1 Answer
The **RMS (Root Mean Square)** value of an AC (Alternating Current) signal is a measure of its equivalent DC value that would produce the same amount of heat or power in a resistor. It helps us compare AC signals with DC in terms of energy delivery.
For a sinusoidal AC signal, the RMS value is calculated using the following formula:
\[
\text{RMS value} = \frac{I_{\text{peak}}}{\sqrt{2}}
\]
Where:
- \(I_{\text{peak}}\) is the peak value of the AC current.
In simpler terms, the RMS value is the "effective" value of an AC signal. For sinusoidal AC, the RMS voltage or current gives you the same power as a DC source of the same value. It is usually about **0.707** times the peak value for sinusoidal waveforms.
For general AC waveforms, the RMS value is calculated by squaring the instantaneous values, finding their average, and then taking the square root of that average.
If the waveform is **not sinusoidal**, you'd need to use the formula:
\[
\text{RMS value} = \sqrt{\frac{1}{T} \int_0^T v^2(t) \, dt}
\]
Where \(v(t)\) is the instantaneous voltage and \(T\) is the period of the waveform.
In summary, the RMS value tells you how much power an AC signal would deliver, just like a DC signal of the same value.
For a sinusoidal AC signal, the RMS value is calculated using the following formula:
\[
\text{RMS value} = \frac{I_{\text{peak}}}{\sqrt{2}}
\]
Where:
- \(I_{\text{peak}}\) is the peak value of the AC current.
In simpler terms, the RMS value is the "effective" value of an AC signal. For sinusoidal AC, the RMS voltage or current gives you the same power as a DC source of the same value. It is usually about **0.707** times the peak value for sinusoidal waveforms.
For general AC waveforms, the RMS value is calculated by squaring the instantaneous values, finding their average, and then taking the square root of that average.
If the waveform is **not sinusoidal**, you'd need to use the formula:
\[
\text{RMS value} = \sqrt{\frac{1}{T} \int_0^T v^2(t) \, dt}
\]
Where \(v(t)\) is the instantaneous voltage and \(T\) is the period of the waveform.
In summary, the RMS value tells you how much power an AC signal would deliver, just like a DC signal of the same value.