Solving Physics Integral: V^2_\textrm{rms}

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Homework Help Overview

The discussion revolves around the calculation of the root mean square (rms) voltage, specifically focusing on the formula for \( V^2_\textrm{rms} \) involving an integral of a sine function squared over a period \( T \). Participants are attempting to derive a sensible answer from the given expression.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to evaluate the integral but encounters difficulties leading to incorrect results. Some participants suggest clarifying the expression under the integral sign and offer trigonometric identities to aid in the solution.

Discussion Status

Participants are actively engaging with the problem, with some providing guidance on mathematical techniques and identities that may assist in solving the integral. However, there is no clear consensus on the correct approach or solution as further clarification and attempts are ongoing.

Contextual Notes

There appears to be confusion regarding the proper setup of the integral and the application of trigonometric identities. The original poster has acknowledged an error in their initial formulation but continues to seek a resolution.

tmc
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I have this formula, and I just can't seem to be able to find any sensible answer:

[tex]V^2_\textrm{rms}=\frac{1}{T}\int_{0}^{T}V^2_0sin^2(2ft\pi)dt[/tex]

Depending on what I do, I either get an obviously wrong answer, 0, or [tex]V_0[/tex].
 
Last edited:
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The stuff under the integral sign needs to be squared. This is the S part of rms.

Regards,
George
 
yeah, my bad. Edited it.
Still don't get how to solve it though.
 
Use [itex]cos(2\theta) = 1 - 2sin^2 (\theta)[/itex] and [itex]f = 1/T[/itex].

Regards,
George
 

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