What value of an AC signal produces the same power dissipation in a resistor as a DC voltage of the same value?
The correct answer is C: The RMS value. The value of an AC signal that produces the same power dissipation in a resistor as a DC voltage of the same value is the RMS value. RMS (Root Mean Square) voltage is the equivalent DC voltage that produces the same heating effect. For amateur radio operators, this is why RMS is used for power calculations. Understanding this helps when working with AC power.
Exam Tip
AC equivalent to DC for power = RMS value. Think 'R'MS = 'R'eal 'M'easured 'S'trength (equivalent DC). RMS voltage produces same power dissipation as DC voltage of same value. Not peak-to-peak, not peak, not reciprocal - just RMS.
Memory Aid
"AC equivalent to DC for power = RMS value. Think 'R'MS = 'R'eal 'M'easured 'S'trength. RMS voltage produces same power dissipation as DC voltage of same value. Standard for AC power calculations."
Real-World Application
120 volts RMS AC produces the same power in a resistor as 120 volts DC. The RMS value is the equivalent DC voltage for power calculations. Peak voltage (170V) would produce more power, but RMS (120V) equals DC (120V) for power dissipation.
Key Concepts
Why Other Options Are Wrong
Option A (Peak-to-peak value): Incorrect. Peak-to-peak value is too high - it's about 2.8 times RMS, so it would produce much more power. Peak-to-peak doesn't equal DC for power.
Option B (Peak value): Incorrect. Peak value is too high - it's about 1.414 times RMS, so it would produce more power. Peak doesn't equal DC for power.
Option D (Reciprocal of RMS): Incorrect. Reciprocal of RMS would be much smaller and produce less power. Reciprocal isn't the equivalent.
题目解析
The correct answer is C: The RMS value. The value of an AC signal that produces the same power dissipation in a resistor as a DC voltage of the same value is the RMS value. RMS (Root Mean Square) voltage is the equivalent DC voltage that produces the same heating effect. For amateur radio operators, this is why RMS is used for power calculations. Understanding this helps when working with AC power.
考试技巧
AC equivalent to DC for power = RMS value. Think 'R'MS = 'R'eal 'M'easured 'S'trength (equivalent DC). RMS voltage produces same power dissipation as DC voltage of same value. Not peak-to-peak, not peak, not reciprocal - just RMS.
记忆口诀
AC equivalent to DC for power = RMS value. Think 'R'MS = 'R'eal 'M'easured 'S'trength. RMS voltage produces same power dissipation as DC voltage of same value. Standard for AC power calculations.
实际应用示例
120 volts RMS AC produces the same power in a resistor as 120 volts DC. The RMS value is the equivalent DC voltage for power calculations. Peak voltage (170V) would produce more power, but RMS (120V) equals DC (120V) for power dissipation.
错误选项分析
Option A (Peak-to-peak value): Incorrect. Peak-to-peak value is too high - it's about 2.8 times RMS, so it would produce much more power. Peak-to-peak doesn't equal DC for power. Option B (Peak value): Incorrect. Peak value is too high - it's about 1.414 times RMS, so it would produce more power. Peak doesn't equal DC for power. Option D (Reciprocal of RMS): Incorrect. Reciprocal of RMS would be much smaller and produce less power. Reciprocal isn't the equivalent.
知识点
RMS value, AC signal, Power dissipation, Equivalent DC
Verified Content
Question from official FCC General Class question pool. Explanation reviewed by licensed amateur radio operators.