For a sinusoidal voltage with RMS value V_rms, the peak value is approximately which factor of V_rms?

For a sinusoidal voltage with RMS value V_rms, the peak value is approximately which factor of V_rms?

• A. 0.707 × V_rms
• B. V_rms
• C. 2 × V_rms
• D. 1.414 × V_rms

Answer: (D)

For a sinusoidal voltage, the peak value is related to the RMS value by the factor √2. A sine wave can be written as v(t) = V_peak sin(ωt). The RMS value is defined as the root mean square of the instantaneous voltage, and for a sine, the average of sin^2 is 1/2, giving V_rms^2 = V_peak^2 / 2. Solving for V_peak gives V_peak = √2 × V_rms. Numerically, √2 ≈ 1.414, so the peak value is about 1.414 times V_rms. That matches the option 1.414 × V_rms.

For a sinusoidal voltage, the peak value is related to the RMS value by the factor √2. A sine wave can be written as v(t) = V_peak sin(ωt). The RMS value is defined as the root mean square of the instantaneous voltage, and for a sine, the average of sin^2 is 1/2, giving V_rms^2 = V_peak^2 / 2. Solving for V_peak gives V_peak = √2 × V_rms. Numerically, √2 ≈ 1.414, so the peak value is about 1.414 times V_rms. That matches the option 1.414 × V_rms.