4 - Single-phase a.c. circuits

Abstract

This chapter discusses various aspects of single-phase A.C. circuits. A quantity that is continually changing its sign from positive to negative and back again is called an alternating quantity, usually referred to simply as an A.C. quantity. A graph of the quantity to a base of time is called the waveform of the quantity and when a waveform has completed one complete series of changes and is about to start repeating itself it is said to have completed one cycle. In general an alternating quantity changes its magnitude from instant to instant over the cycle time and these values are called the instantaneous values of the quantity. Conventionally, the phasors rotate in an anticlockwise direction so that the current leads the voltage. The average value of a sine wave over a complete cycle is zero, which is rather meaningless, so the average value is taken to be the average over a half cycle. Steady-state operation means that any transient effects following the switching on of a circuit have died away and that the waveforms of voltages and currents are continuous sine waves. In practice resistive circuits will have some inductance, however small, because the circuit must contain at least one loop of connecting wire. It is found that inductive circuits must have some resistance due to the resistance of the wire making up the coil.