FCC Exam Question: 3-12B4

What is the equivalent to the root-mean-square value of an AC voltage?

A. AC voltage is the square root of the average AC value.
B. The DC voltage causing the same heating in a given resistor at the peak AC voltage.
C. The AC voltage found by taking the square of the average value of the peak AC voltage.
D. The DC voltage causing the same heating in a given resistor as the RMS AC voltage of the same value.
Correct Answer: D

Explanation: The Root-Mean-Square (RMS) value of an AC voltage is a way to express its effective heating power compared to a DC voltage. **Option D is correct** because the RMS value of an AC voltage is precisely defined as the DC voltage that would dissipate the same amount of power (i.e., cause the same heating) in a given resistive load. This is why household AC voltages are specified as RMS values (e.g., 120V AC RMS) – they produce the same effective power as 120V DC. **Option A is incorrect.** The average value of a symmetrical AC waveform over a full cycle is zero. RMS involves the square root of the average of the *squares* of the instantaneous voltage values, not the average of the voltage itself. **Option B is incorrect.** The RMS value is not the peak AC voltage. For a sine wave, the RMS voltage is approximately 0.707 times the peak voltage ($V_{RMS} = V_{peak} / \sqrt{2}$). Therefore, a DC voltage causing the same heating as the peak AC voltage would be a higher voltage than the RMS equivalent. **Option C is incorrect.** Taking the square of the average value of the peak AC voltage does not yield the RMS value; it's a mathematically incorrect operation in this context.

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Includes Elements 1, 3, 6, 7R, 8, and 9.