Deep Dive: G5B08
The correct answer is D: 339.4 volts. The peak-to-peak voltage of a sine wave with an RMS voltage of 120 volts is 339.4 volts. Vpeak = Vrms × √2 = 120 × 1.414 = 169.7V. Vpeak-to-peak = 2 × Vpeak = 2 × 169.7 = 339.4V. For amateur radio operators, this is a basic AC voltage calculation. Understanding this helps when working with AC voltages.
Why Other Answers Are Wrong
Option A (84.8 volts): Incorrect. 84.8 volts is too low - that's about Vrms/√2, not peak-to-peak. Calculation error. Option B (169.7 volts): Incorrect. 169.7 volts is the peak voltage, not peak-to-peak. Peak-to-peak is 2× peak = 339.4V. Option C (240.0 volts): Incorrect. 240.0 volts is 2× RMS, not peak-to-peak. Peak-to-peak is 2× peak = 2× (RMS×√2) = 339.4V.
Exam Tip
Peak-to-peak from RMS: Vpeak = Vrms × √2 = 120 × 1.414 = 169.7V, Vpp = 2 × Vpeak = 339.4V. Think 'P'eak-to-'P'eak = '2' × 'P'eak = '2' × ('R'MS × √2). Not 84.8V, not 169.7V (peak), not 240V (2×RMS) - just 339.4V.
Memory Aid
Peak-to-peak from RMS: Vpp = 2 × Vpeak = 2 × (Vrms × √2) = 339.4V. Think 'P'eak-to-'P'eak = '2' × 'P'eak. For 120V RMS: Vpp = 339.4V. Standard AC voltage conversion.
Real-World Example
A sine wave has 120 volts RMS. Peak voltage = 120 × √2 = 120 × 1.414 = 169.7 volts. Peak-to-peak voltage = 2 × 169.7 = 339.4 volts. This is the peak-to-peak voltage of a 120V RMS sine wave.
Source & Coverage
Question Pool: 2023-2027 Question Pool
Subelement: G5B
Reference: 2023-2027 Question Pool · G5 - Electrical Principles
Key Concepts
Verified Content
Question from the official FCC General Class pool. Explanation reviewed by licensed amateur radio operators and mapped to the G5B topic.