The magnetic flux through a coil perpendicular to its plane is varying according to the relation $$\phi = (5t^3 + 4t^2 + 2t - 5)$$ Weber. If the resistance of the coil is $$5$$ ohm, then the induced current through the coil at $$t = 2$$ s will be,

The magnetic flux through a coil is $$\phi = 5t^3 + 4t^2 + 2t - 5$$ Weber, and the resistance of the coil is $$5$$ ohm.

According to Faraday’s law, the magnitude of the induced EMF is given by $$\varepsilon = \left|\frac{d\phi}{dt}\right|$$. Differentiating the flux with respect to time gives $$\frac{d\phi}{dt} = 15t^2 + 8t + 2$$.

Substituting $$t = 2$$ s into this expression yields $$\varepsilon = 15(2)^2 + 8(2) + 2 = 15 \times 4 + 16 + 2 = 60 + 16 + 2 = 78$$ V.

Since the resistance of the coil is $$5$$ ohm, Ohm’s law gives the induced current as $$I = \frac{\varepsilon}{R} = \frac{78}{5} = 15.6$$ A.

Therefore, the correct answer is Option A.