What is the RMS voltage of a sine wave with a value of 17 volts peak?
The correct answer is B: 12 volts. The RMS voltage of a sine wave with a value of 17 volts peak is 12 volts. Vrms = Vpeak/√2 = 17/1.414 = 12.02V ≈ 12V. For amateur radio operators, this is a basic AC voltage calculation. Understanding this helps when working with AC voltages.
Exam Tip
RMS from peak: Vrms = Vpeak/√2 = 17/1.414 = 12V. Think 'R'MS = 'R'eal 'M'easured = 'P'eak/√2. RMS voltage is peak divided by √2. Not peak/2 (8.5V), not peak (17V), not 2×peak (34V) - just peak/√2 (12V).
Memory Aid
"RMS from peak: Vrms = Vpeak/√2 = 17/1.414 = 12V. Think 'R'MS = 'R'eal 'M'easured = 'P'eak/√2. RMS voltage is peak divided by √2. Standard AC voltage conversion."
Real-World Application
A sine wave has 17 volts peak. RMS voltage = 17/√2 = 17/1.414 = 12.02 volts ≈ 12 volts. RMS is the equivalent DC voltage for power calculations. This is the RMS voltage of a 17V peak sine wave.
Key Concepts
Why Other Options Are Wrong
Option A (8.5 volts): Incorrect. 8.5 volts is half the peak (Vpeak/2), not RMS. RMS = Vpeak/√2, not Vpeak/2.
Option C (24 volts): Incorrect. 24 volts is too high - that would be if RMS = peak, but RMS is less than peak. Calculation error.
Option D (34 volts): Incorrect. 34 volts is 2× peak, not RMS. RMS is less than peak, not more.
题目解析
The correct answer is B: 12 volts. The RMS voltage of a sine wave with a value of 17 volts peak is 12 volts. Vrms = Vpeak/√2 = 17/1.414 = 12.02V ≈ 12V. For amateur radio operators, this is a basic AC voltage calculation. Understanding this helps when working with AC voltages.
考试技巧
RMS from peak: Vrms = Vpeak/√2 = 17/1.414 = 12V. Think 'R'MS = 'R'eal 'M'easured = 'P'eak/√2. RMS voltage is peak divided by √2. Not peak/2 (8.5V), not peak (17V), not 2×peak (34V) - just peak/√2 (12V).
记忆口诀
RMS from peak: Vrms = Vpeak/√2 = 17/1.414 = 12V. Think 'R'MS = 'R'eal 'M'easured = 'P'eak/√2. RMS voltage is peak divided by √2. Standard AC voltage conversion.
实际应用示例
A sine wave has 17 volts peak. RMS voltage = 17/√2 = 17/1.414 = 12.02 volts ≈ 12 volts. RMS is the equivalent DC voltage for power calculations. This is the RMS voltage of a 17V peak sine wave.
错误选项分析
Option A (8.5 volts): Incorrect. 8.5 volts is half the peak (Vpeak/2), not RMS. RMS = Vpeak/√2, not Vpeak/2. Option C (24 volts): Incorrect. 24 volts is too high - that would be if RMS = peak, but RMS is less than peak. Calculation error. Option D (34 volts): Incorrect. 34 volts is 2× peak, not RMS. RMS is less than peak, not more.
知识点
RMS voltage, Peak voltage, Sine wave, Voltage conversion
Verified Content
Question from official FCC General Class question pool. Explanation reviewed by licensed amateur radio operators.