001 Electronics Reviewer1

7/31/2019 001 Electronics Reviewer1

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AC CIRCUITSGive thanks for God is good and His love endures forever.

Engr. Rex Jason H. Agustin


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ALTERNATING CURRENT

ALTERNATING CURRENT A current that is constantly changing in amplitude and

direction.

Advantages of AC:

Magnitude can easily be changed (stepped-up or stepped down) with the use of atransformer

Can be produced either single phase for light loads, two phase for control motors,three phase for power distribution and large motor loads or six phase for large

scale AC to DC conversion.

BASIC AC THEORY


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AC WAVEFORMS

BASIC AC THEORY


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AC WAVEFORMS

Period (T) the time of one complete cycle in seconds

Frequency (f) the number of cycles per second (Hertz)

a. 1 cycle/second (cps) = 1 Hertz (Hz)b. Proper operation of electrical equipmnent requires specific frequency

c. Frequencies lower than 60 Hz would cause flicker when used in lightning

Wavelength () the length of one complete cycle

Propagation Velocity (v) the speed of the signal

Phase () an angilar measurement that specifies the position of a sine wave relative

to reference

f = 1

T

= v

f

Parameters of Alternating Signal

BASIC AC THEORY


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AC WAVEFORMS

THE SINUSOIDAL WAVE

Is the most common AC waveform that is practicallygenerated by generators used in household and industries

General equation for sine wave:

Where:

a(t) instantaneous amplitude of voltage or current at a given time (t)Am maximum voltage or current amplitude of the signal

angular velocity in rad/sec; = 2f

t time (sec)

phase shift ( + or in degrees)

A(t) = Am sin (t + )

BASIC AC THEORY


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AC WAVEFORMS

AMPLITUDE

It is the height of an AC waveform as depicted on a graph over time(peak, peak-to-peak, average, or RMS quantity)

PEAK AMPLITUDE the height of an AC waveform as measured from the

zero mark to the highest positive or lowest negative point on a graph. Also

known as the crest amplitude of a wave.

Measurements of AC Magnitude

BASIC AC THEORY


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AC WAVEFORMS

PEAK-TO-PEAK AMPLITUDE the total height of an AC waveform as

measured from maximum positive to maximum negative peaks on a

graph. Often abbreviated as P-P

BASIC AC THEORY


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AC WAVEFORMS

AVERAGE AMPLITUDE the mathematical mean of all a waveforms pointsover the period of one cycle. Technically, the average amplitude of anywaveform with equal-area portions above and below the zero line on agraph is zero.

For a sine wave, the average value so calculated is approximately 0.637 of itspeak value.

BASIC AC THEORY


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AC WAVEFORMS

RMS AMPLITUDE - RMS stands for Root Mean Square, and is a way of

expressing an AC quantity of voltage or current in terms functionally

equivalent to DC. Also known as the equivalent or DC equivalent

value of an AC voltage or current.

For a sine wave, the RMS value is approximately 0.707 of its peak value.

BASIC AC THEORY


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AC WAVEFORMS

The crest factor of an AC

waveform is the ratio of

its peak (crest) to its RMSvalue.

Theform factor of an AC

waveform is the ratio of

its RMS value to itsaverage value.

BASIC AC THEORY


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AC QUANTITIES

BASIC AC THEORY


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AC QUANTITIES

Inductive Reactance (XL) The property of the inductor to oppose the alternating current

Inductive Susceptance (BL)

Reciprocal of inductive reactance

Capacitive Reactance (XC)

The property of a capacitor to oppose alternating current

Capacitive Susceptance (BC)

Reciprocal of capacitive reactance

d

XL = 2fL

BL = 1 BL = 1XL 2fL

XC = 1

2fC

BL = 1 BL = 2fC

XC

BASIC AC THEORY


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AC QUANTITIES

IMPEDANCE (Z) Total opposition to the flow of Alternating current

Combination of the resistance in a circuit and the reactancesinvolved

Z = R + jXeq Z = |Z|

Where: |Z| = R2 + X2

= Arctan XeqR

BASIC AC THEORY


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AC QUANTITIES

If I = Im is the resulting current drawn by a passive, linear RLC circuit from asource voltage V = Vm , then

Where: Z = Vm = R2 + X2 = magnitude of the impedance

Im

= = tan

-1

X = phase angle of the impedanceR

R = Zcos = active or real component of the impedance

X = Zsin = reactive or quadrature component of impedance

Z = V = Vm = Z

I Im

Z cos + jZsin = R + jX = R2 + X2 tan-1 XR

BASIC AC THEORY


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AC QUANTITIES

ADMITTANCE (Y) The reciprocal of impedance

Expressed in siemens or mho (S)

