Physics-
General
Easy

Question

A 50 H z ac current of peak value 2 A flows through one of the pair of coils. If the mutual inductance between the pair of coils is 150 m H, then the peak value of voltage induced in the second coil is

  1. 30 blank pi blank V  
  2. 60 blank pi blank V  
  3. 15 blank pi blank V  
  4. 300 blank pi blank V  

The correct answer is: 30 blank pi blank V


    The current flows through the coil 1 is I subscript 1 end subscript equals I subscript 0 end subscript sin invisible function application omega t
    Where I subscript 0 end subscript is the peak value of current
    Magnetic flux linked with the coil 2 is
    ϕ subscript 2 end subscript equals M I subscript 1 end subscript equals M I subscript 0 end subscript sin invisible function application omega t
    Where M is the mutual inductance between the two coils
    The magnitude of induced emf in coil 2 is
    open vertical bar epsilon subscript 2 end subscript close vertical bar equals fraction numerator d ϕ subscript 2 end subscript over denominator d t end fraction equals fraction numerator d over denominator d t end fraction open parentheses M I subscript 0 end subscript sin invisible function application omega t close parentheses equals M I subscript 0 end subscript omega cos invisible function application omega t
    therefore Peak value of voltage induced in the coil 2 is
    equals M I subscript 0 end subscript omega equals 150 cross times 10 to the power of negative 3 end exponent cross times 2 cross times 2 pi cross times 50 equals 30 pi blank V

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