RMS-to-peak-to-peak conversion (sine wave): What is the peak-to-peak voltage of a sinusoidal AC waveform whose RMS value is 56 V?

Introduction:
Converting between RMS, peak, and peak-to-peak values is essential for power calculations, component voltage ratings, and oscilloscope interpretation. For a pure sine wave, fixed ratios relate these quantities.

Given Data / Assumptions:

• Sine wave with Vrms = 56 V.
• Standard sine relationships apply.
• No distortion or DC offset.

Concept / Approach:

For a sine wave: Vrms = Vp / √2, so Vp = Vrms * √2. Peak-to-peak is Vpp = 2 * Vp. Compute Vp, then double it to obtain Vpp. Keep sufficient precision for rounding to the nearest integer volt if options are whole numbers.

Step-by-Step Solution:

Verification / Alternative check:

Reverse check: If Vpp = 158 V ⇒ Vp ≈ 79 V, then Vrms ≈ 79 / √2 ≈ 55.9 V, which rounds to 56 V, confirming consistency.

Why Other Options Are Wrong:

• 164 V: Would imply Vrms ≈ 58 V; too high.
• 82 V: That is approximately Vp, not Vpp.
• 79 V: Exactly the peak, not peak-to-peak.
• 112 V: Corresponds to 2 * Vrms, not a standard sine relation.

Common Pitfalls:

• Confusing peak with peak-to-peak (factor of 2).
• Applying Vrms = Vavg (true only for DC) or mixing rectified-wave formulas.

Final Answer:

158 V