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Find the value of t/τ for which the current in an LR circuit builds up to (a) 90%, (b ) 99% and (c) 99.9% of the steady-state value.

Find the value of t/τ for which the current in an LR circuit builds up to (a) 90%, (b ) 99% and (c) 99.9% of the steady-state value.

Grade:upto college level

1 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
Sol. We know i = i0 ( 1- e^–t/r) (a) 90/100 i base 0 = i base 0 ( 1-e^-t/r) ⇒ 0.9 = 1 – e^-t/r ⇒ e^-t/r = 0.1 Taking ℓn from both sides ℓn e^–t/r = ℓn 0.1 ⇒ –t = –2.3 ⇒ t/r = 2.3 (b) 99/100 i base 0 = i base 0 (1 – e^-t/r) ⇒ e^–t/r = 0.01 ℓne^–t/r = ℓn 0.01 or, –t/r = –4.6 or t/r = 4.6 (c) 99.9/100 i base 0 = i base 0 (1-e^-t/r) e^–t/r = 0.001 ⇒ lne^–t/r = ln 0.001 ⇒ e^–t/r = –6.9 ⇒ t/r = 6.9.

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