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IntroductIon
Electrical power generation, transmission and distribution employ a particular system of three 
sinusoidal voltages/currents with certain symmetry in voltage/current magnitude and relative phase. 
This system of three sinusoidal voltage/current waveforms is called a three-phase voltage/current and 
Chapter 
8

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8.2


SinusoidalSteady-StateinThree-PhaseCircuits
a circuit employing a three-phase voltage/current system is called a three-phase circuit. A three-phase 
circuit, like any other circuit, will have to go through a transient period subsequent to the application 
of source functions before it can settle down to a sinusoidal steady-state condition. We focus on 
analysis of three-phase circuits under sinusoidal steady-state condition in this chapter.
No new concepts are required for analysis of three-phase circuits under sinusoidal steady-state 
conditions. It requires only the application of all the concepts we developed in the last two chapters. 
But before we take up the analysis of three-phase circuits, let us see why electrical engineers thought 
up three-phase system in the first place.
8.1 
three-Phase system Versus sIngle-Phase system
Industrial heaters are used in various material processing industries for a variety of heating 
applications. Typically, heater boxes that contain heating elements powered by AC supply, transfer the 
heat developed to a gaseous (usually air) or liquid medium which conducts the heat to the material that 
is to be heated up. Resistor elements made of some specially constructed wire are laid out uniformly 
inside the heater box to develop uniform heating of the contact surface. Many such heating elements 
are finally connected in parallel to form the heater resistive load. Consider such a heater which, after 
all parallel connection of sub-elements, is finally represented by three equal resistors of R each. These 
three resistors may be connected in parallel and supplied from a single-phase AC source or they may 
be supplied individually from different AC sources – for instance, for redundancy and reliability.