For a sinusoidal signal, what is the relation between V_peak and V_rms?

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Multiple Choice

For a sinusoidal signal, what is the relation between V_peak and V_rms?

Explanation:
For a sinusoidal signal, the RMS value is the peak value divided by sqrt(2). If you write the signal as v(t) = V_peak sin(ωt), squaring and averaging over a full cycle gives the mean of v^2 as V_peak^2/2. The RMS is the square root of that, so V_rms = V_peak / sqrt(2). Solving for the peak in terms of RMS yields V_peak = sqrt(2) × V_rms. This is the standard relationship for a pure sine wave. The other options don’t fit this relationship: V_peak = V_rms would imply the RMS equals the peak, which isn’t true for a sine; V_peak = V_rms / sqrt(2) would invert the correct relation; and V_pp = 2 V_peak is true for peak-to-peak, but it doesn’t express the V_peak–V_rms link.

For a sinusoidal signal, the RMS value is the peak value divided by sqrt(2). If you write the signal as v(t) = V_peak sin(ωt), squaring and averaging over a full cycle gives the mean of v^2 as V_peak^2/2. The RMS is the square root of that, so V_rms = V_peak / sqrt(2). Solving for the peak in terms of RMS yields V_peak = sqrt(2) × V_rms. This is the standard relationship for a pure sine wave.

The other options don’t fit this relationship: V_peak = V_rms would imply the RMS equals the peak, which isn’t true for a sine; V_peak = V_rms / sqrt(2) would invert the correct relation; and V_pp = 2 V_peak is true for peak-to-peak, but it doesn’t express the V_peak–V_rms link.

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