Where: Y = Im = G2 + B2 = 1 = magnitude of the admittance

Z

y = = = tan-1 B = phase angle of the admittance

G

G = Ycos y = conductive/conductance component

B = Ysin y = susceptive/susceptance component

Y = Im = Y = Ycos y + jYsin y = G + jB

Vm

Y = G2 + B2 tan-1 B

G

BASIC AC THEORY


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AC RESISTOR CIRCUIT

With an AC circuit like this which is purely resistive, the relationship of the voltageand current is as shown:

Voltage (e) is in phase with the current (i) Power is never a negative value. When the current is positive (above the line),

the voltage is also positive, resulting in a power (p=ie) of a positve value

This consistent polarity of a power tell us that the resistor is alwaysdissipating power, taking it from the source and releasing it in the form of heatenergy. Whether the current is negative or positive, a resistor still dissipated

energy. AC CIRCUITS

Impedance (Z) = R


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AC INDUCTOR CIRCUIT

The most distinguishing electrical characteristics of an L circuit is that current lagsvoltage by 90 electrical degrees

Because the current and voltage waves arae 90o out of phase, there sre times when oneis positive while the other is negative, resulting in equally frequent occurences ofnegative instantaneous power.

Negative power means that the inductor is releasing power back to the circuit, while apositive power means that it is absorbing power from the circuit.

The inductor releases just as much power back to the circuit as it absorbs over the span

of a complete cycle.

Impedance (Z) = jXL

AC CIRCUITS


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AC INDUCTOR CIRCUIT

o Inductive reactance is the opposition that an inductor offers to alternating

current due to its phase-shifted storage and release of energy in its

magnetic field. Reactance is symbolized by the capital letter X and is

measured in ohms just like resistance (R).

o Inductive reactance can be calculated using this formula: XL = 2fL

o The angular velocity of an AC circuit is another way of expressing its

frequency, in units of electrical radians per second instead of cycles per

second. It is symbolized by the lowercase Greek letter omega, or .

o Inductive reactance increases with increasing frequency. In other words,

the higher the frequency, the more it opposes the AC flow of electrons.

AC CIRCUITS


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AC CAPACITOR CIRCUIT

The most distinguishing electrical characteristics of an C circuit is that leads the voltageby 90 electrical degrees

The current through a capacitor is a reaction against the change in voltage across it

A capacitors opposition to change in voltage translates to an opposition to alternatingvoltage in general, which is by definition always changing in instantaneous magnitudeand direction. For any given magnitude of AC voltage at a given frequency, a capacitorof given size will conduct a certain magnitude of AC current.

The phase angle of a capacitors opposition to current is -90o,meaning that a capacitors

opposition to current is a negative imaginary quantity

Impedance (Z) = -jXC

AC CIRCUITS


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AC CAPACITOR CIRCUIT

o Capacitive reactance is the opposition that a capacitor offers to alternating

current due to its phase-shifted storage and release of energy in its electric

field. Reactance is symbolized by the capital letter X and is measured in

ohms just like resistance (R).

o Capacitive reactance can be calculated using this formula: XC = 1/(2fC)

o Capacitive reactance decreases with increasing frequency. In other words,

the higher the frequency, the less it opposes (the more it conducts) theAC flow of electrons.

AC CIRCUITS


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SERIES RESITOR-INDCUTOR CIRCUIT

For a series resistor-inductor circuit, the voltage and current relation isdetermined in its phase shift. Thus, current lags voltage by a phase shift()

Impedance (Z) = R + jXL

Admittance (Y) = 1 = RjXLR + jXL R

2 + jXL2

AC CIRCUITS


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SERIES RESITOR-INDCUTOR CIRCUIT

o When resistors and inductors are mixed together in circuits, the totalimpedance will have a phase angle somewhere between 0o and +90o. The

circuit current will have a phase angle somewhere between 0o and -90o.

Series AC circuits exhibit the same fundamental properties as series DC

circuits: current is uniform throughout.

