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

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15.6 A

16.6 A

17.6 A

18.6 A

answer is A.

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Detailed Solution

$\begin{array}{l} ϕ = 5 t^{3} + 4 t^{2} + 2 t - 5 \\ | e | = \frac{d ϕ}{dt} = 15 t^{2} + 8 t + 2 \\ At t = 2, | e | = 15 \times 2^{2} + 8 \times 2 + 2 \\ \Rightarrow e = 78 V \Rightarrow I = \frac{e}{R} = \frac{78}{5} = 15.60 A \end{array}$

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