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

The RMS value is defined as $V_{rms}$ = sqrt($\frac{1}{T}$*integral($V^2$ dt)) over one period. For a sinusoid: $V_{rms}$ = $\frac{V_0}{sqrt}$(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 $V_0$: $V_{rms}$ = $\frac{V_0}{sqrt}$(3). For a half-wave rectified sinusoid: $V_{rms}$ = $V_0$/2. For a full-wave rectified sinusoid: $V_{rms}$ = $\frac{V_0}{sqrt}$(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 $V_0$^$\frac{2}{2R}$).