In AC circuits, RMS value is defined as

In AC circuits, RMS value is defined as

• A. RMS value is the peak value.
• B. RMS value is the DC equivalent that would produce the same heating effect in a resistor.
• C. RMS value is the average value.
• D. RMS value is the instantaneous value at the peak of the cycle.

Answer: (B)

RMS value represents the DC level that would produce the same heating effect in a resistor. Since power in a resistor is proportional to the square of the voltage (P = V^2/R), the varying AC voltage over a cycle can be replaced by a constant DC voltage whose square gives the same average power. That constant value is the RMS value. For a sinusoidal voltage, the RMS value equals the peak (maximum) voltage divided by the square root of 2, so a 10 V peak has an RMS of about 7.07 V. This is why RMS is called the effective or equivalent DC value: it tells you how much heating the AC waveform would cause if it were a steady DC voltage. The other notions—the peak value, the average value, or the instantaneous value at the peak—do not reflect the overall heating effect over time. The peak is just the highest momentary value, not the average power. The average value over a cycle doesn’t correspond to the power, since power depends on the square of the voltage. And the instantaneous peak is just a single point in time, not a measure of the waveform’s overall heating effect.

RMS value represents the DC level that would produce the same heating effect in a resistor. Since power in a resistor is proportional to the square of the voltage (P = V^2/R), the varying AC voltage over a cycle can be replaced by a constant DC voltage whose square gives the same average power. That constant value is the RMS value.

For a sinusoidal voltage, the RMS value equals the peak (maximum) voltage divided by the square root of 2, so a 10 V peak has an RMS of about 7.07 V. This is why RMS is called the effective or equivalent DC value: it tells you how much heating the AC waveform would cause if it were a steady DC voltage.

The other notions—the peak value, the average value, or the instantaneous value at the peak—do not reflect the overall heating effect over time. The peak is just the highest momentary value, not the average power. The average value over a cycle doesn’t correspond to the power, since power depends on the square of the voltage. And the instantaneous peak is just a single point in time, not a measure of the waveform’s overall heating effect.