RMS (Root Mean Square) or Effective Value

 

 RMS (Root Mean Square) or Effective Value

Definition:
The RMS value of an alternating current (AC) signal is the equivalent value of direct current (DC) that would produce the same amount of heat in a resistor as the AC signal. It is also called the effective value because it reflects the real power delivered by the AC signal.

For a sinusoidal signal, the RMS value of the voltage or current is calculated as:

$$V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}, \quad I_{\text{rms}} = \frac{I_{\text{max}}}{\sqrt{2}}$$

Example:
If the peak (maximum) voltage of a sinusoidal AC signal is 100V, the RMS voltage is:

$$V_{\text{rms}} = \frac{100}{\sqrt{2}} \approx 70.7V$$