Which formula defines the root-mean-square (Vrms) value in terms of Vmax?

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Prepare for the Michelin ECT Exam. Study with comprehensive flashcards and multiple choice questions, each with detailed hints and explanations. Get ready to excel in your exam!

Multiple Choice

Which formula defines the root-mean-square (Vrms) value in terms of Vmax?

Explanation:
For a sinewave, the root-mean-square value is the peak value divided by the square root of 2. If v(t) = Vmax sin(ωt), then Vrms^2 = (1/T) ∫ v(t)^2 dt over a full cycle, which evaluates to Vmax^2/2. Taking the square root gives Vrms = Vmax/√2, which is about 0.7071 times Vmax. Expressing this as Vrms = Vmax × 0.707 captures that relationship. The form with 0.5 would be incorrect for a sinewave, since it would imply Vrms = Vmax/2, not Vmax/√2. Vrms = Vmax would only apply to a constant (DC) value, not a varying sine.

For a sinewave, the root-mean-square value is the peak value divided by the square root of 2. If v(t) = Vmax sin(ωt), then Vrms^2 = (1/T) ∫ v(t)^2 dt over a full cycle, which evaluates to Vmax^2/2. Taking the square root gives Vrms = Vmax/√2, which is about 0.7071 times Vmax. Expressing this as Vrms = Vmax × 0.707 captures that relationship. The form with 0.5 would be incorrect for a sinewave, since it would imply Vrms = Vmax/2, not Vmax/√2. Vrms = Vmax would only apply to a constant (DC) value, not a varying sine.

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