Alternating Current & RMS — A/L Physics

Alternating Current (AC) A current that periodically reverses direction, with its magnitude varying sinusoidally with time. In AC, electrons oscillate back and forth rather than drifting steadily. The standard waveform is sinusoidal: I(t) = I₀ sin(ω t) , where I₀ is the peak current. Mains electricity (230 V, 50 Hz in Sri Lanka) is AC because it is easily transformed to different voltages for transmission.

Peak Value ( I₀ , V₀ ) The maximum instantaneous value of current or voltage in one cycle. For a sinusoidal AC, the peak value occurs at ω t = (π)/(2) and (3π)/(2) . It is the amplitude of the sine wave. Example: A 230 V RMS supply has a peak voltage of V₀ = 230 × √2 ≈ 325 V .

Root Mean Square (RMS) Value The equivalent DC value that produces the same average power dissipation in a pure resistor. RMS is calculated by squaring the instantaneous values, averaging over one cycle, then taking the square root. For a sinusoidal waveform: I_rms = I₀√2 . Intuition: A 5 A RMS AC current heats a resistor exactly as much as a 5 A DC current.