Alternating Current (AC) Fundamentals

Introduction

• Direct current (DC) is limited in applications such as charging batteries and electroplating.
• Alternating current (AC) has advantages for large-scale power distribution.
• AC systems can efficiently change voltages using transformers.
• AC motors are generally cheaper and simpler than DC motors.
• AC switchgear is simpler compared to DC systems.
• AC is converted to DC using rotary converters or rectifiers when needed.
• This chapter focuses on the fundamentals of alternating currents.

Alternating Voltage and Current

• Alternating voltage changes polarity at regular intervals.
• The current direction depends on the voltage polarity.
• Alternating current flows in alternating directions in the circuit.

Sinusoidal Alternating Voltage and Current

• Commercial alternators produce sinusoidal alternating voltage, which is a sine wave.
• A sinusoidal alternating voltage can be produced by rotating a coil at a constant angular velocity in a uniform magnetic field.
• The equation for sinusoidal alternating voltage is: v = Vm sin ωt
  • v: Instantaneous value of alternating voltage
  • Vm: Maximum value of alternating voltage
  • ω: Angular velocity of the coil
• Sinusoidal voltages produce sinusoidal currents in linear circuits.
• A sinusoidal current can be expressed as: i = Im sin ωt
• Both magnitude and direction change continuously in sinusoidal voltage or current.
• Instantaneous quantities are denoted by lowercase letters (e.g., v, i).
• An alternating current can be represented as a cosine function: i = Im cos ωt
• Reasons for choosing sinusoidal waveform:
  • Least iron and copper losses in machines and transformers
  • Less interference on telephone lines
  • Smoothest and most efficient waveform
• Electric supply companies worldwide generate sinusoidal voltages/currents.

Generation of Alternating Voltages and Currents

• Alternating voltage can be generated by:
  • Rotating a coil at constant angular velocity in a uniform magnetic field, or
  • Rotating a magnetic field at a constant angular velocity within a stationary coil
• The generated voltage will be sinusoidal.
• The magnitude depends on the number of turns of coil, magnetic field strength, and speed of rotation.
• Method for generating an alternating voltage by rotating a coil at constant angular velocity in a magnetic field will result in a sinusoidal waveform
• The first method (rotating coil) is for small AC generators, the second (rotating magnetic field) for large AC generators.

Equation of Alternating Voltage and Current

• Consider a rectangular coil with n turns rotating in a anticlockwise direction with an angular velocity of ω rad/sec in a uniform magnetic field.
• The EMF induced in the coil is sinusoidal.
• Flux linkages of the coil at the considered instant (i.e. at θ) is related to the number of turns and magnetic flux
• According to Farraday's Laws; v = n * φmax * ω * sin ωt
• The voltage Vm = n * φmax * ω
• The alternating current equation is i = Im sin ωt

Important AC Terminology

• Alternating voltage and current changes continuously over time
• Rises from zero to a max positive value, to zero, to max reverse value, then back to zero
• important terminology is defined below:
• Waveform: The shape of the curve, plotted as voltage/current against time
• Instantaneous Value: The value of alternating quantity at any instant (v or i)
  • E.g. at 90 deg, instanatious value is Vm
• Cycle: Complete set of +ve and -ve values of an AC quantity
  • One cycle corresponds to 360 electrical degrees or 2 pi radians
  • AC generated will span 360 electrical whe passing a North and South pole
• Alternation: One-half cycle of an alternating voltage is the alternation of the signal - alternation spans 180 degrees electrical
• Time Period: Time in seconds for one cycle denoted as 'T'
• Frequency: Number of AC cycles in 1 second 'f', measured in cycles/sec/Hertz (HZ)
  • 50 Hz is common for balancing lights and machines
• Amplitude: Is Vm (ie. the max (+/-) voltage attained by an alternating quantity

Important Relations

• Time and Period Frequency; T = 1/f or f = 1/T
• Angular and Period Frequency: Angular velocity, ω = 2π/T
• Angular velocity, ω = 2πf
• Consider a coil rotation at speed N r.p.m in the field of P pules
• Frequency, f = (P*W) / 120, where N = 60

Different Forms of Alternating Voltage

• Standard form v = Vm sin θ = Vm sin ωt expressed as:
• Standard form v = Vm sin 2π*ft = Vm sin 2πf/T
• The equations use depends upon the data
• Max alternating voltage - coefficient of time in sine angle
• Frequency f - coefficient of time by dividing by 2*pi

R.M.S or Effective Value

• Average value cannot specify a sinosoudal voltage or curent
  • Because it is zero, RMS makes it more suitable
• RMS : measure AC in terms of a DC current that is equivilent for amount of work The effective or r.m.s. value of an alternating current is that steady current (d.c.) which when flowing through a given resistance for a given time produces the same amount of heat as produced by the alternating current when flowing through the same resistance for the same time.

RMS Value of Effective value

• Equation i = Im sin θ is given by:
• R.M.S value = Square root of the mean of the squares of the current

Form Factor and Peak factor

• There is a definited relation between Peak, Average RMS value of AC quanitites
• (i) Form factor*. The ratio of r.m.s. value to the average value of an alternating quantity is known as form factor i.e.: Form factor = R.M.S. value /Average value
  • For a sinusoidal voltage: From Factor = RMS/Average Value = 0.707x / Max. value / 0.637x Max. value =1.11
• (ii) Peak factor*. The ratio of maximum value to the r.m.s. value of an alternating quantity is known as peak factor i.e.: Peak factor = Max. value of AC value/ R.M.S. value
  • For a sinusoidal voltage = Max. value/ 0.707× Max.value = 1.414

Phase

• Waves of alternating V and Current are continuous are continuous. - They do not stop after one cucle

Phase Difference

• Apply alternative voltage -> leads to frequency and current change is the circuits We say that voltage and current have a phase difference

Phasor Representation of Sinusoidal Quantities

• The above difficulty has been overcome by representing sinusoidal alternating voltage or current by a line of definite length rotating in *anticlockwise direction at a constant angular velocity (w). Such a rotating line is called a phasor. The length of the phasor is taken equal to the maximum value (on suitable scale) of the alternating quantity and angular velocity equal to the angular velocity of the alternating quantity

Phasor Diagram of Sine Waves of the Same Frequency*

= 0

• M
• 1 m 4 ( ) 810

Introduction to alternating current (AC) and its advantages over direct current (DC). Includes sinusoidal voltage, current, and generation using alternators. Covers basic AC principles.