Which statement is true about RMS values for sine waves?

Which statement is true about RMS values for sine waves?

• A. They are less than the peak value
• B. They are equal to the peak value
• C. They are greater than the peak value
• D. They are unrelated to the peak value

Answer: (A)

The RMS value represents the effective voltage that would produce the same heating in a resistor as the actual AC waveform. For a sine wave with peak voltage Vp, the instant value is v(t) = Vp sin(ωt). When you average the square of this over a full cycle, you get Vrms^2 = (1/T) ∫ Vp^2 sin^2(ωt) dt = Vp^2/2, so Vrms = Vp/√2 ≈ 0.707 Vp. This means the RMS value is always smaller than the peak value for a sine wave (about 29% lower). The peak is the maximum instantaneous voltage, while RMS reflects the waveform’s effective power, which is why the statement that RMS values are less than the peak value is true.

The RMS value represents the effective voltage that would produce the same heating in a resistor as the actual AC waveform. For a sine wave with peak voltage Vp, the instant value is v(t) = Vp sin(ωt). When you average the square of this over a full cycle, you get Vrms^2 = (1/T) ∫ Vp^2 sin^2(ωt) dt = Vp^2/2, so Vrms = Vp/√2 ≈ 0.707 Vp. This means the RMS value is always smaller than the peak value for a sine wave (about 29% lower). The peak is the maximum instantaneous voltage, while RMS reflects the waveform’s effective power, which is why the statement that RMS values are less than the peak value is true.