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The magnetic flux through a coil perpendicular to its plane is varying according to the relation $ϕ = (5 t^{4} + 4 t^{3} + 2 t^{2} + 6 t + 1)$ Weber. If the resistance of the coil is 6 ohm. then the current through the coil is at t=2 sec. will be.

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37 A

16.6 A

17.6 A

18.6 A

answer is A.

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Detailed Solution

$I = - \frac{1}{R} . \frac{d ϕ}{d t}$

$\frac{d ϕ}{d t} = 20 t^{3} + 12 t^{2} + 4 t + 6$

at t=2s,

$\frac{d ϕ}{d t} = 20 \times 8 + 12 \times 4 + 4 \times 2 + 6 = 222$

$i = \frac{222}{6} = 37 A$

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