Irms

Irms, short for root-mean-square current, is a measure of the effective current in an electrical circuit. It reflects the heating effect the current would produce if it were a steady direct current of the same value, and it is the quantity used to calculate power in resistive components.

Definition and calculation

For a time-varying current i(t) over a time interval T, Irms is defined as the square root of the average of i(t) squared: Irms = sqrt( (1/T) ∫0^T i(t)^2 dt ). For a DC current, Irms equals the absolute value of the current. For periodic waveforms, the interval T is one period. In practical terms, Irms is the value that transforms a varying current into an equivalent steady current in terms of heating.

Common waveforms

- Sine wave: i(t) = I_peak sin(ωt) gives Irms = I_peak / √2.

- Square wave with amplitude I0: Irms = I0.

- Triangular wave with peak I0: Irms = I0 / √3.

- DC: Irms = |I|

Applications and measurement

Irms is used to determine power in resistive loads via P = Irms^2 R. In AC circuits with linear loads, Irms relates to voltage by Irms = Vrms / |Z| for a given impedance Z, and real power is P = Vrms Irms cos φ, where φ is the phase angle between voltage and current.

Measurement devices may be true RMS meters, which compute Irms from the actual waveform, or average-responding meters that assume a sine waveform and can misrepresent Irms for non-sinusoidal currents, common in switching power supplies.

Irms is a fundamental concept in electrical engineering, essential for heating calculations, conductor and fuse sizing, and safety analyses involving alternating currents.