15 - a.c. circuit analysis

Abstract

This chapter focuses on the analysis of alternating current (a.c.) circuit. Circuit theory and the analysis of a.c. circuits is invariably achieved by using complex numbers—otherwise known as symbolic or jnotation. The effect of multiplying a phasor by j is to rotate it in a positive direction, that is, anticlockwise, on an Argand diagram through 90° without altering its length. Similarly, multiplying a phasor by—j rotates the phasor through—90°. These facts are used in the a.c. theory as certain quantities in the phasor diagrams lie at 90° to each other. There are a number of circuit theorems that have been developed for solving problems in a.c. electrical networks. These include the superposition theorem, Thévénins theorem, Norton's theorem, and the maximum power transfer theorem. As a preliminary to using circuit theorems, star-delta and delta-star transformations can be used.