Physics-
General
Easy

Question

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

  1. fraction numerator V open parentheses R subscript 1 end subscript plus R subscript 2 end subscript close parentheses over denominator R subscript 1 end subscript R subscript 2 end subscript end fraction at t equals 0 and fraction numerator V over denominator R subscript 2 end subscript end fraction at t equals infinity  
  2. fraction numerator V open parentheses R subscript 1 end subscript plus R subscript 2 end subscript close parentheses over denominator square root of R subscript 1 end subscript superscript 2 end superscript R subscript 2 end subscript superscript 2 end superscript end root end fraction at t equals 0 and fraction numerator V over denominator R subscript 2 end subscript end fraction at t equals infinity  
  3. fraction numerator V over denominator R subscript 2 end subscript end fraction at t equals 0 andfraction numerator V open parentheses R subscript 1 end subscript plus R subscript 2 end subscript close parentheses over denominator R subscript 1 end subscript R subscript 2 end subscript end fraction at t equals infinity  
  4. fraction numerator V over denominator R subscript 2 end subscript end fraction at t equals 0 andfraction numerator V open parentheses R subscript 1 end subscript plus R subscript 2 end subscript close parentheses over denominator square root of R subscript 1 end subscript superscript 2 end superscript R subscript 2 end subscript superscript 2 end superscript end root end fraction at t equals infinity  

The correct answer is: fraction numerator V over denominator R subscript 2 end subscript end fraction at t equals 0 andfraction numerator V open parentheses R subscript 1 end subscript plus R subscript 2 end subscript close parentheses over denominator R subscript 1 end subscript R subscript 2 end subscript end fraction at t equals infinity


    At t equals 0 inductor behaves as broken wire then i equals fraction numerator V over denominator R subscript 2 end subscript end fraction

    At t equals infinity Inductor behaves as conducting wire
    i equals fraction numerator V over denominator R subscript 2 end subscript R subscript 2 end subscript divided by left parenthesis R subscript 1 end subscript plus R subscript 2 end subscript right parenthesis end fraction equals fraction numerator V left parenthesis R subscript 1 end subscript plus R subscript 2 end subscript right parenthesis over denominator R subscript 1 end subscript R subscript 2 end subscript end fraction

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