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Find the value of t/(time constant) for which the current in an L/R circuit builds upto (a)99% and (b)99.9% of steady state value

(1)4.6,6.9

(2) 6.9,4.6

(3) 2.3, 6.9

(4)6.9,2.3

1 Answer

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answered by (14.6k points)

We know the Current formula in L/R circut

I(t) = Io [1 - e-t/τ ]

, where Io = ε/R is the maximum current 

and the time constant τ = L/R 

if current reaches 99 % of steady state,  then 

[1 - e-t/τ ]

 = 0.99    or e-t/τ

 = 0.01 = 10-2  . 

Hence t/τ = 2 × ln10 = 4.6

if current reaches 99.9 % of steady state,  then 

[1 - e-t/τ ]

 = 0.999 or e-t/τ 

 = 0.001 = 10-3  . 

Hence t/τ = 3 × ln10 = 6.9

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