Calculating Vrms: Homework Equations & Solutions Explained

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    Rms Voltage
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SUMMARY

The discussion centers on calculating the root mean square voltage (Vrms) for a given voltage function, specifically V(t) = 20 + 60cos(100t). The user initially applies the formula V_{rms} = √(1/T ∫_T v² dt) but arrives at an incorrect result of approximately 79.88 V. The correct calculation, as per the solution manual, simplifies to Vrms = √(20² + (60²/2)), yielding approximately 46.9 V. The discrepancy arises from the integration method used by the user, which does not align with the manual's approach.

PREREQUISITES
  • Understanding of root mean square (RMS) calculations
  • Familiarity with trigonometric functions and their properties
  • Basic knowledge of calculus, specifically integration
  • Experience with voltage functions in electrical engineering
NEXT STEPS
  • Review the derivation of the RMS voltage formula in electrical engineering contexts
  • Study integration techniques for periodic functions
  • Explore the implications of RMS values in AC circuit analysis
  • Learn about the differences between average and RMS voltage calculations
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Students in electrical engineering, physics enthusiasts, and anyone seeking to understand voltage calculations and their applications in AC circuits.

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Homework Statement



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Homework Equations



The Attempt at a Solution


[/B]
Shouldn't I use V_{rms} = \sqrt{\frac{1}{T}\int_T v^2 dt}?

Which would be

\sqrt{\frac{100}{2\pi}\int_0^{2\pi/100}(20+60cos(100t))^2dt}

This equals \approx 79.88 V

The answer is given as \approx 46.9V and the solution manual shows the following working

\sqrt{20^2 + \frac{60^2}{2}}

Why do they apply that solution and not the one I used?
 
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You might want to check your integration. I find that the integral matches the manual's result.
 
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