Can you show your work, please? Thanks.
1 answer:
9514 1404 393
Answer:
t = (L/R)ln(V/(V -iR))
Step-by-step explanation:
Undo what is done to t. The exponential is undone using logarithms.
![i=\dfrac{V}{R}\left[1-e^{-(R/L)t}\right]\qquad\text{given}\\\\\dfrac{iR}{V}=1-e^{-(R/L)t}\qquad\text{multiply by $R/V$}\\\\e^{-(R/L)t}=1-\dfrac{iR}{V}\qquad\text{add $e^{( )}-iR/V$}\\\\-(R/L)t=\ln{\left[1-\dfrac{iR}{V}\right]}\qquad\text{take natural log}\\\\t=-\dfrac{L}{R}\ln{\left[1-\dfrac{iR}{V}\right]}\qquad\text{divide by the coefficient of t}\\\\\boxed{t=\dfrac{L}{R}\ln\left[\dfrac{V}{V-iR}\right]}\qquad\text{eliminate leading minus sign}](https://tex.z-dn.net/?f=i%3D%5Cdfrac%7BV%7D%7BR%7D%5Cleft%5B1-e%5E%7B-%28R%2FL%29t%7D%5Cright%5D%5Cqquad%5Ctext%7Bgiven%7D%5C%5C%5C%5C%5Cdfrac%7BiR%7D%7BV%7D%3D1-e%5E%7B-%28R%2FL%29t%7D%5Cqquad%5Ctext%7Bmultiply%20by%20%24R%2FV%24%7D%5C%5C%5C%5Ce%5E%7B-%28R%2FL%29t%7D%3D1-%5Cdfrac%7BiR%7D%7BV%7D%5Cqquad%5Ctext%7Badd%20%24e%5E%7B%28%20%29%7D-iR%2FV%24%7D%5C%5C%5C%5C-%28R%2FL%29t%3D%5Cln%7B%5Cleft%5B1-%5Cdfrac%7BiR%7D%7BV%7D%5Cright%5D%7D%5Cqquad%5Ctext%7Btake%20natural%20log%7D%5C%5C%5C%5Ct%3D-%5Cdfrac%7BL%7D%7BR%7D%5Cln%7B%5Cleft%5B1-%5Cdfrac%7BiR%7D%7BV%7D%5Cright%5D%7D%5Cqquad%5Ctext%7Bdivide%20by%20the%20coefficient%20of%20t%7D%5C%5C%5C%5C%5Cboxed%7Bt%3D%5Cdfrac%7BL%7D%7BR%7D%5Cln%5Cleft%5B%5Cdfrac%7BV%7D%7BV-iR%7D%5Cright%5D%7D%5Cqquad%5Ctext%7Beliminate%20leading%20minus%20sign%7D)
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