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Question

A coil of resistance 20 Ω and inductance 5 H has been connected to a 100 V battery and the switch is closed at t=0. After how much time will the current acquire half of its steady state value. (ln2=0.693)

A
0.17 s
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B
0.34 s
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C
0.09 s
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D
0.69 s
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Solution

The correct option is A 0.17 s
If the current in the inductor is constant, there is no emf induced. But if the current changes, an emf is induced across the inductor.



emf induced ϵ=Ldidt=iR

For the entire circuit,
VLdidtiR=0
where V=100 V is the battery voltage.

Solving the above differential equation, we get
i=i0(1etτ)
where i0=VR is the steady state current
and τ=LR

The graph of current w.r.t time is


i=i02=i0(1etτ)
etτ=2
tτ=ln2
t=ln2×τ=0.693×LR
=0.693×520=0.17 s

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