For a standard sinusoidal alternating voltage, the root mean square (rms) voltage ($V$ or $V_{rms}$) is defined as $V = \frac{v_m}{\sqrt{2}} = 0.707 v_m$, where $v_m$ (or $V_0$) is the peak or maximum voltage amplitude . This relationship is derived from the average power dissipated in a resistor over a complete cycle.