Peak voltage is equal to RMS voltage times which factor?

Peak voltage in an AC circuit refers to the maximum voltage reached by the waveform, while RMS (Root Mean Square) voltage is a measure that relates to the effective value of the voltage in terms of its ability to do work – analogous to a DC voltage. The relationship between RMS voltage and peak voltage is derived from the mathematical properties of sine waves.

For a pure sine wave, the RMS voltage is calculated as the peak voltage divided by the square root of two. This relationship can be expressed mathematically as:

RMS Voltage = Peak Voltage / √2

By rearranging this equation, you find that:

Peak Voltage = RMS Voltage × √2

Since the square root of two is approximately 1.414, it becomes clear that the peak voltage is equal to the RMS voltage multiplied by the factor of 1.414. Therefore, this factor converts the RMS value to the corresponding peak value in a sine wave context, making it the correct choice.

Using this understanding, one can also observe how the other factors do not accurately describe the relationship between peak voltage and RMS voltage according to the sine wave properties.