The magnetic flux through a coil perpendicular to the plane is varying according to the relation $\phi=(7t^3+3t^2-2t-2) Wb$. If the resistance of the coil is 10 Ω, the induced current through the coil at t = 2 s, will be

9.4 A

The correct answer is Option (2) → 9.4 A

Given magnetic flux: $\phi = (7t^{3} + 3t^{2} - 2t - 2)\ \text{Wb}$

Induced emf: $e = -\frac{d\phi}{dt}$

$\frac{d\phi}{dt} = 21t^{2} + 6t - 2$

At $t = 2\ \text{s}$:

$\frac{d\phi}{dt} = 21(2)^{2} + 6(2) - 2$

$\frac{d\phi}{dt} = 84 + 12 - 2 = 94$

Induced emf, $e = -94\ \text{V}$

Resistance, $R = 10\ \Omega$

Induced current, $I = \frac{e}{R} = \frac{-94}{10} = -9.4\ \text{A}$

∴ Induced current = 9.4 A (direction opposite to flux increase)