The current in a LR circuit builds up to 3 / 4 text th of its steady state value in 4 s. The time constant of this circuit is :-

Question

The current in a LR circuit builds up to 3 / 4 text th of its steady state value in 4 s. The time constant of this circuit is :- (A) (1/ ln 2) s (B) (2/ ln 2) s (C) (3/ ln 2) s (D) (4/ ln 2) s

Tardigrade Admin · Accepted Answer

Current in (L/ R ) circuit I = I 0(1- e -( t /τ))=(3/4) I 0 ⇒ e -( t /τ)=(1/4) ⇒ e ( t /τ)=4 ( t /τ)= ln 4=2 ln 2, τ=( t /2 ln 2) t =4 sec , τ=(2/ ln 2) sec

Q. The current in a LR circuit builds up to $3/ 4^{th}$ of its steady state value in $4 s$ . The time constant of this circuit is :-

$\frac{1}{l n 2} s$

$\frac{2}{l n 2} s$

$\frac{3}{l n 2} s$

$\frac{4}{l n 2} s$

Current in $\frac{L}{R}$ circuit
$I = I_{0} (1 - e^{- \frac{t}{τ}}) = \frac{3}{4} I_{0}$
$\Rightarrow e^{- \frac{t}{τ}} = \frac{1}{4}$
$\Rightarrow e \frac{t}{τ} = 4$
$\frac{t}{τ} = ln 4 = 2 ln 2, τ = \frac{t}{2 l n 2}$
$t = 4 sec, τ = \frac{2}{l n 2} sec$

Q. The current in a LR circuit builds up to 3/4th of its steady state value in 4s. The time constant of this circuit is :-

ln21​s

ln22​s

ln23​s

ln24​s