Problem with a 'simple' equation?

  • Context: Undergrad 
  • Thread starter Thread starter rudderbird
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SUMMARY

The discussion centers on the equation i = E/R + Ae^[-(RT)/L] and the confusion surrounding the transformation to e^(t/λ) when λ = R/L. The user identifies an error in the original equation, noting that the exponent should include a negative sign, indicating that it should be e^(-t/λ) instead of e^(t*λ). The user concludes that the correct interpretation of the equation is crucial for understanding its behavior as t approaches infinity, emphasizing the importance of proper notation in mathematical expressions.

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rudderbird
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Okay so, the main equation was this-
i = E/R + Ae^[-(RT)/L]

My problem is with the equation no. 2.
How do we get e^t/lamda when lamda = R/L? It should be e^t*lamda and where did the minus symbol go (the one in the power of e). And to equate i = i not it has to be (1 - e^t/lamda) = 1 and if t tends to infinity that's not possible in any way!

Please tell me where I am doing wrong! HELP!
 
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The page has an error. Lambda should be L/R. The typography of the book puts a minus sign on the same level as the line for a fraction, so I think the exponent that looks like \frac{t}{\lambda} is really \frac{-t}{\lambda}. To be correct, it should have the minus sign.
 
Thanks so much! I just needed a confirmation!
 

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