The current in an LR circuit builds up to 3th 4of its steady state value in 4 s. The time constant of this circuit is
1ln2 s
2ln2 s
3ln2 s
4ln2 s
We know that i=io1-e-RtL or 34io=io1-e-t/τ
(where τ=LR= time constant
34=1-e-t/τ or e-t/τ=1-34=14
et/τ=4 or tτ=ln 4
⇒τ=tln4=42ln2⇒τ=2ln2 s