Introduction

Almost every socket in a home, and every large power station feeding a whole town, ultimately supplies alternating current (AC) rather than the steady, one-directional direct current (DC) that a battery or a cell provides. An alternating current does not merely flow through a circuit -- it periodically REVERSES its own direction, rising smoothly to a maximum value, falling back through zero, reversing, reaching a maximum in the opposite direction, and returning to zero again, over and over, at a fixed frequency (in India, 50 complete cycles every second). The overwhelming preference for AC over DC in power generation and distribution comes down to one single practical fact worked out in this chapter: AC voltages can be stepped up or stepped down almost losslessly using a transformer, which lets power be transmitted over long distances at a very high voltage (and correspondingly low current, cutting resistive $I^2R$ losses in the transmission wires) and then stepped back down to a safe level right before it reaches a home or factory -- something a purely DC system of this era could not do nearly as efficiently.

This chapter builds up the physics of AC circuits in the order WBCHSE's syllabus lists it. Section 7.2 first defines the peak and rms values used to give a single alternating quantity one representative number. Section 7.3 introduces the phasor-diagram method, the geometric tool used throughout the chapter to track how far out of phase two alternating quantities are. Sections 7.4-7.6 work out a pure resistor, a pure inductor and a pure capacitor taken one at a time, each connected alone to an AC source. Section 7.7 then defines reactance and impedance in general, before Sections 7.8-7.10 combine these elements into the LR, CR and full series LCR circuits. Section 7.11 studies the striking phenomenon of resonance, and Section 7.12 looks briefly, and only qualitatively as WBCHSE requires, at the LC oscillator. Section 7.13 works out how much power an AC circuit genuinely consumes on average, introducing the power factor and the wattless current. The chapter closes with the two great practical machines built on everything above: the AC generator, which produces the alternating emf in the first place (Section 7.14), and the transformer, which changes its voltage almost without loss (Section 7.15).