In an AC circuit, the effective (RMS) voltage is

In an AC circuit, the effective (RMS) voltage is

• A. Less than the maximum instantaneous voltage
• B. Greater than the maximum instantaneous voltage
• C. Equal to the maximum instantaneous voltage
• D. Twice the maximum instantaneous voltage

Answer: (A)

The main idea here is how RMS relates to the peak value for an AC waveform. RMS (root-mean-square) is the value that would produce the same heating effect in a resistor as a DC voltage. For a pure sinusoidal voltage, v(t) = Vpeak sin(ωt), if you square it and average over a full cycle, you get an average of Vpeak^2/2. Taking the square root gives Vrms = Vpeak/√2, which is about 0.707 times the peak value. So the effective voltage is smaller than the maximum instantaneous voltage that occurs at the peak of the sine wave. It’s not equal to the peak, not greater than it, and not twice it. This is why the correct statement is that the RMS voltage is less than the maximum instantaneous voltage.

The main idea here is how RMS relates to the peak value for an AC waveform. RMS (root-mean-square) is the value that would produce the same heating effect in a resistor as a DC voltage. For a pure sinusoidal voltage, v(t) = Vpeak sin(ωt), if you square it and average over a full cycle, you get an average of Vpeak^2/2. Taking the square root gives Vrms = Vpeak/√2, which is about 0.707 times the peak value. So the effective voltage is smaller than the maximum instantaneous voltage that occurs at the peak of the sine wave. It’s not equal to the peak, not greater than it, and not twice it. This is why the correct statement is that the RMS voltage is less than the maximum instantaneous voltage.