SQRT1_2.CONST

Application:

Root Mean Square (RMS) Voltage

In AC circuits, the voltage and current are constantly changing over time. When we talk about "120V AC" from a wall outlet, we're not talking about the peak voltage. We're talking about the Root Mean Square (RMS) voltage, which represents the equivalent DC voltage that would deliver the same amount of power.

For a sinusoidal AC waveform, the relationship between the peak voltage (Vpeak​) and the RMS voltage (VRMS​) is given by:

$V_{\text{RMS}}=\frac{V_{\text{peak}}}{\sqrt{2}}$

This is where the value $1/\sqrt{2}$ comes into play directly.

Example Scenario:

Imagine you have a device that runs on a standard North American wall outlet, which is rated at 120V AC. The 120V is the RMS voltage. You want to know the maximum (peak) voltage that the device's components will experience, as this is critical for selecting capacitors and other components that can handle the stress.

You can use the formula to find the peak voltage:

$V_{\text{peak}}=V_{\text{RMS}}\times \sqrt{2}$

Let's also consider another common voltage in Europe, which is 230V AC RMS.

Application and Table:

We can create a table that shows how to calculate the peak voltage for different RMS voltages using the constant $1/\sqrt{2}$​. The constant is used to find the RMS from the peak, and its reciprocal ($\sqrt{2}$​) is used to find the peak from the RMS.