Physics-
General
Easy

Question

Switch S is closed for a long time at t = 0. It is opened, then:

  1. total heat produced in resistor R after opening the switch is fraction numerator 1 over denominator 2 end fraction fraction numerator L epsilon to the power of 2 end exponent over denominator R to the power of 2 end exponent end fraction    
  2. total heat produced in resistor R1 after opening the switch is fraction numerator 1 over denominator 2 end fraction fraction numerator L epsilon to the power of 2 end exponent over denominator R to the power of 2 end exponent end fraction open parentheses fraction numerator R subscript 1 end subscript over denominator R subscript 1 end subscript plus R subscript 2 end subscript end fraction close parentheses    
  3. heat produced in resistor R1 after opening the switch is fraction numerator 1 over denominator 2 end fraction fraction numerator R subscript 2 end subscript L epsilon to the power of 2 end exponent over denominator open parentheses R subscript 1 end subscript plus R subscript 2 end subscript close parentheses R to the power of 2 end exponent end fraction    
  4. no heat will be produced in R subscript 1 end subscript    

The correct answer is: heat produced in resistor R1 after opening the switch is fraction numerator 1 over denominator 2 end fraction fraction numerator R subscript 2 end subscript L epsilon to the power of 2 end exponent over denominator open parentheses R subscript 1 end subscript plus R subscript 2 end subscript close parentheses R to the power of 2 end exponent end fraction


    Just before opening the switch, the current in the inductor is epsilon divided by R. Energy stored in it=fraction numerator 1 over denominator 2 end fraction L open parentheses fraction numerator b over denominator R end fraction close parentheses to the power of 2 end exponent
    This energy will dissipate in the resistors R subscript 1 end subscript and R subscript 2 end subscript in the ratio
    fraction numerator 1 over denominator R subscript 1 end subscript end fraction & fraction numerator 1 over denominator R subscript 2 end subscript end fraction

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