Alternating Current

Notes

1.1 Alternating Current An alternating current (AC) is an electric current whose magnitude changes continuously with time and direction reverses periodically. The instantaneous value of sinusoidal alternating current is i=i 0 ​ sinωt ​ where: i = instantaneous current i 0 ​ = peak or maximum current ω = angular frequency t = time Similarly, alternating voltage is v=v 0 ​ sinωt ​ where v 0 ​ is the peak voltage. Angular Frequency ω=2πf= T 2π ​ ​ where: f = frequency T = time period and f= T 1 ​ ​ 1.2 AC Cycle During one complete cycle, alternating current flows in one direction for half a cycle and in the opposite direction for the remaining half. i ↑ | / \ / \ | / \ / \ |-----/-----\------/-----\----→ t | / \ / \ | / \ / | / \/ | One complete cycle corresponds to: 2π rad=360 ∘ 1.3 Mean or Average Value of AC Over one complete cycle, the average value of sinusoidal AC is zero because the positive and negative halves cancel each other. I avg ​ =0 ​ However, the average value over one half-cycle is I avg ​ = π 2I 0 ​ ​ ​ Therefore, I avg ​ =0.637I 0 ​ ​ Similarly, V avg ​ = π 2V 0 ​ ​ 1.4 RMS Value of AC RMS means Root Mean Square. The RMS value of AC is the value of steady DC that produces the same heating effect in a resistor as the AC does during the same time. For sinusoidal current, I rms ​ = 2 ​ I 0 ​ ​ ​ or I rms ​ =0.707I 0 ​ ​ Similarly, V rms ​ = 2 ​ V 0 ​ ​ ​ Important When we say household supply is, for example, 230 V AC, the quoted voltage is its RMS value, not its peak value. Therefore, V…