Which formula represents effective current in an AC circuit?

In an AC circuit, the effective current, often referred to as RMS (Root Mean Square) current, provides a way to express the amount of current that delivers the same power as a comparable DC circuit. The formula for converting peak current (Ipk) to RMS current is represented by Irms = Ipk / sqrt(2).

This relationship is derived from the nature of sinusoidal waveforms. The peak current is the maximum value of the current waveform, but for practical purposes in AC circuits, we want a value that represents equivalent power delivery, which is achieved using the RMS value. The factor of sqrt(2) (approximately 1.414) arises because the power in an AC circuit is proportional to the square of the voltage or current. Therefore, to find the effective value that conveys the same power consumption, dividing the peak current by sqrt(2) provides the correct calculation for RMS current.

While the other options may seem to present valid relationships at a glance, the most direct and mathematically accurate representation of the effective current in an AC circuit aligns with the first formula. The others may simplify or misrepresent the relationship required for calculating RMS from peak values.