Rms Value Of Sinusoidal Alternating Current — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
RMS Value of Sinusoidal Alternating Current Applicable only to sinusoidal time-varying currents or voltages. Define RMS current as the square root of the mean of the square of the instantaneous current over one cycle: I rms = sqrt((1/T) integral(i 2 dt)). Substitute instantaneous current i = I 0 sin(wt). Integrate sin 2(wt) over one period T, which yields T/2. Simplify to sqrt((I 0 2 T/2) / T) = sqrt(I 0 2 / 2) = I 0 / sqrt(2). The waveform must be strictly sinusoidal. For non-sinusoidal waves (e.g., square, triangular), the factor dividing the peak value differs. Confusing RMS value with the Average value (which is 2I 0/pi for a half-cycle or 0 for a full cycle). Assuming the formula applies to non-sinusoidal AC waveforms. Thinking that household voltage (e.g., 220V) represents the peak value rather than the RMS value.