A sine wave has an amplitude of 100 mV peak-to-peak (Vpp). What RMS voltage would a typical true-RMS voltmeter read for this signal?

Introduction:Converting between peak-to-peak, peak, and RMS values is a standard AC measurement task. A correct conversion prevents order-of-magnitude mistakes when reading or specifying instrumentation levels.

Given Data / Assumptions:

• Sine wave with Vpp = 100 mV.
• We seek the RMS value as a voltmeter would report.
• True-RMS behavior assumed for sinusoidal input.

Concept / Approach:For a sine wave: Vpp = 2 * Vp and Vrms = Vp / sqrt(2). Combining, Vrms = Vpp / (2 * sqrt(2)). This formula directly converts peak-to-peak to RMS for sinusoids.

Step-by-Step Solution:1) Compute peak: Vp = Vpp / 2 = 100 mV / 2 = 50 mV.2) Convert to RMS: Vrms = Vp / sqrt(2) = 50 mV / 1.414 ≈ 35.36 mV.3) Round appropriately: ≈ 35.4 mV.4) Select the matching option.

Verification / Alternative check:Use the combined formula: Vrms = 100 mV / (2 * 1.414) = 100 / 2.828 ≈ 35.36 mV, consistent with the step-by-step result.

Why Other Options Are Wrong:14.14 mV: equals 10 mV * sqrt(2); not related to 100 mVpp.63.7 mV and 70.7 mV: correspond to RMS values for much larger peaks; numerically inconsistent with 100 mVpp.

Common Pitfalls:Using Vpp / 2 as RMS or forgetting the sqrt(2) factor; both errors overstate the RMS value by 1.414×.

Final Answer:35.4 mV