In a sinusoidal AC signal, the peak value is equal to what multiple of the RMS value?

In a sinusoidal AC signal, the peak value is equal to what multiple of the RMS value?

• A. RMS value
• B. RMS value times 0.5
• C. RMS value times 2
• D. RMS value times sqrt(2)

Answer: (D)

For a sinusoidal AC signal, the RMS value is the effective DC value that would deliver the same power as the AC. For a sine wave, the relationship between peak value and RMS is Vrms = Vp/√2. This comes from v(t) = Vp sin(ωt) and averaging v^2 over a full cycle: the average of sin^2 is 1/2, so Vrms^2 = Vp^2/2, giving Vrms = Vp/√2. Rearranging gives Vp = Vrms · √2. So the peak value is the RMS value times √2. The other options don’t match because they would imply the peak is equal to the RMS, half of it, twice it, or a different factor, none of which aligns with the actual sine-wave relationship.

For a sinusoidal AC signal, the RMS value is the effective DC value that would deliver the same power as the AC. For a sine wave, the relationship between peak value and RMS is Vrms = Vp/√2. This comes from v(t) = Vp sin(ωt) and averaging v^2 over a full cycle: the average of sin^2 is 1/2, so Vrms^2 = Vp^2/2, giving Vrms = Vp/√2. Rearranging gives Vp = Vrms · √2. So the peak value is the RMS value times √2. The other options don’t match because they would imply the peak is equal to the RMS, half of it, twice it, or a different factor, none of which aligns with the actual sine-wave relationship.