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Question

The current in an LR circuit builds up to (34)th of its steady state value in 4 s. The time constant of this circuit is

A
1ln2 s
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B
2ln2 s
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C
3ln2 s
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D
4ln2 s
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Solution

The correct option is B 2ln2 s
We know that,

i=i0 ⎢ ⎢1eRtL⎥ ⎥

34i0=i0 ⎢ ⎢1eRtL⎥ ⎥

34=1eRtL


eRtL=14

eRtL=22

eRtL=22

Taking natural log on both sides, we get,

RtL=2ln2

At, t=4 s

4RL=2ln2

τ=2ln2

Hence, (B) is the correct option.

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