RMS VALUE OF SINUSOIDAL CURRENT

An alternating current varying sinusoidally is given by the following equation:

 

i = I_m sin θ

To determine the rms value, the squared wave of the alternating current is drawn as shown in Figure 6.11.

Fig. 6.11  Squared-wave shape of a sine wave

Considering an elementary strip of thickness dθ in the first half-cycle of the squared wave, let i² be its mid-ordinate.

Then,

 

Area of strip = i²dθ

Area of first half cycle of squared wave

Base = 0 to π = π − 0 = π

Effective or rms value,

Usually, rms value of an AC is simply represented by I instead of I_rms. Similarly, rms value of an alternating voltage is represented by E or V.