How is the effective value of a sine wave calculated?

The effective value, also known as the root mean square (RMS) value, of a sine wave is calculated using a specific relationship to its peak value. For a pure sine wave, the RMS value is derived from the peak value by multiplying it by approximately 0.707. This factor comes from the mathematical integration of the sine function over one complete cycle, which essentially averages out the square of the sine function.

This calculation is significant in electrical engineering because it allows for the comparison of AC (alternating current) and DC (direct current) values in terms of power. The RMS value represents the effective voltage or current that would deliver the same power to a resistive load as a corresponding DC voltage or current.

The other options do not provide the correct relationship needed to derive the effective value of a sine wave. The first two choices suggest adjustments involving addition or multiplication by 0.5, which do not reflect the mathematical principles related to sine waves. The final option, dividing by 0.707, would yield an incorrect result that does not adhere to the established formula for finding the RMS of a sine wave. Thus, multiplying the peak value by 0.707 is the correct method for calculating the effective value of a sine wave.