Characteristics of alternating currents — common mistakes

Always check if a question refers to peak or RMS values, as using the wrong one is a common error in calculations. Remember that standard household voltage (e.g., 230 V in the UK) is almost always given as an RMS value!

AC is favoured for mains power primarily because its voltage can be easily stepped up or down using transformers. This allows for high-voltage, low-current transmission over long distances, which significantly reduces power loss ($P=I^2R$) in the cables.

Frequency ($f$) is the number of complete cycles per second, measured in Hertz (Hz). Angular frequency ($\omega$) describes the rate of change of the phase angle of the waveform, measured in radians per second (rad s⁻¹). They are related by $\omega = 2\pi f$, where $2\pi$ is the number of radians in one full cycle.

No, this specific relationship ($V_{rms} = V_{peak}/\sqrt{2}$) is only valid for sinusoidal alternating currents. For other waveform shapes (e.g., square waves, triangular waves), the relationship between RMS and peak values is different.