Physics-
General
Easy

Question

The output current versus time curve of a rectifier is shown in the figure. The average value of output current in this case is

  1. 0    
  2. fraction numerator I subscript 0 end subscript over denominator 2 end fraction    
  3. fraction numerator 2 I subscript 0 end subscript over denominator pi end fraction    
  4. I subscript 0 end subscript    

The correct answer is: fraction numerator 2 I subscript 0 end subscript over denominator pi end fraction


    I subscript a v end subscript equals fraction numerator not stretchy integral subscript 0 end subscript superscript T divided by 2 end superscript i d t over denominator not stretchy integral subscript 0 end subscript superscript T divided by 2 end superscript d t end fraction equals fraction numerator not stretchy integral subscript 0 end subscript superscript T divided by 2 end superscript I subscript 0 end subscript sin invisible function application left parenthesis omega t right parenthesis d t over denominator T divided by 2 end fraction
    equals fraction numerator 2 I subscript 0 end subscript over denominator T end fraction open square brackets fraction numerator negative cos invisible function application omega t over denominator omega end fraction close square brackets subscript 0 end subscript superscript T divided by 2 end superscript equals fraction numerator 2 I subscript 0 end subscript over denominator T end fraction open square brackets negative fraction numerator cos invisible function application open parentheses fraction numerator omega T over denominator 2 end fraction close parentheses over denominator omega end fraction plus fraction numerator cos invisible function application 0 to the power of o end exponent over denominator omega end fraction close square brackets
    equals fraction numerator 2 I subscript 0 end subscript over denominator omega T end fraction left square bracket negative cos invisible function application pi plus cos invisible function application 0 to the power of o end exponent right square bracket equals fraction numerator 2 I subscript 0 end subscript over denominator 2 pi end fraction left square bracket 1 plus 1 right square bracket equals fraction numerator 2 I subscript 0 end subscript over denominator pi end fraction

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