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Sunday, 12 February 2017

What is Pure Resistive AC Circuit

Definition of Pure Resistive AC Circuit:

The circuit containing only a pure resistance of R ohms in the AC circuit is known as Pure Resistive AC Circuit. The presence of inductance and capacitance does not exist in a pure resistive circuit. The Alternating current and voltage both move forward as well as backward in both the direction of the circuit. Hence, the Alternating current and voltage follows a shape of Sine wave or known as the sinusoidal waveform.

Contents:

Explanation of Resistive Circuit

Phase Angle and Waveform of Resistive Circuit

Power in Pure Resistive Circuit

Explanation of Resistive Circuit:

In an AC circuit, the ratio of voltage to current depends upon the supply frequency, phase angle, and phase difference. In an AC resistive circuit, the value of resistance of the resistor will be same irrespective of the supply frequency.

Let the alternating voltage applied across the circuit be given by the equation

Then the instantaneous value of current flowing through the resistor shown in the figure below will be

The value of current will be maximum when ωt= 90 degrees or sinωt = 1

Putting the value of sinωt in equation (2) we will get

Phase Angle and Waveform of Resistive Circuit:

From equation (1) and (3), it is clear that there is no phase difference between applied voltage and current flowing through a pure resistive circuit, i.e. phase angle between voltage and current is zero.hence, in an AC circuit containing pure resistance, current is in phase with the voltage as shown in the waveform figure below.

Power in Pure Resistive Circuit :

The three colors red, blue and pink shown in the power curve or the waveform indicate the curve for current, voltage and power respectively. From the phasor diagram, it is clear that the current and voltage are in phase with each other that means the value of current and voltage attains its peak at the same instant of time, and the power curve is always positive for all the values of current and voltage.

As in DC supply circuit the product of voltage and current is known as the Power in the circuit similarly the power is same in the AC circuit also, the only difference is that in AC circuit the instantaneous value of voltage and current is taken into consideration. Therefore, the instantaneous power in a pure resistive circuit is given by the equation shown below

Instantaneous power, p= vi

The average power consumed in the circuit over a complete cycle is given by

As valve of cosωt is zero

Putting the value of cosωt in equation (4) the value of power will be given by

Where,

P – average power

Vr.m.s – root mean square value of supply voltage

Ir.m.s – root mean square value of the current

Hence, the power in a pure resistive circuit is given by

P=VI

The voltage and the current in the pure resistive circuit are in phase with each other having no phase difference with phase angle zero. The alternating quantity reaches their peak value at the interval of the same time period that is the rise and fall of the voltage and current occurs at the same time.

What is Form Factor??

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Definition of Form Factor :

The ratio of the root mean square value to the average value of an alternating quantity (current or voltage) is called Form Factor. The average of all the instantaneous values of current and voltage over one complete cycle is known as the average value of the alternating quantities. Mathematically, it is expressed as

Ir.m.s and Er.m.s are the roots mean square value of the current and the voltage respectively, and Iav and Eav are the average value of the alternating current and the voltage respectively.

For the current varying sinusoidally, the Form Factor is given as

The value of Form Factor is '1.11'

There is a relation between the peak value, the average value, and the root means square (R.M.S) value of an alternating quantity. Therefore, to express the relationship between all these three quantities, the two factors are used, namely as Peak Factor and Form Factor.

The Form Factor for the various sinusoidal waveforms are as follows

For sine wave, it is π/2√2 = 1.11072073

For half wave rectified sine wave, it is π/2 = 1.5707963

For full wave rectified sine wave, it is π/2√2 = 1.11072073

For square wave, it is equal to 1

For triangle waveform, it is 2/√3 = 1.15470054

For sawtooth waveform, it is 2/√3 = 1.15470054

What is Peak, Average, and RMS Value???

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Definition of Peak Value :

The maximum value attained by an alternating quantity during one cycle is called its Peak value. It is also known as the maximum value or amplitude or crest value. The sinusoidal alternating quantity obtains its peak value at 90 degrees as shown in the figure below.

The peak values of alternating voltage and current is represented by Em and Im respectively.

