The effective value of a waveform is equal to the peak value multiplied by which factor?

The effective value of a waveform, particularly when dealing with alternating current (AC), is commonly referred to as the root mean square (RMS) value. For a sinusoidal waveform, the RMS value is indeed calculated by multiplying the peak value by the factor of approximately 0.707. This relationship arises from the mathematical derivation of the RMS value, which takes into account the shape of the waveform.

In the case of a sinusoidal waveform, the peak value represents the maximum voltage or current in the waveform. The RMS value provides a measure of the equivalent direct current (DC) that would deliver the same power to a load. The factor of 0.707 comes from the formula RMS = Peak Value × 1/√2, which numerically evaluates to approximately 0.707.

This specific relationship is critical in electrical engineering and practice because it allows engineers and electricians to convert between peak and effective values, ensuring accurate calculations for circuit design and analysis. Understanding this factor aids in properly sizing circuit components and ensuring reliable operation of electrical systems that operate on AC.