The magnetic flux linked with coil, in weber is given by the equation, $ϕ = 5 t^{2} + 3 t + 16$ . The induced emf in the coil in the fourth second is

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10 V

30 V

90 V

45 V

answer is A.

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Detailed Solution

$| e | = \frac{dϕ}{dt} = \frac{d}{dt} (5 t^{2} + 3 t + 16) = (10 t + 3)$

when $t = 3 \sec, e_{3} = (10 \times 3 + 3) = 33 V$
when $t = 4 \sec, e_{4} = (10 \times 4 + 3) = 43 V$
Hence emf induced in fourth second
$= e_{4} - e_{3} = 43 - 33 = 10 V$

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