Phase shift () = Arctan ( XL ) |Z| = R2 + jXL

2 = e

R i

AC CIRCUITS


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SERIES RESISTOR-CAPACITOR CIRCUIT

Phase shift () = Arctan ( XC ) |Z| = R2 + jXC

2 = e

R i

AC CIRCUITS


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PARALLEL RESISTOR-INDUCTOR

Y = GjL where: G conductance = 1/R

L susceptance = 1/XL

Z = E , by Ohms Law

I

The basic approachwith regarda to parallel circuits is using admittance

because it is additive AC CIRCUITS


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PARALLEL RESISTOR-INDUCTOR

o When resistors and inductors are mixed together in parallel circuits (just

like in series cicuits), the total impedance will have a phase angle

somewhere between 0o and +90o. The circuit current will have a phase

angle somewhere between 0o and -90o.

o Parallel AC circuits exhibit the same fundamental properties as parallel DC

circuits: voltage is uniform throughour the circuit, brach currents add to

form the total current, and impedances diminish (through the reciprocal

formula) to form the total impedance.

AC CIRCUITS


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PARALLEL RESISTOR-CAPACITOR

Y = G + jC where: G conductance = 1/R

C susceptance = 1/XC

o When resistors and capacitors are mixxed together in circuits, the total

impedance will have a phase angle somewhere between 0o and -90o.

AC CIRCUITS


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APPARENT POWER (S)

APPARENT POWER Represents the rate at which the total energy is supplied to the

system

Measured in volt-amperes (VA)

It has two components, the Real Power and the Capacitive orInductive Reactive Power

POWER IN AC CIRCUITS

S = Vrms Irms = Irms2

|Z|


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APPARENT POWER (S)

Power Triangle

Complex Power

S = P jQ



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REAL POWER (R)

REAL POWER The power consumed by the resistive component

Also called True Power, Useful Power and Productive Power

Measured in Watts (W)

It is equal to the product of the apparent power and the power factor

Cosine of the power factor angle ()

Measure of the power that is dissipated by the cicuit in relation to the

apparent power and is usually given as a decimal or percentage


Pf = cos

P = Scos Power Factor


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REAL POWER (R)

Ratio of the Real Power to the Apparent Power ( P )S

when:

Pf = 1.0 I is in phase with V; resistive system

Pf = lagging I lags V by ; inductive system

Pf = leading I leads V by ; capacitive system

Pf = 0.0 lag I lags V by 90o; purely inductivePf = 0.0 lead I leads V by 90o; purely capacitive

The angle between the apparent power and the real poweer in the power triangle

Let v(t) = Vm cos(t + v) voltsV = Vrms v

i(t) = Im cos(t + i) A

I = Irms i


Power factor Angle ()


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REAL POWER (R)

Where: = phase shfit between v(t) and i(t) or the phase angle of the

equivalent impedance


Instantaneous Power (watts)

Average Power (watts)

P(t) = v(t) i(t)

P(t) = VmIm cos (v i) + VmIm cos (2t + v + i)

P(t) = VmIm cos (v i) = VmIm cos


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REACTIVE POWER (QL or QC)

REACTIVE POWER Represents the rate at which energy is stored or released in any of the

energy storing elements (the inductor or the capacitor)

Also called the imaginary power, non-productive or wattless power

Measured in volt-ampere reactive (Var)

When the capacitor and inductor are both present, the reactive powerassociated with them take opposite signs since they do not store orrelease energy at the same time

It is positive for inductive power (QL) and negative for capacitivepower (QC)

Ratio of the Reactive Power to the Apparent Power

Sine of the power factor angle ()


Q = VmIm sin

Reactive factor

Rf = sin


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BALANCED THREE PHASE SYSTEMS

BALANCED 3-PHASE SYSTEM Comprises of three identical single-phase systems operating at a 120o

phase displacement from one another. This means that a balancethree-phase system provides three voltages(and currents) that areequal in magnitude and separated by 120o from each other

Three-Phase, 3-wire systems

Provide only one type of voltage(line to line) both single phase andthree phase loads

Three-Phase, 4-wire systems

Provide two types of voltages(line to line and line to neutral) to bothsingle phase and three phase loads

BALANCED THREE PHASE SYSTEM

CLASSIFICATION


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BALANCED THREE PHASE SYSTEMS

and

VLL and VLN are out of phase by 30o

BALANCED Y-system

VLL = 3 VLN IL = IP

and

IL

and IP

are out of phase by 30o

Where: VLL or VL - line to line or line voltage

VLN or VP - line to neutral or phase voltage

IL - line current

IP - phase current

BALANCED -system

IL = 3 IP VLL = VLN



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ALTERNATING CURRENT

VJH

watts

vars

va


Note: for balanced 3-phase systems:

IA + IB + IC = 0

VAN + VBN + VCN = 0

VAB + VBC + VCA = 0

P = 3VPIPcos = 3 VLIL cos

Q = 3VPIPsin = 3 VLIL sin

S = 3VPIP = 3 VLIL

THREE-PHASE POWER


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THANk YOU

001 Electronics Reviewer1

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