16.1.1 Alternating Current

During the 1880s, Thomas Edison and Nikola Tesla were embroiled in a battle called the War of the Currents. Edison favoured direct current (DC), with constant voltages and steady currents. Tesla favoured alternating current (AC), with voltages and currents that vary sinusoidally with time. AC emerged victorious in the end, largely because of DC’s pathetically low efficiency during power transmission. Throughout the world today, AC power grids deliver power via a sinusoidal emf.

$V={{V}_{{pk}}}\sin \omega t$

The voltage and frequency vary from country to country though. Singapore operates on a 230 V (rms) supply voltage and 50 Hz frequency. This implies peak voltage ${{V}_{{pk}}}\approx 330\text{ V}$ and angular frequency $\omega =2\pi f=2\pi (50)=100\pi \text{ rad }{{\text{s}}^{{-1}}}$ . Or