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  • The current in a LR circuit builds up to 2/3rd of its steady state value in 4 s. The time constant of this circuit is  Option: 1 <img

The current in a LR circuit builds up to 2/3rd of its steady state value in 4 s. The time constant of this circuit is

 

Option: 1

\frac{1}{ln (2)} S
 


Option: 2

\frac{2}{ln (3)} S


Option: 3

\frac{4}{ln \; 3} S


Option: 4

\frac{3}{ln \; (4)} S


Answers (1)

best_answer

The correct option is (3)

\begin{aligned} &i=i_{0}\left(1-e^{-t / t}\right) \\ &\frac{2}{3} i_{0}=i_{0}\left(1-e^{-4 / t}\right) \\ &\frac{2}{3}=1-e^{-4 / t} \end{aligned}

\begin{aligned} &\ln \left(\frac{1}{3}\right)=\frac{-4}{t} \ln (e) \\ &\ln (3)=\frac{4}{t} \\ &\tau=\frac{4}{\ln (3)} \end{aligned}

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