Definition of Average Value :

The average of all the instantaneous values of an alternating voltage and currents over one complete cycle is called Average Value.

If we consider symmetrical waves like sinusoidal current or voltage waveform, the positive half cycle will be exactly equal to negative half cycle. Therefore, the average value over a complete cycle will be zero. The work is done by both, positive and negative cycle and hence the average value is determined without considering the signs.

So the only positive half cycle is considered to determine the average value of alternating quantities of sinusoidal waves. Let us take an example to understand it.

Divide the positive half cycle into (n) number of equal parts as shown in the above figure

Let i1, i2, i3…….. in be the mid ordinates

The Average value of current Iav = mean of the mid ordinates

Definition of R.M.S Value :

That steady current which, when flows through a resistor of known resistance for a given period of time than as a result the same quantity of heat is produced by the alternating current when flows through the same resistor for the same period of time is called R.M.S or effective value of the alternating current.

In other words, the R.M.S value is defined as the square root of means of squares of instantaneous values.

Let I be the alternating current flowing through a resistor R for time t seconds, which produces the same amount of heat as produced by the direct current (Ieff). The base of one alteration is divided into n equal parts so that each interval is of t/n seconds as shown in the figure below.

Let i1, i2, i3,………..in be the mid ordinates

Then the heat produced in

Since Ieff is considered as the effective value of this current, then the total heat produced by this current will be

Now, equating equation (1) and (2) we will get

Ieff = square root of mean of squares of instantaneous values = R.M.S value

Root Mean Square is the actual value of an alternating quantity which tells us an energy transfer capability of an AC source. The ammeter records the RMS value of alternating current and voltmeter record’s the root mean square (R.M.S) value of alternating voltage. The domestic single phase AC supply is 230 V, 50 hertz, where 230 V is the R.M.S value of alternating voltage.

The values of voltage and the current system in a DC circuit is constant, so there is no issue in evaluating their magnitudes, but in an AC system, the alternating voltage and current vary from time to time and hence it is necessary to evaluate their magnitudes. The following three ways (peak value, Average value and R.M.S value) given above are adopted to express the magnitude of the voltage and current.

Saturday, 11 February 2017

What is Peak Factor???

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Definition of Peak Factor:

Peak Factor is defined as the ratio of maximum value to the R.M.S value of an alternating quantity.

The alternating quantities can be voltage or current. The maximum value is the peak value or the crest value or the amplitude of the voltage or current and the root mean square value is the amount of heat produced by the alternating current will be same when the direct supply of current is passed through the same resistance in the same given time.

Mathematically it is expressed as

Where,
Im and Em are the maximum value of the current and the voltage respectively, and Ir.m.s and Er.m.s are the root mean square value of the alternating current and the voltage respectively.

For the current varying sinusoidally, the peak factor is given as

The value of Peak Factor is 1.4142

What is AC Circuit

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Definition of AC circuit:

The path for the flow of alternating current is called an AC Circuit. The alternating current (AC) is used for domestic and industrial purposes. In an AC circuit, the value of the magnitude and the direction of current and voltages is not constant, it changes at a regular interval of time. It travels as a sinusoidal wave completing one cycle as half positive and half negative cycle and is a function of time (t) or angle (θ=wt).

In DC Circuit, the opposition to the flow of current is the only resistance of the circuit whereas the opposition to the flow of current in the AC circuit is because of resistance (R), Inductive Reactance (XL=2πfL) and capacitive reactance (XC = 1/2 πfC) of the circuit.

In AC Circuit, the current and voltages are represented by magnitude and direction. The alternating quantity may or may not be in phase with each other depending upon the various parameters of the circuit like resistance, inductance, and capacitance.

The sinusoidal alternating quantities are voltage and current which varies according to the sine of angle θ.For the generation of electric power, in all over the world the sinusoidal voltage and current are selected because of the following reasons are given below.

The sinusoidal voltage and current produce low iron and copper losses in the transformer and rotating electrical machines, which in turns improves the efficiency of the AC machines.
They offer less interference to the nearby communication system.
They produce less disturbance in the electrical circuit.

