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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

a
1ln2 s
b
2ln2 s
c
3ln2 s
d
4ln2 s

detailed solution

Correct option is B

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=14et/τ=4 or tτ=ln 4⇒τ=tln4=42ln2⇒τ=2ln2 s

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