First slide
Time -Varying current in L-R circuit
Question

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

Moderate
Solution

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=42ln2τ=2ln2 s

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