Alternating Voltage and Current in an AC Circuit :

The voltage that changes its polarity and magnitude at regular interval of time is called an alternating voltage. Similarly the direction of the current is changed and the magnitude of current changes with time it is called alternating current.When an alternating voltage source is connected across a load resistance as shown in the figure below, the current through it flows in one direction and then in the opposite direction when the polarity is reversed.

The waveform of the alternating voltage with respect to the time and the current flowing through the resistance (R) in the circuit is shown below.

There are various types of AC circuit such as AC circuit containing only resistance (R), AC circuit containing only capacitance (C), AC circuit containing only inductance (L), the combination of RL Circuit, AC circuit containing resistance and capacitance (RC), AC circuit containing inductance and capacitance (LC) and resistance inductance and capacitance (RLC) AC circuit.

The various terms which are frequently used in an AC Circuit are as follows

Amplitude: The maximum positive or negative value attained by an alternating quantity in one complete cycle is called Amplitude or peak value or maximum value. The maximum value of voltage and current is represented by Em or Vm and Im respectively.

Alternation : One half cycle is termed as alternation. An alternation span is of 180 degrees electrical.

Cycle : When one set of positive and negative values completes by an alternating quantity or it goes through 360 degrees electrical, it is said to have one complete Cycle.

Instantaneous Value : The value of voltage or current at any instant of time is called an instantaneous value.It is denoted by (i or e).

Frequency : The number of cycles made per second by an alternating quantity is called frequency. It is measured in cycle per second (c/s) or hertz (Hz) and is denoted by (f).

Time Period : The time taken in seconds by a voltage or a current to complete one cycle is called Time Period. It is denoted by (T).

Wave Form : The shape obtained by plotting the instantaneous values of an alternating quantity such as voltage and current along the y axis and the time (t) or angle (θ=wt) along the x axis is called waveform.

Define and Explain Active , Reactive and Apparent Power???

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Definition of Active Power : The power which is actually consumed or utilized in an AC Circuit is called True power or Active Power or real power.

It is measured in kilo watt (kW) or MW.

Definition of Reactive Power : The power which flows back and froth that mean it moves in both the direction in the circuit or react upon itself, is called Reactive Power.

The reactive power is measured in kilo volt ampere reactive (kVAR) or MVAR.

Definition of Apparent Power : The product of root mean square (RMS) value of voltage and current is known as Apparent Power.

This apparent power is measured in kVA or MVA.

It has been seen that the power is consumed only in resistance. A pure inductor and a pure capacitor do not consume any power, since in a half cycle whatever power is received from the source by these components, the same power is returned to the source. This power which returns and flows in both the direction in the circuit is called Reactive power. This reactive power does not perform any useful work in the circuit.

In the pure resistive circuit, the current is in phase with the applied voltage, whereas in pure inductive and capacitive circuit the current is 90 degrees out of phase. i.e If the inductive load is connected in the circuit the current lags voltage by 90 degrees and if the capacitive load is connected the current leads the voltage by 90 degrees.

Hence, from the above all discussion, it is concluded that the current in phase with the voltage produces true or active power, whereas, the current 90 degrees out of phase with the voltage contributes to reactive power in the circuit.

Therefore,

True power = voltage x current in phase with the voltage

Reactive power = voltage x current out of phase with the voltage

The phasor diagram for an inductive circuit is shown below

Taking voltage V as reference, the current I lags behind the voltage V by an angle ϕ. The current I is divided into two components

I Cos ϕ in phase with the voltage V

I Sin ϕ which is 90 degrees out of phase with the voltage V

Therefore, the following expression shown below gives the active, reactive and apparent power respectively

Active power P = V x I cosϕ = V I cosϕ

Reactive power Pr or Q = V x I sinϕ = V I sinϕ

Apparent power Pa or S = V x I = VI

Active component of the current:

The current component which is in phase with the circuit voltage and contributes to the active or true power of the circuit is called active component or wattfull component or in-phase component of the current.

Reactive component of the current:

The current component which is in quadrature or 90 degrees out of phase to the circuit voltage and contributes to the reactive power of the circuit is called reactive component of the current.