• Tags: RMS, square-wave, triangular
• Difficulty: Advanced

The RMS value is defined as V_rms = sqrt((1/T)*integral(V^2 dt)) over one period. For a sinusoid: V_rms = V_0/sqrt(2). For a square wave of amplitude V_0: V_rms = V_0 (since V^2 = V_0^2 always). For a triangular wave of amplitude V_0: V_rms = V_0/sqrt(3). For a half-wave rectified sinusoid: V_rms = V_0/2. For a full-wave rectified sinusoid: V_rms = V_0/sqrt(2) (same as full sinusoid — squaring eliminates the sign). JEE occasionally tests these, especially asking to compare power dissipated by different waveforms in a resistor: P = V_rms^2/R. A square wave of the same amplitude as a sinusoid delivers twice the power (since V_0^2/R vs V_0^2/(2R)).