A DC voltage has an average value of 68 V. What is the rMS value?
The correct answer and explanation is :
If a DC voltage has an average value of 68 V, then its RMS (Root Mean Square) value is also 68 V.
Correct Answer: 68 V
Explanation (Approx. 300 words)
The Root Mean Square (RMS) value of a voltage or current is a measure of its effective value—essentially, how much work it can do or how much power it can deliver. It is most commonly used in AC (alternating current) systems where the voltage or current is continuously varying with time. For a time-varying waveform like a sine wave, the RMS value is less than the peak value and gives an equivalent value of DC that would produce the same heating effect in a resistor.
In contrast, a DC (direct current) voltage is constant over time. That means there are no fluctuations—it’s a steady, unchanging value. Since there are no variations, the instantaneous value is always equal to the average value.
Now, the RMS value is defined as:
$$
V_{\text{RMS}} = \sqrt{\frac{1}{T} \int_0^T v(t)^2 dt}
$$
But if the voltage is a constant DC value, $v(t) = V_{\text{DC}}$ for all time $t$. Substituting this into the formula:
$$
V_{\text{RMS}} = \sqrt{\frac{1}{T} \int_0^T V_{\text{DC}}^2 dt} = \sqrt{V_{\text{DC}}^2} = V_{\text{DC}}
$$
So for any constant DC voltage, the RMS value is equal to the DC value itself. Therefore, if the average value of the DC voltage is 68 V, this is also the RMS value.
This contrasts with AC voltages, where the average value over a full cycle is typically zero, and the RMS value is calculated based on the waveform’s shape.
Summary
- Given: Average (DC) voltage = 68 V
- Since DC is constant, RMS = Average = 68 V
- Answer: 68 V