Home » Computer Science » Electronic Principles

A sinusoidal voltage source has a peak (maximum) value of 50 V. What is the corresponding rms (root-mean-square) voltage for this sine wave?

Difficulty: Easy

37.4 V
35.4 V
38.74 V
30.4 V
None of the above

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:

Peak value Vp = 50 V.
Pure sinusoid (no distortion).
Standard rms definition for sine waves.

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.

A sinusoidal voltage source has a peak (maximum) value of 50 V. What is the corresponding rms (root-mean-square) voltage for this sine wave?

More Questions from Electronic Principles

Discussion & Comments