What is the relationship between RMS voltage and peak voltage for a sine wave?

What is the relationship between RMS voltage and peak voltage for a sine wave?

• A. RMS voltage is always higher than peak voltage
• B. RMS voltage equals peak voltage
• C. Peak voltage is 1.414 times the RMS voltage
• D. RMS voltage is double the peak voltage

Answer: (C)

The correct understanding of the relationship between RMS voltage and peak voltage for a sine wave is that peak voltage is approximately 1.414 times the RMS voltage. This relationship stems from the mathematical properties of sinusoidal waveforms. In a sine wave, the peak voltage is the maximum voltage level that the waveform reaches, while the RMS (Root Mean Square) voltage represents the effective voltage of that waveform, which is useful for comparing the power delivery of AC and DC sources. The RMS value is calculated as the square root of the mean of the squares of all instantaneous values over one complete cycle. For a sine wave, the RMS voltage is obtained by taking the peak voltage and dividing it by the square root of 2, i.e., RMS = Peak Voltage / √2. Therefore, when rearranged, the peak voltage can be expressed as Peak Voltage = RMS × √2, which numerically is approximately 1.414 times the RMS voltage. This ratio is fundamental in AC circuit analysis, allowing engineers to convert between peak and RMS values to correctly calculate power and other electrical parameters in sinusoidal systems.

The correct understanding of the relationship between RMS voltage and peak voltage for a sine wave is that peak voltage is approximately 1.414 times the RMS voltage. This relationship stems from the mathematical properties of sinusoidal waveforms.

In a sine wave, the peak voltage is the maximum voltage level that the waveform reaches, while the RMS (Root Mean Square) voltage represents the effective voltage of that waveform, which is useful for comparing the power delivery of AC and DC sources. The RMS value is calculated as the square root of the mean of the squares of all instantaneous values over one complete cycle.

For a sine wave, the RMS voltage is obtained by taking the peak voltage and dividing it by the square root of 2, i.e., RMS = Peak Voltage / √2. Therefore, when rearranged, the peak voltage can be expressed as Peak Voltage = RMS × √2, which numerically is approximately 1.414 times the RMS voltage.

This ratio is fundamental in AC circuit analysis, allowing engineers to convert between peak and RMS values to correctly calculate power and other electrical parameters in sinusoidal systems.