Question

Certain heavy industrial equipment uses AC power that has a peak voltage of 679 V. What is the rms voltage?

Short answer

The rms voltage is found to be \({\rm{480\;V}}\).

Step-by-step solution

Definition of rms voltage and relation between rms voltage and \({{\rm{V}}_{{\rm{max}}}}\)

The rms voltage in an AC circuit in which the voltage varies sinusoidally is given as-

\({\bf{\Delta }}{{\bf{V}}_{{\bf{rms}}}}{\bf{ = }}\frac{{{\bf{\Delta }}{{\bf{V}}_{{\bf{max}}}}}}{{\sqrt {\bf{2}} }}\)

\({\bf{\Delta }}{{\bf{V}}_{{\bf{rms}}}}{\bf{ = }}\;{\bf{0}}{\bf{.707\Delta }}{{\bf{V}}_{{\bf{max}}}}\)

Where\({\bf{\Delta }}{{\bf{V}}_{{\bf{max}}}}\)is the maximum voltage.

Given data

The maximum voltage of the equipment is: \(\Delta {V_{\max }} = 679\;\;{\rm{V}}\)

Calculation of rms voltage

The rms voltage of the equipment is found by using equation :

\(\Delta {V_{rms}} = \frac{{\Delta {V_{max}}}}{{\sqrt 2 }}\)

Entering the value for\({\rm{\Delta }}{{\rm{V}}_{{\rm{max}}}}\)we obtain:

\(\begin{array}{c}\Delta {V_{rms}} = \frac{{679\;\;{\rm{V}}}}{{\sqrt 2 }}\\ = 480\;\;{\rm{V}}\end{array}\)

Therefore, the value of rms voltage is \({\rm{480\;V}}\).