Question

Can you show your work, please? Thanks.

Answer 1

9514 1404 393

Answer:

t = (L/R)ln(V/(V -iR))

Explanation:

Undo what is done to t. The exponential is undone using logarithms.

`i=(V)/(R)\left[1-e^(-(R/L)t)\right]\qquad\text{given}\\\\(iR)/(V)=1-e^(-(R/L)t)\qquad\text{multiply by $R/V$}\\\\e^(-(R/L)t)=1-(iR)/(V)\qquad\text{add $e^(( ))-iR/V$}\\\\-(R/L)t=\ln{\left[1-(iR)/(V)\right]}\qquad\text{take natural log}\\\\t=-(L)/(R)\ln{\left[1-(iR)/(V)\right]}\qquad\text{divide by the coefficient of t}\\\\\boxed{t=(L)/(R)\ln\left[(V)/(V-iR)\right]}\qquad\text{eliminate leading minus sign}`