Difficulty: Easy
Correct Answer: 35.4 V
Explanation:
Introduction / Context:Rms (root-mean-square) voltage is the effective value of a time-varying voltage, equating a sinusoidal source to a dc level that would deliver the same average power into a resistive load. Converting between peak and rms is a routine AC analysis task.
Given Data / Assumptions:
Concept / Approach:For a sinusoid, Vrms = Vp / sqrt(2). This comes from integrating the square of a sine wave over a full period and taking the square root of the mean.
Step-by-Step Solution:
1) Use Vrms = Vp / sqrt(2).2) Substitute Vp = 50 V.3) Vrms = 50 / 1.4142 ≈ 35.36 V.4) Rounded to one decimal place, Vrms ≈ 35.4 V.Verification / Alternative check:Another common identity is Vp ≈ 1.414 * Vrms; solving gives Vrms ≈ 50 / 1.414 ≈ 35.4 V, confirming the result.
Why Other Options Are Wrong:
37.4 V or 38.74 V: Not consistent with division by sqrt(2).30.4 V: Too low; implies an incorrect conversion factor.None of the above: Incorrect because 35.4 V is correct.Common Pitfalls:Confusing rms with average or peak-to-peak values; using 2 instead of sqrt(2) as the divisor is a frequent error.
Final Answer:35.4 V.
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