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Current Electricity

Question
CBSEENPH12039558

In the circuit shown below, the key K is closed at t = 0. The current through the battery is

  • fraction numerator VR subscript 1 straight R subscript 2 over denominator square root of straight R subscript 1 superscript 2 plus straight R subscript 2 superscript 2 end root end fraction space at space straight t space equals space 0 space and space straight V over straight R subscript 2 space at space straight t space equals space infinity
  • straight V over straight R subscript 2 space at space straight t space equals space 0 space and space fraction numerator straight V left parenthesis straight R subscript 1 plus straight R subscript 2 right parenthesis over denominator straight R subscript 1 straight R subscript 2 end fraction space at space equals space infinity
  • straight V over straight R subscript 2 space at space straight t space equals space 0 space and space fraction numerator VR subscript 1 straight R subscript 2 over denominator square root of straight R subscript 1 superscript 2 space plus space straight R subscript 2 superscript 2 end root end fraction space at space straight t space equals space infinity
  • fraction numerator straight V space left parenthesis straight R subscript 1 space plus space straight R subscript 2 right parenthesis over denominator straight R subscript 1 straight R subscript 2 end fraction space at space straight t space equals space 0 space and space straight V over straight R subscript 2 space at space straight t space equals space infinity

Solution

B.

straight V over straight R subscript 2 space at space straight t space equals space 0 space and space fraction numerator straight V left parenthesis straight R subscript 1 plus straight R subscript 2 right parenthesis over denominator straight R subscript 1 straight R subscript 2 end fraction space at space equals space infinity

At t = 0, inductor behaves like an infinite resistance so , at t = 0,
i = V/R2
and at t = ∞, inductor behaves like a conducting wire i.e., resistance less wire
then, 
straight i space equals space straight V over straight R subscript eq space equals space fraction numerator straight V space left parenthesis straight R subscript 1 space plus space straight R subscript 2 right parenthesis over denominator straight R subscript 1 straight R subscript 2 end fraction