Q39 / 117 · NTA Abhyas (NEET) 2020 · Physics · Alternating Current

A coil having inductance L and resistance R is connected to a battery of emf ε at t=0. If t1 and t2 are the times for 90% and 99% completion of the current growth in the circuit, then t1t2 will be

  • Correct answer
    A
    1:2
  • B
    2:1
  • C
    1:5
  • D
    5:1

Solution

I=I01-e-tτ

910I0=I01-e-t1τ

⇒   e-t1τ=110

⇒   et1τ=10

⇒   t1=τln10    ............(1)

and 99100I0=I01-e-t2τ

⇒   e-t2τ=1100

⇒   t2=τln100=2τln10   ..............(2)

From equations (1) and (2), we have
⇒   t1t2=12

Hence, the correct answer is option: 'A'.

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