Ratio of effective and average voltage

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SUMMARY

The discussion centers on calculating the ratio of effective voltage ($U_{ef}$) to average voltage ($U_{avg}$) using the formulas $U_{ef}=\frac{U_m}{\sqrt{3}}$ and $U_{avg}=\frac{U_m}{2}$. The correct ratio is derived as $\frac{U_{ef}}{U_{avg}} = \frac{2}{\sqrt{3}} \approx 1.154$. The user initially miscalculated by not properly applying the coefficients for the two different voltage functions, $u=5/3 t$ and $u=-5/4t+35/4$, leading to confusion about the validity of their approach. The error was identified as neglecting to multiply by the necessary factors of $\frac{3}{7}$ and $\frac{4}{7}$, as well as the square roots.

PREREQUISITES
  • Understanding of effective voltage and average voltage concepts
  • Familiarity with trigonometric functions and their applications in electrical engineering
  • Knowledge of voltage equations and their derivations
  • Ability to manipulate and simplify algebraic expressions
NEXT STEPS
  • Study the derivation of effective and average voltage formulas in AC circuits
  • Learn about the application of coefficients in voltage calculations
  • Explore the concept of root mean square (RMS) voltage in electrical engineering
  • Investigate the impact of different waveform shapes on effective and average voltage
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Electrical engineering students, educators, and professionals involved in circuit analysis and voltage calculations will benefit from this discussion.

crom1
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Homework Statement


See the diagram. Find $$\frac{U_{ef}}{U_{avg}}$$ .

Homework Equations

[/B]
$$ U_{ef}=\frac{U_m}{\sqrt3} , U_{avg} = \frac{U_m}{2} $$

The Attempt at a Solution


This one should be easy.I know that official solution probably divided $$\frac{2}{\sqrt3} \approx 1.154$$ (which is correct), but I am not sure why can we do that in this case, when we have 2 different kinds of lines, one with
u=5/3 t and second one u=-5/4t+35/4 . What did was found the effective of the first one and the second one, average of first one and second one , used $$ U_{avg}= U_{avg1}+U_{avg2}$$ , and $$U_{ef}^2 = U_{ef1}^2+U_{ef2}^2$$. My question is why is mine incorrect, and the solution shown above correct?
 

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Nevermind, I found my mistake, I forgot to multiply with 3/7 and 4/7 and with sqrt(3/7) and sqrt(4/7).
 

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