Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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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. - Physics

Sum

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.

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Solution

Current i in the LR circuit at time t is given by

i = i0(1 − e−t)

Here,

i0 = Steady-state value of the current


(a) When the value of the current reaches 90% of the steady-state value:-

\[i = \frac{90}{100} \times i_0\]

\[\frac{90}{100} i_0\] = io(1 − e−t)

⇒ 0.9 = 1 − e−t

⇒ e−t = 0.1

On taking natural logarithm (ln) of both sides, we get

ln (e−t) = ln 0.1

`-t/tau=-2.3`

`rArr t/tau=2.3`


(b) When the value of the current reaches 99% of the steady-state value:-

\[\frac{99}{100} i_0\] = i0(1 − e−t)

e−t = 0.01

On taking natural logarithm (ln) of both sides, we get

ln e−t = ln 0.01

`rArr -t/tau=-4.6`

`rArr t/tau=4.6`


(c) When the value of the current reaches 99.9% of the steady-state value:-

\[\frac{99 . 9}{100} i_0\] = i0(1 − e−t)

⇒ e−t = 0.001

On taking natural logarithm (ln) of both sides, we get

ln e−t = ln 0.001

`rArr -t/tau=-6.9`

`rArr t/tau=6.9`

  Is there an error in this question or solution?
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 16 Electromagnetic Induction
Q 69 | Page 312
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