1 Answer
The formula for alternating current (AC) typically refers to the general mathematical expression for an AC waveform. The most common form of AC is a sinusoidal waveform, which is represented by:
\[
I(t) = I_{\text{max}} \sin(\omega t + \phi)
\]
Where:
- \(I(t)\) is the instantaneous current at time \(t\),
- \(I_{\text{max}}\) is the maximum (peak) current (also called the amplitude),
- \(\omega\) is the angular frequency of the wave, which is related to the frequency \(f\) by \(\omega = 2\pi f\),
- \(t\) is the time,
- \(\phi\) is the phase angle, which represents a horizontal shift of the wave.
For voltage, it would be similar:
\[
V(t) = V_{\text{max}} \sin(\omega t + \phi)
\]
Where \(V_{\text{max}}\) is the maximum (peak) voltage.
In the context of AC power systems, we often use the **root mean square (RMS)** values for current and voltage, because they give us the equivalent DC values that would produce the same amount of heat. For a sinusoidal AC signal, the RMS values are related to the peak values by:
\[
I_{\text{rms}} = \frac{I_{\text{max}}}{\sqrt{2}}
\]
\[
V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}
\]
RMS values are used for practical purposes because they provide the effective power used by devices.
\[
I(t) = I_{\text{max}} \sin(\omega t + \phi)
\]
Where:
- \(I(t)\) is the instantaneous current at time \(t\),
- \(I_{\text{max}}\) is the maximum (peak) current (also called the amplitude),
- \(\omega\) is the angular frequency of the wave, which is related to the frequency \(f\) by \(\omega = 2\pi f\),
- \(t\) is the time,
- \(\phi\) is the phase angle, which represents a horizontal shift of the wave.
For voltage, it would be similar:
\[
V(t) = V_{\text{max}} \sin(\omega t + \phi)
\]
Where \(V_{\text{max}}\) is the maximum (peak) voltage.
In the context of AC power systems, we often use the **root mean square (RMS)** values for current and voltage, because they give us the equivalent DC values that would produce the same amount of heat. For a sinusoidal AC signal, the RMS values are related to the peak values by:
\[
I_{\text{rms}} = \frac{I_{\text{max}}}{\sqrt{2}}
\]
\[
V_{\text{rms}} = \frac{V_{\text{max}}}{\sqrt{2}}
\]
RMS values are used for practical purposes because they provide the effective power used by devices.