How to calculate the .707 value used in rms voltage

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    Rms Value Voltage
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SUMMARY

The .707 value used in the calculation of root mean square (Vrms) voltage for a sine wave is derived from the formula 1 / (√2). This value represents the ratio of the root mean square to the peak voltage (Vp) in AC circuits. To calculate .707, one can integrate the square of the voltage function V(t) over one complete cycle, divide by the cycle duration, and then take the square root of the result. This mathematical approach confirms that .707 is specifically applicable to sine waves.

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  • Understanding of calculus, specifically integration
  • Familiarity with sine wave properties in electrical engineering
  • Knowledge of root mean square (RMS) calculations
  • Basic concepts of alternating current (AC) voltage
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  • Study the integral calculus methods for calculating RMS values
  • Research the properties of sine waves in electrical engineering
  • Learn about the derivation of RMS voltage for different waveforms
  • Explore the implications of RMS voltage in AC circuit analysis
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Electrical engineers, physics students, and anyone involved in AC circuit analysis will benefit from this discussion, particularly those seeking to understand the mathematical foundations of RMS voltage calculations.

scoot15638
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I need help, and can't find anywhere how to calculate the .707 value using calculus. The value used when calculating Vrms =Vp*.707, i need to know how to calculate the .707. Any help would be great, Thanks!

Scott
 
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.707 is for a sine wave only, and you could determine it by taking the integral of V(t)2 over a full cycle, dividing by the time of the cycle, and then taking the square root of the answer (hence the name "root mean square").
 

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