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

Options

A. `(1) /("in"2)s`
B. `(2)/( "in"2)s`
C. `(3) /("in"2)s`
D. `(4) /("in"2)s`

Answer

B

Explanation

Current in `(L )/(R ) ` circuit
` I-I_(0) (1-e^(-(1)/(tau)))=(3)/(4) I_(0)`
`implies e^(-(t )/(tau))=(1)/(4) implies e ^((t)/(tau)) =4 `
` (t) /(tau) = "in" 4 = 2 "in" 2, Z=(t) /(2"in"2)`
`t=4 sec , z=(2) /("In"2)`