Question

A coil having n turns and resistance 4R Ω. This combination is moved in time t seconds from a magnetic field W₁ weber to W₂ weber. The induced current in the circuit is

$fraction numerator negative straight W subscript 2 minus straight W subscript 1 over denominator 5 Rnt end fraction$
$fraction numerator negative left parenthesis straight W subscript 2 minus straight W subscript 1 right parenthesis over denominator 5 Rt end fraction$
$fraction numerator negative straight W subscript 2 minus straight W subscript 1 over denominator Rnt end fraction$
$fraction numerator straight n left parenthesis straight W subscript 2 minus straight W subscript 1 right parenthesis over denominator Rt end fraction$

Solution

fraction numerator negative left parenthesis straight W subscript 2 minus straight W subscript 1 right parenthesis over denominator 5 Rt end fraction

straight I equals space straight n over straight R comma dϕ over dt or space straight I equals space 1 over straight R comma space straight n space open square brackets fraction numerator straight W subscript 2 minus straight W subscript 1 over denominator straight t subscript 2 minus space straight t subscript 1 end fraction close square brackets straight I equals space fraction numerator negative 1 over denominator left parenthesis straight R space plus 4 straight R right parenthesis end fraction fraction numerator straight n left parenthesis straight W subscript 2 minus straight W subscript 1 right parenthesis over denominator straight t end fraction or comma space straight I space equals space fraction numerator straight n left parenthesis straight W subscript 2 minus straight W subscript 1 right parenthesis over denominator 5 Rt end fraction

(W₁ and W₂ are not the magnetic fields, but the values of flux associated with one turn of coil)

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