motors are cheaper in cost, simpler in construction, moreefficient and robust than dc motors.The high transmission efficiency in ac system makes thegeneration of electrical energy economical by generating in largequantities in a single station and distributing over a large territory.


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Types of AC Waveform


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Generation of voltage and current


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An alternating voltage (emf) can be generated by:

1. By rotating a coil within a stationary magnetic field as shown infig 1.

2. By rotating magnetic field at a constant angular velocity withina stationary coil as shown in fig 2.

The value of the voltage generated depends, in each case uponthe number of turns in the coil, strength of the field and the speedat which the coil or magnetic field rotates.

Alternating voltage may be generated in either of the two waysshown in fig, rotating field method is the one which is mostly usedin practice

.


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Generation of Alternating Voltage

Generation of Alternating emf.


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So the emf generated varies as the sine function of the time angle t.This emf is plotted against time angle t, a curve of sine wave is

obtained as shown in fig. Such an emf is called sinusoidal emf.The sine curve is completed when the coil rotates through an angle of

2 radians.The induced emf e will have maximum value, represented by Em, when

the coil has turned through 90 degree in counter clockwise direction.


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Sinusoidal function terminology.1. Waveform: The shape of the curve obtained by

plotting the instantaneous values of the alternatingquantity.2. Alternation: A complete set of positive and negativevalues plotted as ordinates against time or time angle is

known as alternation.One alternation is equal to half cycle.3.Instantaneous Value: The value of the alternatingquantity at a given instant of time is defined as

instantaneous value. It varies from instant to instant.These values are denoted as smaller case letters.In case of sinusoidal waveform, they are equal to theproduct of the maximum value and the sine of the angle

corresponding to a given instant.


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4. Amplitude: The maximum value (positive or negative)attained by an alternating quantity in one cycle is calledits amplitude or peak value or crest value.

5. Cycle: When an alternating quantity goes through acomplete set of positive and negative values ,it is said tohave completed one cycle. Thus one complete set ofpositive and negative values of an alternating quantity is

known as cycle.6. Time Period (T) The time taken to complete one cycleby alternating quantity is called its time period or periodictime. It is equal to the reciprocal of frequency.

7. Frequency: (f) The number of cycles completed by analternating quantity per second is called frequency of thealternating quantity. Its unit is Hz. In India, the frequencyof ac system is 50Hz. In USA and some other countries,60Hz frequency is used.


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Average and R.M.S Values of sinusoidal

These notes relate primarily to cyclic variations of a variable.The principles also apply to variables which are constantly changing over time.Two methods of quantifying a representive value are available : "The AverageValue" and "The Root Mean Square Value."

The Average ValueThe average value of the current or the voltage is the one which provides auseful practical measure of its magnitude.It is equal to the sum of all instantaneous values divided by the number ofvalues taken over that interval.Average value = Area under the curve

length of the base of the curve


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Root mean square

The Rms value is defined as that value of DC whichwhen flowing through a given circuit for a given timeproduces the same heating effect as produced by thealternating current when flowing through the same circuitfor the same time.For a sinusoidal current The RMS value for the current(I)I = 0,707.I m


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1) Average value for a sinusoidal variable

Consider a Sinusoidal current i = Im sin over a half Cycle...

2) Root Mean Square value for a sinusoidal variableConsider a Sinusoidal current i = I m sin


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Phasor Diagram of a SinusoidalWaveform

Phasor Diagram of a Sinusoidal Waveform


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AC Series and Parallel CircuitComponents of an electrical circuit or electronic circuit can be connected

in many different ways .The two simplest of these are called series and parallel and occur veryfrequently. Components connected in series are connected along a single

path, so the same current flows through all of the components.Components connected in parallel are connected so the same voltage is

applied to each component.A circuit composed solely of components connected in series is known asa series circuit ; likewise, one connected completely in parallel is known asa parallel circuit .In a series circuit, the current through each of the components is the same,

and the voltage across the circuit is the sum of the voltages across eachcomponent. .

In a parallel circuit, the voltage across each of the components is the same,and the total current is the sum of the currents through each component. .
http://en.wikipedia.org/wiki/Electrical_networkhttp://en.wikipedia.org/wiki/Electronic_circuithttp://en.wikipedia.org/wiki/Topology_(electronics)http://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Topology_(electronics)http://en.wikipedia.org/wiki/Electronic_circuithttp://en.wikipedia.org/wiki/Electrical_network


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A series circuit with a voltage source (suchas a battery) and 3 resistors
http://en.wikipedia.org/wiki/Voltage_sourcehttp://en.wikipedia.org/wiki/Voltage_source


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Parallel Circuit

If two or more components are connected in parallel theyhave the same potential difference ( voltage ) across theirends.The potential differences across the components are thesame in magnitude, and they also have identicalpolarities. The same voltage is applicable to all circuit componentsconnected in parallel. The total current is the sum of thecurrents through the individual components, inaccordance with Kirchhoffs current law .
http://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_lawshttp://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_lawshttp://en.wikipedia.org/wiki/Voltage

Ch-1 Fundamentals of Alternating Voltage & Current

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