Question 3-12B4

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.