NEIEP Electrical Theory And Application (430) Practice Exam

How do you compute the RMS value of a sine-wave voltage from its peak value?

V_rms = V_peak / √2 V_rms = V_peak V_rms = √2 V_peak V_rms = V_peak / 2

Correct Answer:

V_rms = V_peak / √2

Explanation:

For a sine wave, the RMS value is the peak value divided by the square root of 2. If the instantaneous voltage is v(t) = Vp sin(ωt), squaring gives v(t)^2 = Vp^2 sin^2(ωt). The average value of sin^2 over a full cycle is 1/2, so the average of v(t)^2 is Vp^2/2. Taking the square root yields Vrms = sqrt(Vp^2/2) = Vp / √2. This means the RMS voltage is about 0.707 times the peak voltage. So the correct relationship is Vrms = Vpeak / √2. The other options don’t fit because they either equate RMS to the peak (which ignores the averaging of the squared value), multiply by √2 (which would give a value larger than the peak), or divide by 2 (which is not the proper factor after taking the square root).

Access more questions from this quiz

Continue to NEIEP Electrical Theory and Application (430) Practice Exam for more practice questions and the full quiz experience.

Access More Questions