What is the RMS voltage of a sine wave equal to?

What is the RMS voltage of a sine wave equal to?

• A. Peak voltage
• B. Peak to peak voltage
• C. Effective voltage
• D. Square root of 2

Answer: (C)

The RMS voltage, or Root Mean Square voltage, of a sine wave is indeed equal to what is termed the effective voltage. This value provides a way to express the average power delivered by an AC signal as compared to DC voltage. It is particularly important in HVAC applications where the voltage supplied to equipment determines the effective power that these devices can use. RMS voltage is calculated by taking the square of the instantaneous voltage over one full cycle, averaging those values, and then taking the square root of that average. For a pure sine wave, the RMS voltage is approximately 0.707 times the peak voltage. This relationship reflects the effective capability of AC voltage to do work, similar to how a DC voltage would perform. In contrast, peak voltage refers to the maximum positive or negative value of the sine wave, while peak-to-peak voltage is the total voltage difference between the highest and lowest points of the wave. The square root of 2 is a mathematical constant often cited in calculations related to converting peak values to RMS values, but it is not itself a representation of RMS voltage. Therefore, the characterization of RMS as effective voltage is the most accurate and relevant for understanding its practical applications in electrical engineering, including HVAC systems.

The RMS voltage, or Root Mean Square voltage, of a sine wave is indeed equal to what is termed the effective voltage. This value provides a way to express the average power delivered by an AC signal as compared to DC voltage. It is particularly important in HVAC applications where the voltage supplied to equipment determines the effective power that these devices can use.

RMS voltage is calculated by taking the square of the instantaneous voltage over one full cycle, averaging those values, and then taking the square root of that average. For a pure sine wave, the RMS voltage is approximately 0.707 times the peak voltage. This relationship reflects the effective capability of AC voltage to do work, similar to how a DC voltage would perform.

In contrast, peak voltage refers to the maximum positive or negative value of the sine wave, while peak-to-peak voltage is the total voltage difference between the highest and lowest points of the wave. The square root of 2 is a mathematical constant often cited in calculations related to converting peak values to RMS values, but it is not itself a representation of RMS voltage. Therefore, the characterization of RMS as effective voltage is the most accurate and relevant for understanding its practical applications in electrical engineering, including HVAC systems.